{"id":524,"date":"2020-08-21T19:41:03","date_gmt":"2020-08-21T23:41:03","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-properties-of-rectangles-triangles-and-trapezoids\/"},"modified":"2021-03-24T10:53:25","modified_gmt":"2021-03-24T14:53:25","slug":"use-properties-of-rectangles-triangles-and-trapezoids","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/use-properties-of-rectangles-triangles-and-trapezoids\/","title":{"raw":"3.2 Use Properties of Rectangles, Triangles, and Trapezoids","rendered":"3.2 Use Properties of Rectangles, Triangles, and Trapezoids"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Understand linear, square, and cubic measure<\/li>\n \t<li>Use properties of rectangles<\/li>\n \t<li>Use properties of triangles<\/li>\n \t<li>Use properties of trapezoids<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Understand Linear, Square, and Cubic Measure<\/h1>\n<p id=\"fs-id1171505779061\">When you measure your height or the length of a garden hose, you use a ruler or tape measure <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_001\">(Figure.1)<\/a>. A tape measure might remind you of a line\u2014you use it for linear measure, which measures length. Inch, foot, yard, mile, centimetre and metre are units of linear measure.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_04_001\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">This tape measure measures inches along the top and centimetres along the bottom.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"670\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_09_04_001.jpg\" alt=\"A picture of a portion of a tape measure is shown. The top shows the numbers 1 through 5. The portion from the beginning to the 1 has a red circle and an arrow to a picture from 0 to 1 inch, with 1 sixteenth, 1 eighth, 3 eighths, 1 half, and 3 fourths labeled. Above this, it is labeled \u201cStandard Measures.\u201d The bottom of the tape measure shows the numbers 1 through 10, then 1 and 2. The region from the edge to about 3 and a half has a red circle with an arrow pointing to a picture from 0 to 3.5. It is labeled 0, 1 cm, 1.7 cm, 2.3 cm and 3.5 cm. Above this, it is labeled \u201cMetric (S).\u201d\" width=\"670\" height=\"117\" data-media-type=\"image\/jpeg\"> Figure.1[\/caption]\n<p id=\"fs-id1467500\">When you want to know how much tile is needed to cover a floor, or the size of a wall to be painted, you need to know the area, a measure of the region needed to cover a surface. Area is measured is square units. We often use square inches, square feet, square centimetres, or square miles to measure area. A square centimetre is a square that is one centimetre (cm) on each side. A square inch is a square that is one inch on each side <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_002\">(Figure.2)<\/a>.<\/p>\nSquare measures have sides that are each \\(1\\) unit in length.\n<div id=\"CNX_BMath_Figure_09_04_002\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"556\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_002.jpg\" alt=\"Two squares are shown. The smaller one has sides labeled 1 cm and is 1 square centimetre. The larger one has sides labeled 1 inch and is 1 square inch.\" width=\"556\" height=\"124\" data-media-type=\"image\/jpeg\"> Figure.2[\/caption]\n<p id=\"fs-id1100308\"><a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_003\">(Figure.3)<\/a> shows a rectangular rug that is \\(2\\) feet long by \\(3\\) feet wide. Each square is \\(1\\) foot wide by \\(1\\) foot long, or \\(1\\) square foot. The rug is made of \\(6\\) squares. The area of the rug is\\(6\\) square feet.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_04_003\" class=\"bc-figure figure\">\n<div><\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"212\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_003.jpg\" alt=\"A rectangle is shown. It has 3 squares across and 2 squares down, a total of 6 squares.\" width=\"212\" height=\"142\" data-media-type=\"image\/jpeg\"> Figure 3 The rug contains six squares of 1 square foot each, so the total area of the rug is 6 square feet.[\/caption]\n<p id=\"fs-id1588170\">When you measure how much it takes to fill a container, such as the amount of gasoline that can fit in a tank, or the amount of medicine in a syringe, you are measuring volume. Volume is measured in cubic units such as cubic inches or cubic centimetres. When measuring the volume of a rectangular solid, you measure how many cubes fill the container. We often use cubic centimetres, cubic inches, and cubic feet. A cubic centimetre is a cube that measures one centimetre on each side, while a cubic inch is a cube that measures one inch on each side <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_004\">(Figure.4)<\/a>.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_04_004\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"323\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_004.jpg\" alt=\"Two cubes are shown. The smaller one has sides labeled 1 cm and is labeled as 1 cubic centimetre. The larger one has sides labeled 1 inch and is labeled as 1 cubic inch.\" width=\"323\" height=\"253\" data-media-type=\"image\/jpeg\"> Figure 4 Cubic measures have sides that are 1 unit in length.[\/caption]\n<p id=\"fs-id1054320\">Suppose the cube in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_005\">(Figure.5)<\/a> measures \\(3\\) inches on each side and is cut on the lines shown. How many little cubes does it contain? If we were to take the big cube apart, we would find \\(27\\) little cubes, with each one measuring one inch on all sides. So each little cube has a volume of \\(1\\) cubic inch, and the volume of the big cube is \\(27\\) cubic inches.<\/p>\nA cube that measures 3 inches on each side is made up of 27 one-inch cubes, or 27 cubic inches.\n<div id=\"CNX_BMath_Figure_09_04_005\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"97\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_005.jpg\" alt=\"A cube is shown, comprised of smaller cubes. Each side of the cube has 3 smaller cubes across, for a total of 27 smaller cubes.\" width=\"97\" height=\"81\" data-media-type=\"image\/jpeg\"> Figure.5[\/caption]\n\n<\/div>\n<div data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505120904\" data-type=\"problem\">\n<p id=\"fs-id2147044\">For each item, state whether you would use linear, square, or cubic measure:<\/p>\n<p id=\"fs-id1171505279541\">a) amount of carpeting needed in a room<\/p>\n<p id=\"fs-id1171505781802\">b) extension cord length<\/p>\n<p id=\"fs-id1600939\">c) amount of sand in a sandbox<\/p>\n<p id=\"fs-id962051\">d) length of a curtain rod<\/p>\n<p id=\"fs-id2166824\">e) amount of flour in a canister<\/p>\n<p id=\"fs-id1161888\">f) size of the roof of a doghouse.<\/p>\n\n<\/div>\n<div id=\"fs-id1447944\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-104\" class=\"unnumbered unstyled\" summary=\"...\" data-label=\"\">\n<tbody>\n<tr>\n<td>a) You are measuring how much surface the carpet covers, which is the area.<\/td>\n<td>square measure<\/td>\n<\/tr>\n<tr>\n<td>b) You are measuring how long the extension cord is, which is the length.<\/td>\n<td>linear measure<\/td>\n<\/tr>\n<tr>\n<td>c) You are measuring the volume of the sand.<\/td>\n<td>cubic measure<\/td>\n<\/tr>\n<tr>\n<td>d) You are measuring the length of the curtain rod.<\/td>\n<td>linear measure<\/td>\n<\/tr>\n<tr>\n<td>e) You are measuring the volume of the flour.<\/td>\n<td>cubic measure<\/td>\n<\/tr>\n<tr>\n<td>f) You are measuring the area of the roof.<\/td>\n<td>square measure<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1481876\" data-type=\"problem\">\n<p id=\"fs-id1935428\">Determine whether you would use linear, square, or cubic measure for each item.<\/p>\n<p id=\"fs-id1954512\">a) amount of paint in a can b) height of a tree c) floor of your bedroom d) diametre of bike wheel e) size of a piece of sod f) amount of water in a swimming pool<\/p>\n\n<\/div>\n<div id=\"fs-id1807421\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168467254475\" class=\"circled\" type=\"a\">\n \t<li>cubic<\/li>\n \t<li>linear<\/li>\n \t<li>square<\/li>\n \t<li>linear<\/li>\n \t<li>square<\/li>\n \t<li>cubic<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171505547635\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1772635\" data-type=\"exercise\">\n<div id=\"fs-id1807421\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171513624342\" data-type=\"problem\">\n<p id=\"fs-id1362401\">Determine whether you would use linear, square, or cubic measure for each item.<\/p>\n<p id=\"fs-id1895627\">a) volume of a packing box b) size of patio c) amount of medicine in a syringe d) length of a piece of yarn e) size of housing lot f) height of a flagpole<\/p>\n\n<\/div>\n<div id=\"fs-id1161229\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168468780837\" class=\"circled\" type=\"a\">\n \t<li>cubic<\/li>\n \t<li>square<\/li>\n \t<li>cubic<\/li>\n \t<li>linear<\/li>\n \t<li>square<\/li>\n \t<li>linear<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1171505778736\">Many geometry applications will involve finding the perimeter or the area of a figure. There are also many applications of perimeter and area in everyday life, so it is important to make sure you understand what they each mean.<\/p>\n<p id=\"fs-id958752\">Picture a room that needs new floor tiles. The tiles come in squares that are a foot on each side\u2014one square foot. How many of those squares are needed to cover the floor? This is the area of the floor.<\/p>\n<p id=\"fs-id1171511544941\">Next, think about putting new baseboard around the room, once the tiles have been laid. To figure out how many strips are needed, you must know the distance around the room. You would use a tape measure to measure the number of feet around the room. This distance is the perimeter.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Perimeter and Area<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1858719\">The perimeter is a measure of the distance around a figure.<\/p>\n<p id=\"fs-id1171499420654\">The area is a measure of the surface covered by a figure.<\/p>\n\n<\/div>\n<\/div>\n<p id=\"fs-id1922361\"><a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_006\">(Figure. 6)<\/a> shows a square tile that is \\(1\\) inch on each side. If an ant walked around the edge of the tile, it would walk \\(4\\) inches. This distance is the perimeter of the tile.<\/p>\n<p id=\"fs-id1171488172599\">Since the tile is a square that is \\(1\\) inch on each side, its area is one square inch. The area of a shape is measured by determining how many square units cover the shape.<\/p>\n\\(\\begin{array}{c}\\text{Perimeter}=4\\phantom{\\rule{0.2em}{0ex}}\\text{inches}\\\\ \\text{Area}=1\\phantom{\\rule{0.2em}{0ex}}\\text{square inch}\\end{array}\\)\n<div id=\"CNX_BMath_Figure_09_04_006\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"229\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_006.jpg\" alt=\"A 5 square by 5 square checkerboard is shown with each side labeled 1 inch. An image of an ant is shown on the top left square.\" width=\"229\" height=\"178\" data-media-type=\"image\/jpeg\"> Figure 6 When the ant walks completely around the tile on its edge, it is tracing the perimeter of the tile. The area of the tile is 1 square inch.[\/caption]\n\n<div data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1490358\" data-type=\"problem\">\n<p id=\"fs-id1594194\">Each of two square tiles is \\(1\\) square inch. Two tiles are shown together.<\/p>\n<p id=\"fs-id1877892\">a) What is the perimeter of the figure?<\/p>\n<p id=\"fs-id1711457\">b) What is the area?<\/p>\n<span id=\"fs-id1879440\" data-type=\"media\" data-alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_007.jpg\" alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id2110859\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1327911\">a) The perimeter is the distance around the figure. The perimeter is \\(6\\) inches.<\/p>\n<p id=\"fs-id1690172\">b) The area is the surface covered by the figure. There are \\(2\\) square inch tiles so the area is \\(2\\) square inches.<\/p>\n<span id=\"fs-id1171505480664\" data-type=\"media\" data-alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side. The top and bottom each have two adjacent 1 inch labels across, the sides have 1 inch labels.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_008.jpg\" alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side. The top and bottom each have two adjacent 1 inch labels across, the sides have 1 inch labels.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n&nbsp;\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487500930\" data-type=\"problem\">\n<p id=\"fs-id1044430\">Find the a) perimeter and b) area of the figure:<\/p>\n<span data-type=\"media\" data-alt=\"A rectangle is shown comprised of 3 squares.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_009_img.jpg\" alt=\"A rectangle is shown comprised of 3 squares.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168469834117\" class=\"circled\" type=\"a\">\n \t<li>8 inches<\/li>\n \t<li>3 sq. inches<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1915814\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1931650\" data-type=\"exercise\">\n<div id=\"fs-id1171487500930\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1875231\" data-type=\"problem\">\n<p id=\"fs-id974965\">Find the a) perimeter and b) area of the figure:<\/p>\n<span id=\"fs-id1171513624489\" data-type=\"media\" data-alt=\"A square is shown comprised of 4 smaller squares.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_010_img.jpg\" alt=\"A square is shown comprised of 4 smaller squares.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1171498004127\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168468326099\" class=\"circled\" type=\"a\">\n \t<li>8 centimetres<\/li>\n \t<li>4 sq. centimetres<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use the Properties of Rectangles<\/h1>\n<p id=\"fs-id1556861\">A rectangle has four sides and four right angles. The opposite sides of a rectangle are the same length. We refer to one side of the rectangle as the length, \\(L\\), and the adjacent side as the width, \\(W\\). See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_012\">(Figure.7)<\/a>.<\/p>\nA rectangle has four sides, and four right angles. The sides are labeled L for length and W for width.\n<div id=\"CNX_BMath_Figure_09_04_012\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"189\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_012.jpg\" alt=\"A rectangle is shown. Each angle is marked with a square. The top and bottom are labeled L, the sides are labeled W.\" width=\"189\" height=\"123\" data-media-type=\"image\/jpeg\"> Figure.7[\/caption]\n<p id=\"fs-id1171505275854\">The perimeter, \\(P\\), of the rectangle is the distance around the rectangle. If you started at one corner and walked around the rectangle, you would walk \\(L+W+L+W\\) units, or two lengths and two widths. The perimeter then is<\/p>\n\\(\\begin{array}{c}P=L+W+L+W\\hfill \\\\ \\hfill \\text{or}\\hfill \\\\ P=2L+2W\\hfill \\end{array}\\)\n<p id=\"fs-id1753081\">What about the area of a rectangle? Remember the rectangular rug from the beginning of this section. It was \\(2\\) feet long by \\(3\\) feet wide, and its area was \\(6\\) square feet. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_013\">(Figure.8)<\/a>. Since \\(A=2\\cdot 3\\), we see that the area, \\(A\\), is the length, \\(L\\), times the width, \\(W\\), so the area of a rectangle is \\(A=L\\cdot W\\).<\/p>\nThe area of this rectangular rug is \\(6\\) square feet, its length times its width.\n<div id=\"CNX_BMath_Figure_09_04_013\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"241\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_013.jpg\" alt=\"A rectangle is shown. It is made up of 6 squares. The bottom is 2 squares across and marked as 2, the side is 3 squares long and marked as 3.\" width=\"241\" height=\"178\" data-media-type=\"image\/jpeg\"> Figure.8[\/caption]\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Rectangles<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1171497076758\" data-bullet-style=\"bullet\">\n \t<li>Rectangles have four sides and four right \\(\\left(\\text{90}\\right)\\)\u00b0 angles.<\/li>\n \t<li>The lengths of opposite sides are equal.<\/li>\n \t<li>The perimeter, \\(P\\), of a rectangle is the sum of twice the length and twice the width. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_012\">(Figure 8)<\/a>.\\(P=2L+2W\\)<\/li>\n<\/ul>\n<ul>\n \t<li>The area, \\(A\\), of a rectangle is the length times the width.\\(A=L\\cdot W\\)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1908419\">For easy reference as we work the examples in this section, we will state the Problem Solving Strategy for Geometry Applications here.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Use a Problem Solving Strategy for Geometry Applications<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1170325029073\" class=\"stepwise\" type=\"1\">\n \t<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\n \t<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n \t<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n \t<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n \t<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n \t<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1558949\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1549060\" data-type=\"exercise\">\n<div id=\"fs-id1931478\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1764703\" data-type=\"problem\">\n<p id=\"fs-id1171507005201\">The length of a rectangle is \\(32\\) metres and the width is \\(20\\) metres. Find a) the perimeter, and b) the area.<\/p>\n\n<\/div>\n<div id=\"fs-id1171498003823\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468455627\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. There is an image of a rectangle. The top and bottom are labeled 32 m and the sides are labeled 20 m. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe perimeter of a rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cLet P equal the perimeter.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W, then P equals 2 times 32 plus 2 times 20. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is P equals 64 plus 40, then P equals 104. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P followed by an equal sign with a question mark, then 104. Then 20 plus 32 plus 20 plus 32 followed by an equal sign with a question mark, then 104. Then 104 equals 104. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe perimeter of the rectangle is 104 metres.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468395600\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the perimeter of a rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">P<\/em> = the perimeter<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td><span id=\"eip-id1168467174763\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168469507351\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The perimeter of the rectangle is 104 metres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467114806\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. There is an image of a rectangle. The top and bottom are labeled 32 m and the sides are labeled 20 m. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cLet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals L times W, then A equals 32 m times 20 m. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals 640. Step 6 says, \u201cCheck,\u201d in bold. Beside this is A followed by an equal sign with a question mark, then 640. Then 32 times 20 followed by an equal sign with a question mark, then 640. Then 640 equals 640, followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe area of the rectangle is 640 square metres.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468499149\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of a rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">A<\/em> = the area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td><span id=\"eip-id1168468460104\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168469785286\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The area of the rectangle is 60 square metres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1931478\" data-type=\"problem\">\n<p id=\"fs-id1602689\">The length of a rectangle is \\(120\\) yards and the width is \\(50\\) yards. Find a) the perimeter and b) the area.<\/p>\n\n<\/div>\n<div id=\"fs-id1786251\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168467174146\" class=\"circled\" type=\"a\">\n \t<li>340 yd<\/li>\n \t<li>6000 sq. yd<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1786251\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171511544945\" data-type=\"problem\">\n<p id=\"fs-id1904165\">The length of a rectangle is \\(62\\) feet and the width is \\(48\\) feet. Find a) the perimeter and b) the area.<\/p>\n\n<\/div>\n<div id=\"fs-id1562413\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168469773073\" class=\"circled\" type=\"a\">\n \t<li>220 ft<\/li>\n \t<li>2976 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1564306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1507197\" data-type=\"exercise\">\n<div id=\"fs-id1562413\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505275626\" data-type=\"problem\">\n<p id=\"fs-id1489861\">Find the length of a rectangle with perimeter \\(50\\) inches and width \\(10\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id1717808\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469470101\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. There is an image of a rectangle. The top and bottom are labeled L and the sides are labeled 10 in. Below the rectangle is P equals 50 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length of the rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cLet L equal the length.\u201d Step 4 says, \u201cTranslate. Write the formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W. Below P is 50 in, below 2L is 2L, and below 2W is 2 times 10 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 50 minus a red 20 equals 2L plus 20 minus a red 20, then 30 equals 2L with both sides over a red 2, then 15 equals L. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals 50, then 15 plus 10 plus 15 plus 10 followed by an equal sign with a question mark, then 500. Then 50 equals 50, followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length is 15 inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469784173\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length of the rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">L<\/em> = the length<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td><span id=\"eip-id1168466229487\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168466483065\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length is 15 inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1392754\" data-type=\"problem\">\n<p id=\"fs-id1580362\">Find the length of a rectangle with a perimeter of \\(80\\) inches and width of \\(25\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id1776151\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1934174\">15 in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1478584\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1548995\" data-type=\"exercise\">\n<div id=\"fs-id1776151\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505482456\" data-type=\"problem\">\n<p id=\"fs-id1747478\">Find the length of a rectangle with a perimeter of \\(30\\) yards and width of \\(6\\) yards.<\/p>\n\n<\/div>\n<div id=\"fs-id1406132\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171498421216\">9 yd<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1394303\">In the next example, the width is defined in terms of the length. We\u2019ll wait to draw the figure until we write an expression for the width so that we can label one side with that expression.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1954612\" data-type=\"problem\">\n<p id=\"fs-id1862284\">The width of a rectangle is two inches less than the length. The perimeter is \\(52\\) inches. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1550204\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466427903\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem.\u201d The word \u201cread\u201d is in bold. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length and width of the rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cSince the width is defined in terms of the length, we let L equal length. The width is two feet less than the length, so we let L minus 2 equal width. Now we can draw a figure using these expressions for the length and width.\u201d An image of a rectangle is shown. The top and bottom are labeled L minus 2, the sides are labeled L. Beneath the rectangle is P equals 52 in. Step 4 says, \u201cTranslate. Write the appropriate formula. The formula for the perimeter of a rectangle relates all the information. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W. Below that is 52 equals 2L plus 2 times L minus 2. Step 5 says, \u201cSolve the equation. Combine like terms. Add 4 to each side. Divide by 4.\u201d The word \u201csolve\u201d is in bold. Beside this is 52 equals 2L plus 2L minus 4, then 52 equals 4L minus 4, then 56 equals 4L, then 56 over 4 equals 4L over 4, then 14 equals L. The length is 14 inches. The next part reads, \u201cNow we need to find the width. The width is L minus 2.\u201d Beside this is L minus 2, then a red 14 minus 2, then 12. The width is 12 inches. Step 6 says, \u201cCheck,\u201d in bold. Beside this is \u201csince 14 plus 12 plus 14 plus 12 equals 52, this works!\u201d Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length is 14 inches and the width is 12 inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width of the rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.\n\nNow we can draw a figure using these expressions for the length and width.<\/td>\n<td>Since the width is defined in terms of the length, we let <em data-effect=\"italics\">L<\/em> = length. The width is two feet less that the length, so we let <em data-effect=\"italics\">L<\/em> \u2212 2 = width\n<span id=\"eip-id1168466319758\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_070_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula. The formula for the perimeter of a rectangle relates all the information.\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168466644630\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_070_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td>\\(52=2L+2L-4\\)<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>\\(52=4L-4\\)<\/td>\n<\/tr>\n<tr>\n<td>Add 4 to each side.<\/td>\n<td>\\(56=4L\\)<\/td>\n<\/tr>\n<tr>\n<td>Divide by 4.<\/td>\n<td>\\(\\frac{56}{4}=\\frac{4L}{4}\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\\(14=L\\)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The length is 14 inches.<\/td>\n<\/tr>\n<tr>\n<td>Now we need to find the width.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The width is <em data-effect=\"italics\">L<\/em> \u2212 2.<\/td>\n<td data-align=\"left\"><span id=\"eip-id1168466200890\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_070_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\nThe width is 12 inches.<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong>\nSince \\(14+12+14+12=52\\), this works!<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length is 14 feet and the width is 12 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1932001\" data-type=\"problem\">\n<p id=\"fs-id1863871\">The width of a rectangle is seven metres less than the length. The perimeter is \\(58\\) metres. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1805128\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1377421\">18 m, 11 m<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171512117622\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1684704\" data-type=\"exercise\">\n<div id=\"fs-id1932001\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2052069\" data-type=\"problem\">\n<p id=\"fs-id1915314\">The length of a rectangle is eight feet more than the width. The perimeter is \\(60\\) feet. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1171497978496\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171487568509\">11 ft , 19 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1932001\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1414483\">The length of a rectangle is four centimetres more than twice the width. The perimeter is \\(32\\) centimetres. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1171487493999\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468670350\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem.\u201d The word \u201cread\u201d is in bold. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length and the width.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet w equal width. The length is four more than twice the width. 2w plus 4 equals length.\u201d An image of a rectangle is shown. The top and bottom are labeled 2W plus 4, the sides are labeled W. Beneath the rectangle is P equals 32 cm. Step 4 says, \u201cTranslate. Write the appropriate formula and substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W. Below that is 32 equals 2 times 2W plus 4 plus 2W. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 32 equals 4W plus 8 plus 2W, then 32 equals 6W plus 8, then 24 equals 6W, then 4 equals W width, then 2W plus 4 length, then 2 times a red 4 plus 4, then 12, followed by \u201cThe length is 12 cm.\u201d Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals 2L plus 2W, then 32 followed by an equal sign with a question mark, then 2 times 12 plus 2 times 4, then 32 equals 32 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length is 12 cm and the width is 4 cm.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">W<\/em> = width\nThe length is four more than twice the width.\n2<em data-effect=\"italics\">w<\/em> + 4 = length\n<span id=\"eip-id1168468261144\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula and substitute in the given information.<\/td>\n<td><span id=\"eip-id1168467318309\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164271792878\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length is 12 cm and the width is 4 cm.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1805128\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1929348\" data-type=\"problem\">\n<p id=\"fs-id1668277\">The length of a rectangle is eight more than twice the width. The perimeter is \\(64\\) feet. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1171487568155\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1535645\">8 ft, 24 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1532320\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1715140\" data-type=\"exercise\">\n<div id=\"fs-id1171487568155\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1915022\" data-type=\"problem\">\n<p id=\"fs-id1776454\">The width of a rectangle is six less than twice the length. The perimeter is \\(18\\) centimetres. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1759344\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171505974580\">5 cm, 4 cm<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1673589\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id907273\" data-type=\"exercise\">\n<div id=\"fs-id1759344\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547656\" data-type=\"problem\">\n<p id=\"fs-id1901758\">The area of a rectangular room is \\(168\\) square feet. The length is \\(14\\) feet. What is the width?<\/p>\n\n<\/div>\n<div id=\"fs-id1171487189498\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466072798\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a rectangle. The bottom is labeled 14 ft. and the side is labeled W. Beside the rectangle is Area equals 168 ft. squared. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe width of a rectangular room.\u201d Step 3 says, \u201cName. Choose a variable to represent the width.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet w equal width.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula and substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals LW followed by 168 equals 14 times W. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 168 over 14 equals 14W over 14, then 12 equals W.\u201d Step 6 says, \u201cCheck,\u201d in bold. Beside this is A equals LW, then 168 followed by an equal sign with a question mark, then 14 times 12. Below this is 168 equals 168 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe width of the room is 12 feet.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem.<\/td>\n<td><span id=\"eip-id1168466262188\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the width of a rectangular room<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">W<\/em> = width<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula and substitute in the given information.<\/td>\n<td><span id=\"eip-id1164270730310\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164270730332\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The width of the room is 12 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1257520\" data-type=\"problem\">\n\nThe area of a rectangle is \\(598\\) square feet. The length is \\(23\\) feet. What is the width?\n\n<\/div>\n<div id=\"fs-id1593194\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1685301\">26 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1471916\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171512117693\" data-type=\"exercise\">\n<div id=\"fs-id1257520\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1394027\" data-type=\"problem\">\n<p id=\"fs-id1171505779962\">The width of a rectangle is \\(21\\) metres. The area is \\(609\\) square metres. What is the length?<\/p>\n\n<\/div>\n<div id=\"fs-id1715331\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1550525\">29 m<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1593194\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487569847\" data-type=\"problem\">\n<p id=\"fs-id1171487569639\">The perimeter of a rectangular swimming pool is \\(150\\) feet. The length is \\(15\\) feet more than the width. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1586798\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469520954\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a rectangle. The sides are labeled w and the top and bottom are labeled w plus 15. Below the rectangle is P equals 150 ft. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length and width of the pool.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet w equal width.\u201d Then, \u201cthe length is 15 feet more than the width,\u201d and w plus 15 equals length. Step 4 says, \u201cTranslate. Write the appropriate formula and substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W, then 150 ft. equals 2 times w plus 15 ft. plus 2W. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 150 equals 2W plus 30 plus 2W, then 150 equals 4W plus 30, then 120 equals 4W. Below this is 30 equals W the width of the pool. Next is W plus 15 length of the pool, followed by a red 30 plus 15, then 45. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals 2L plus 2W, then 150 followed by an equal sign with a question mark, then 2 times 45 plus 2 times 30. Below this is 150 equals 150 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length of the pool is 45 feet and the width of the pool is 30 feet.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469562861\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072.img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width of the pool<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.\nThe length is 15 feet more than the width.<\/td>\n<td>Let \\(W=\\text{width}\\)\n\\(W+15=\\text{length}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula and substitute.<\/td>\n<td><span id=\"eip-id1168466467969\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168466463591\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length of the pool is 45 feet and the width is 30 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104048697\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1715331\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487565544\" data-type=\"problem\">\n<p id=\"fs-id1171487566798\">The perimeter of a rectangular swimming pool is \\(200\\) feet. The length is \\(40\\) feet more than the width. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1527584\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1837003\">30 ft, 70 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1772056\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2239997\" data-type=\"exercise\">\n<div id=\"fs-id1171487565544\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id962062\" data-type=\"problem\">\n<p id=\"fs-id1765272\">The length of a rectangular garden is \\(30\\) yards more than the width. The perimeter is \\(300\\) yards. Find the length and width.<\/p>\n\n<\/div>\n<div id=\"fs-id1559124\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>60 yd, 90 yd\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use the Properties of Triangles<\/h1>\n<p id=\"fs-id1571656\">We now know how to find the area of a rectangle. We can use this fact to help us visualize the formula for the area of a triangle. In the rectangle in <a class=\"autogenerated-content\" href=\"#fs-id1901874\">(Figure.9)<\/a>, we\u2019ve labeled the length \\(b\\) and the width \\(h\\), so it\u2019s area is \\(bh\\).<\/p>\nThe area of a rectangle is the base, \\(b\\), times the height, \\(h\\).\n<div id=\"CNX_BMath_Figure_09_04_035\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"151\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_035.jpg\" alt=\"A rectangle is shown. The side is labeled h and the bottom is labeled b. The centre says A equals bh.\" width=\"151\" height=\"89\" data-media-type=\"image\/jpeg\"> Figure.9[\/caption]\n<p id=\"fs-id1171505624044\">We can divide this rectangle into two congruent triangles <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_036\">(Figure.10)<\/a>. Triangles that are congruent have identical side lengths and angles, and so their areas are equal. The area of each triangle is one-half the area of the rectangle, or \\(\\frac{1}{2}bh\\). This example helps us see why the formula for the area of a triangle is \\(A=\\frac{1}{2}bh\\).<\/p>\nA rectangle can be divided into two triangles of equal area. The area of each triangle is one-half the area of the rectangle.\n<div id=\"CNX_BMath_Figure_09_04_036\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"323\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_036.jpg\" alt=\"A rectangle is shown. A diagonal line is drawn from the upper left corner to the bottom right corner. The side of the rectangle is labeled h and the bottom is labeled b. Each triangle says one-half bh. To the right of the rectangle, it says \u201cArea of each triangle,\u201d and shows the equation A equals one-half bh.\" width=\"323\" height=\"107\" data-media-type=\"image\/jpeg\"> Figure.10[\/caption]\n<p id=\"fs-id1171505925447\">The formula for the area of a triangle is \\(A=\\frac{1}{2}bh\\), where \\(b\\) is the base and \\(h\\) is the height.<\/p>\n<p id=\"fs-id1486748\">To find the area of the triangle, you need to know its base and height. The base is the length of one side of the triangle, usually the side at the bottom. The height is the length of the line that connects the base to the opposite vertex, and makes a \\(\\text{90}\\)\u00b0 angle with the base. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_037\">(Figure.11)<\/a> shows three triangles with the base and height of each marked.<\/p>\nThe height \\(h\\) of a triangle is the length of a line segment that connects the the base to the opposite vertex and makes a \\(\\text{90}\\)\u00b0 angle with the base.\n<div id=\"CNX_BMath_Figure_09_04_037\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"563\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_037.jpg\" alt=\"Three triangles are shown. The triangle on the left is a right triangle. The bottom is labeled b and the side is labeled h. The middle triangle is an acute triangle. The bottom is labeled b. There is a dotted line from the top vertex to the base of the triangle, forming a right angle with the base. That line is labeled h. The triangle on the right is an obtuse triangle. The bottom of the triangle is labeled b. The base has a dotted line extended out and forms a right angle with a dotted line to the top of the triangle. The vertical line is labeled h.\" width=\"563\" height=\"107\" data-media-type=\"image\/jpeg\"> Figure.11[\/caption]\n\n<div id=\"fs-id1802095\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Triangle Properties<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1752354\">For any triangle \\(\\Delta ABC\\), the sum of the measures of the angles is \\(\\text{180}\\)\u00b0.<\/p>\n\\(m\\angle A+m\\angle B+m\\angle C=\\text{180}\\)\u00b0\n<p id=\"fs-id1928592\">The perimeter of a triangle is the sum of the lengths of the sides.<\/p>\n\\(P=a+b+c\\)\n\nThe area of a triangle is one-half the base, \\(b\\), times the height, \\(h\\).\n\n\\(A=\\frac{1}{2}\\phantom{\\rule{0.1em}{0ex}}bh\\)\n\n<span id=\"fs-id1930696\" data-type=\"media\" data-alt=\"A triangle is shown. The vertices are labeled A, B, and C. The sides are labeled a, b, and c. There is a vertical dotted line from vertex B at the top of the triangle to the base of the triangle, meeting the base at a right angle. The dotted line is labeled h.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_038_img.jpg\" alt=\"A triangle is shown. The vertices are labeled A, B, and C. The sides are labeled a, b, and c. There is a vertical dotted line from vertex B at the top of the triangle to the base of the triangle, meeting the base at a right angle. The dotted line is labeled h.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1602784\" data-type=\"problem\">\n<p id=\"fs-id1799270\">Find the area of a triangle whose base is \\(11\\) inches and whose height is \\(8\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id1418466\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468457178\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a triangle. The base of the triangle is labeled 11 in and the height of the triangle is labeled 8 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of the triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal area of the triangle.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times b times h. Below this is A equals one-half times 11 in. times 8 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals 44 square inches. Step 6 says, \u201cCheck,\u201d in bold. Beside this is A equals one-half bh, then 44 followed by an equal sign with a question mark, then one-half times 11 times 8, then 44 equals 44 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe area is 44 square inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468388397\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of the triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">A<\/em> = area of the triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td><span id=\"eip-id1168468357737\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272169003\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The area is 44 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171488156140\" data-type=\"problem\">\n<p id=\"fs-id1171498388066\">Find the area of a triangle with base \\(13\\) inches and height \\(2\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id1748718\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1498105\">13 sq. in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1924824\" data-type=\"problem\">\n<p id=\"fs-id1171496946102\">Find the area of a triangle with base \\(14\\) inches and height \\(7\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id1171487146402\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1882186\">49 sq. in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id16795130\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1423184\" data-type=\"exercise\">\n<div id=\"fs-id1171488156140\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1562031\" data-type=\"problem\">\n<p id=\"fs-id1559945\">The perimeter of a triangular garden is \\(24\\) feet. The lengths of two sides are \\(4\\) feet and \\(9\\) feet. How long is the third side?<\/p>\n\n<\/div>\n<div id=\"fs-id1171487511856\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466081900\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a triangle. The sides of the triangle are labeled 4 ft., 9 ft., and c. Below the triangle is P equals 24 ft. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201clength of the third side of the triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet c equal the third side.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals a plus b plus c. Below this is 24 ft. equals 4 ft. plus 9 ft. plus c. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 24 equals 13 plus c, then 11 equals c. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals a plus b plus c, then 24 followed by an equal sign with a question mark, then 4 plus 9 plus 11, then 24 equals 24 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe third side is 11 ft. long.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469745372\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>length of the third side of a triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">c<\/em> = the third side<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168466112852\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272066645\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The third side is 11 feet long.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1748718\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id972955\" data-type=\"problem\">\n<p id=\"fs-id1481576\">The perimeter of a triangular garden is \\(24\\) feet. The lengths of two sides are \\(18\\) feet and \\(22\\) feet. How long is the third side?<\/p>\n\n<\/div>\n<div id=\"fs-id1656452\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171505940975\">8 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171505481383\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1790476\" data-type=\"exercise\">\n<div id=\"fs-id972955\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547798\" data-type=\"problem\">\n<p id=\"fs-id1171506186890\">The lengths of two sides of a triangular window are \\(7\\) feet and \\(5\\) feet. The perimeter is \\(18\\) feet. How long is the third side?<\/p>\n\n<\/div>\n<div id=\"fs-id1171498403869\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1793391\">6 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1656452\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1915793\" data-type=\"problem\">\n<p id=\"fs-id1712158\">The area of a triangular church window is \\(90\\) square metres. The base of the window is \\(15\\) metres. What is the window\u2019s height?<\/p>\n\n<\/div>\n<div id=\"fs-id1376811\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467155173\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a triangle. The base of the triangle is labeled 15 m and the height of the triangle is labeled h. Below the triangle is A equals 90 m squared. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cheight of a triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet h equal the height.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times b times h. Below this is 90 m squared equals one-half times 15 m times h. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 90 equals 15 over 2 times h, then 12 equals h. Step 6 says, \u201cCheck,\u201d in bold. Beside this is A equals one-half bh, then 90 followed by an equal sign with a question mark, then one-half times 15 times 12, then 90 equals 90 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe height of the triangle is 12 metres.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468303076\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>height of a triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">h<\/em> = the height<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168468653388\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164271013482\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The height of the triangle is 12 metres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1435066\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1448113\" data-type=\"exercise\">\n<div id=\"fs-id1171498403869\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1914206\" data-type=\"problem\">\n<p id=\"fs-id1481654\">The area of a triangular painting is \\(126\\) square inches. The base is \\(18\\) inches. What is the height?<\/p>\n\n<\/div>\n<div id=\"fs-id1778473\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1328179\">14 in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171506203651\" data-type=\"problem\">\n<p id=\"fs-id1711674\">A triangular tent door has an area of \\(15\\) square feet. The height is \\(5\\) feet. What is the base?<\/p>\n\n<\/div>\n<div id=\"fs-id1545334\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1587349\">6 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Isosceles and Equilateral Triangles<\/h1>\n<p id=\"fs-id1482074\">Besides the right triangle, some other triangles have special names. A triangle with two sides of equal length is called an isosceles triangle. A triangle that has three sides of equal length is called an equilateral triangle. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_045\">(Figure.12)<\/a> shows both types of triangles.<\/p>\nIn an isosceles triangle, two sides have the same length, and the third side is the base. In an equilateral triangle, all three sides have the same length.\n<div id=\"CNX_BMath_Figure_09_04_045\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"367\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_045.jpg\" alt=\"Two triangles are shown. All three sides of the triangle on the left are labeled s. It is labeled \u201cequilateral triangle\u201d. Two sides of the triangle on the right are labeled s. It is labeled \u201cisosceles triangle\u201d.\" width=\"367\" height=\"231\" data-media-type=\"image\/jpeg\"> Figure.12[\/caption]\n\n<div id=\"fs-id1662237\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Isosceles and Equilateral Triangles<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2037850\">An <strong data-effect=\"bold\">isosceles<\/strong> triangle has two sides the same length.<\/p>\nAn <strong data-effect=\"bold\">equilateral<\/strong> triangle has three sides of equal length.\n\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1888433\" data-type=\"problem\">\n<p id=\"fs-id1171505548057\">The perimeter of an equilateral triangle is \\(93\\) inches. Find the length of each side.<\/p>\n\n<\/div>\n<div id=\"fs-id1549131\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468574026\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of an equilateral triangle. Each side of the triangle is labeled s. Below the triangle is Perimeter equals 93 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length of the sides of an equilateral triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet s equal length of each side.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals a plus b plus c. Below this is 93 in equals s plus s plus s. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 93 equals 3s, then 31 equals s. Step 6 says, \u201cCheck,\u201d in bold. Beside this is an image of an equilateral triangle. Each side is labeled 31. Below the triangle is 93 followed by an equal sign with a question mark, then 31 plus 31 plus 31, then 93 equals 93 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cEach side is 31 inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468738268\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\nPerimeter = 93 in.<\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>length of the sides of an equilateral triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">s<\/em> = length of each side<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td><span id=\"eip-id1168468576504\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272060705\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\">\n\n<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>Each side is 31 inches<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1530946\" data-type=\"problem\">\n<p id=\"fs-id1171506666626\">Find the length of each side of an equilateral triangle with perimeter \\(39\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id1595728\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171488073207\">13 in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1937636\" data-type=\"problem\">\n<p id=\"fs-id1786746\">Find the length of each side of an equilateral triangle with perimeter \\(51\\) centimetres.<\/p>\n\n<\/div>\n<div id=\"fs-id1501535\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1798725\">17 cm<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1786620\" data-type=\"exercise\">\n<div id=\"fs-id1530946\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2167088\" data-type=\"problem\">\n<p id=\"fs-id1171498011638\">Arianna has \\(156\\) inches of beading to use as trim around a scarf. The scarf will be an isosceles triangle with a base of \\(60\\) inches. How long can she make the two equal sides?<\/p>\n\n<\/div>\n<div id=\"fs-id1171488105757\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466073183\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of an isosceles triangle. Two sides of the triangle are labeled s. The base of the triangle is labeled 60 in. Below the triangle is Perimeter equals 156 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe lengths of the two equal sides.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet s equal the length of each side.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals a plus b plus c. Below this is 156 in equals s plus 60 in plus s. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 156 equals 2s plus 60, then 96 equals 2s, then 48 equals s. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals a plus b plus c, then 156 followed by an equal sign with a question mark, then 48 plus 60 plus 48, then 156 equals 156 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cAriana can make each of the two equal sides 48 inches long.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168466315318\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<em data-effect=\"italics\">P<\/em> = 156 in.<\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the lengths of the two equal sides<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">s<\/em> = the length of each side<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168469876808\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272069623\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>Arianna can make each of the two equal sides 48 inches l<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1595728\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1575241\" data-type=\"problem\">\n<p id=\"fs-id1171506203395\">A backyard deck is in the shape of an isosceles triangle with a base of \\(20\\) feet. The perimeter of the deck is \\(48\\) feet. How long is each of the equal sides of the deck?<\/p>\n\n<\/div>\n<div id=\"fs-id1776706\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171505478153\">14 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1786077\" data-type=\"problem\">\n<p id=\"fs-id1783120\">A boat\u2019s sail is an isosceles triangle with base of \\(8\\) metres. The perimeter is \\(22\\) metres. How long is each of the equal sides of the sail?<\/p>\n\n<\/div>\n<div id=\"fs-id1171498469951\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1784277\">7 m<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use the Properties of Trapezoids<\/h1>\n<p id=\"fs-id1064389\">A trapezoid is four-sided figure, a <em data-effect=\"italics\">quadrilateral<\/em>, with two sides that are parallel and two sides that are not. The parallel sides are called the bases. We call the length of the smaller base \\(b\\), and the length of the bigger base \\(B\\). The height, \\(h\\), of a trapezoid is the distance between the two bases as shown in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_052\">(Figure.13)<\/a>.<\/p>\nA trapezoid has a larger base, \\(B\\), and a smaller base, \\(b\\). The height \\(h\\) is the distance between the bases.\n<div id=\"CNX_BMath_Figure_09_04_052\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"291\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_052.jpg\" alt=\"A trapezoid is shown. The top is labeled b and marked as the smaller base. The bottom is labeled B and marked as the larger base. A vertical line forms a right angle with both bases and is marked as h.\" width=\"291\" height=\"129\" data-media-type=\"image\/jpeg\"> Figure.13[\/caption]\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Formula for the A<span class=\"no-emphasis\" data-type=\"term\">rea of a Trapezoid<\/span><\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n\\({\\text{Area}}_{\\text{trapezoid}}=\\frac{1}{2}h\\left(b+B\\right)\\)\n\n<\/div>\n<\/div>\n<p id=\"fs-id1501788\">Splitting the trapezoid into two triangles may help us understand the formula. The area of the trapezoid is the sum of the areas of the two triangles. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_053\">(Figure.14)<\/a>.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_04_053\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Splitting a trapezoid into two triangles may help you understand the formula for its area.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"179\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_053.jpg\" alt=\"An image of a trapezoid is shown. The top is labeled with a small b, the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner.\" width=\"179\" height=\"123\" data-media-type=\"image\/jpeg\"> Figure.14[\/caption]\n<p id=\"fs-id1888313\">The height of the trapezoid is also the height of each of the two triangles. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_078\">(Figure.15)<\/a>.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_04_078\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"193\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_078.jpg\" alt=\"An image of a trapezoid is shown. The top is labeled with a small b, the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner. There is an arrow pointing to a second trapezoid. The upper right-hand side of the trapezoid forms a blue triangle, with the height of the trapezoid drawn in as a dotted line. The lower left-hand side of the trapezoid forms a red triangle, with the height of the trapezoid drawn in as a dotted line.\" width=\"193\" height=\"122\" data-media-type=\"image\/jpeg\"> Figure.15[\/caption]\n\n<\/div>\n<p id=\"fs-id1786318\">The formula for the area of a trapezoid is<\/p>\n<span id=\"fs-id1344340\" data-type=\"media\" data-alt=\"This image shows the formula for the area of a trapezoid and says \u201carea of trapezoid equals one-half h times smaller base b plus larger base B).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_056_img.jpg\" alt=\"This image shows the formula for the area of a trapezoid and says \u201carea of trapezoid equals one-half h times smaller base b plus larger base B).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1864567\">If we distribute, we get,<\/p>\n<span id=\"fs-id1477452\" data-type=\"media\" data-alt=\"The top line says area of trapezoid equals one-half times blue little b times h plus one-half times red big B times h. Below this is area of trapezoid equals A sub blue triangle plus A sub red triangle.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_079_img.jpg\" alt=\"The top line says area of trapezoid equals one-half times blue little b times h plus one-half times red big B times h. Below this is area of trapezoid equals A sub blue triangle plus A sub red triangle.\" data-media-type=\"image\/jpeg\"><\/span>\n<div id=\"fs-id1791445\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Trapezoids<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1429217\" data-bullet-style=\"bullet\">\n \t<li>A trapezoid has four sides. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_052\">(Figure.13)<\/a>.<\/li>\n \t<li>Two of its sides are parallel and two sides are not.<\/li>\n \t<li>The area, \\(A\\), of a trapezoid is \\(\\text{A}=\\frac{1}{2}h\\left(b+B\\right)\\).<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1433391\" data-type=\"problem\">\n<p id=\"fs-id1454196\">Find the area of a trapezoid whose height is 6 inches and whose bases are \\(14\\) and \\(11\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id962767\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468452905\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a trapezoid. The larger base at the top of the trapezoid is labeled 14 in, the smaller base at the bottom is labeled 11 in, the height is shown by a dotted line and is labeled 6 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a trapezoid.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times h times parentheses little b plus big B. Below this is A equals one-half times 6 in times parentheses 11 in plus 14 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals one-half times 6 times 25, then A equals 3 times 25, then A equals 75 square inches. Step 6 says, \u201cCheck,\u201d in bold. Beside this is written, \u201cIs this answer reasonable?\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468774032\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_080_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of the trapezoid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let \\(A=\\text{the area}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td><span id=\"eip-id1168467200978\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_080_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272216853\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_080_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1402808\">If we draw a rectangle around the trapezoid that has the same big base \\(B\\) and a height \\(h\\), its area should be greater than that of the trapezoid.<\/p>\n<p id=\"fs-id1904190\">If we draw a rectangle inside the trapezoid that has the same little base \\(b\\) and a height \\(h\\), its area should be smaller than that of the trapezoid.<\/p>\n<span data-type=\"media\" data-alt=\"A table is shown with 3 columns and 4 rows. The first column has an image of a trapezoid with a rectangle drawn around it in red. The larger base of the trapezoid is labeled 14 and is the same as the base of the rectangle. The height of the trapezoid is labeled 6 and is the same as the height of the rectangle. The smaller base of the trapezoid is labeled 11. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 14 times 6. Below is A sub rectangle equals 84 square inches. The second column has an image of a trapezoid. The larger base is labeled 14, the smaller base is labeled 11, and the height is labeled 6. Below this is A sub trapezoid equals one-half times h times parentheses little b plus big B. Below this is A sub trapezoid equals one-half times 6 times parentheses 11 plus 14. Below this is A sub trapezoid equals 75 square inches. The third column has an image of a trapezoid with a red rectangle drawn inside of it. The height is labeled 6. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 11 times 6. Below is A sub rectangle equals 66 square inches.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_060.jpg\" alt=\"A table is shown with 3 columns and 4 rows. The first column has an image of a trapezoid with a rectangle drawn around it in red. The larger base of the trapezoid is labeled 14 and is the same as the base of the rectangle. The height of the trapezoid is labeled 6 and is the same as the height of the rectangle. The smaller base of the trapezoid is labeled 11. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 14 times 6. Below is A sub rectangle equals 84 square inches. The second column has an image of a trapezoid. The larger base is labeled 14, the smaller base is labeled 11, and the height is labeled 6. Below this is A sub trapezoid equals one-half times h times parentheses little b plus big B. Below this is A sub trapezoid equals one-half times 6 times parentheses 11 plus 14. Below this is A sub trapezoid equals 75 square inches. The third column has an image of a trapezoid with a red rectangle drawn inside of it. The height is labeled 6. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 11 times 6. Below is A sub rectangle equals 66 square inches.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171496188733\">The area of the larger rectangle is \\(84\\) square inches and the area of the smaller rectangle is \\(66\\) square inches. So it makes sense that the area of the trapezoid is between \\(84\\) and \\(66\\) square inches<\/p>\n<p id=\"fs-id1439870\">Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question. The area of the trapezoid is \\(75\\) square inches.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1870546\" data-type=\"problem\">\n<p id=\"fs-id1358434\">The height of a trapezoid is \\(14\\) yards and the bases are \\(7\\) and \\(16\\) yards. What is the area?<\/p>\n\n<\/div>\n<div id=\"fs-id1793537\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>161 sq. yd\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1580621\">The height of a trapezoid is \\(18\\) centimetres and the bases are \\(17\\) and \\(8\\) centimetres. What is the area?<\/p>\n\n<\/div>\n<div id=\"fs-id1171505941020\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1784487\">225 sq. cm<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1914969\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id781068\" data-type=\"exercise\">\n<div id=\"fs-id1793537\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505120215\" data-type=\"problem\">\n<p id=\"fs-id2064937\">Find the area of a trapezoid whose height is \\(5\\) feet and whose bases are \\(10.3\\) and \\(13.7\\) feet.<\/p>\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469577474\" class=\"unnumbered unstyled has-images\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a trapezoid. The smaller base at the top of the trapezoid is labeled 10.3 ft, the larger base at the bottom is labeled 13.7 ft, the height is shown by a dotted line and is labeled h. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a trapezoid.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times h times parentheses little b plus big B. Below this is A equals one-half times 5 ft times parentheses 10.3 ft plus 13.7 ft. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals one-half times 5 times 24, then A equals 12 times 5, then A equals 60 square feet. Step 6 says, \u201cCheck,\u201d in bold. Beside this is written, \u201cIs this answer reasonable? The area of the trapezoid should be less than the area of a rectangle with base 13.7 and height 5, but more than the area of a rectangle with base 10.3 and height 5.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 328.867px;\">Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1168469468737\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_081_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 284.333px;\">the area of the trapezoid<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td style=\"width: 284.333px;\">Let <em data-effect=\"italics\">A<\/em> = the area<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1168469565101\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_081_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\" data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1164272204164\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_081_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 6. <strong data-effect=\"bold\">Check:<\/strong> Is this answer reasonable?\nThe area of the trapezoid should be less than the area of a rectangle with base 13.7 and height 5, but more than the area of a rectangle with base 10.3 and height 5.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1168466684076\" data-type=\"media\" data-alt=\"An image of a trapezoid is shown with a red rectangle drawn around it. The larger base of the trapezoid is labeled 13.7 ft. and is the same as the base of the rectangle. The height of both the trapezoid and the rectangle is 5 ft. Next to this is an image of a trapezoid with a black rectangle drawn inside it. The smaller base of the trapezoid is labeled 10.3 ft. and is the same as the base of the rectangle. Below the images is A sub red rectangle is greater than A sub trapezoid is greater than A sub rectangle. Below this is 68.5, 60, and 51.5.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_063.jpg\" alt=\"An image of a trapezoid is shown with a red rectangle drawn around it. The larger base of the trapezoid is labeled 13.7 ft. and is the same as the base of the rectangle. The height of both the trapezoid and the rectangle is 5 ft. Next to this is an image of a trapezoid with a black rectangle drawn inside it. The smaller base of the trapezoid is labeled 10.3 ft. and is the same as the base of the rectangle. Below the images is A sub red rectangle is greater than A sub trapezoid is greater than A sub rectangle. Below this is 68.5, 60, and 51.5.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td style=\"width: 284.333px;\">The area of the trapezoid is 60 square feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171487575864\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1171505941020\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1550216\">The height of a trapezoid is \\(7\\) centimetres and the bases are \\(4.6\\) and \\(7.4\\) centimetres. What is the area?<\/p>\n\n<\/div>\n<div id=\"fs-id1361907\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1804038\">42 sq. cm<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171506138038\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1712277\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1350237\" data-type=\"problem\">\n<p id=\"fs-id1767992\">The height of a trapezoid is \\(9\\) metres and the bases are \\(6.2\\) and \\(7.8\\) metres. What is the area?<\/p>\n\n<\/div>\n<div id=\"fs-id1612307\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1931241\">63 sq. m<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1361907\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1433882\" data-type=\"problem\">\n<p id=\"fs-id1656994\">Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of \\(3.4\\) yards and the bases are \\(8.2\\) and \\(5.6\\) yards. How many square yards will be available to plant?<\/p>\n\n<\/div>\n<div id=\"fs-id1598220\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469766721\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a trapezoid. The smaller base at the top of the trapezoid is labeled 5.6 yd., the larger base at the bottom is labeled 8.2 yd., the height is shown by a dotted line and is labeled 3.4 yd. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a trapezoid.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times h times parentheses little b plus big B. Below this is A equals one-half times 3.4 yd. times parentheses 5.6 yd. plus 8.2 yd. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals one-half times 3.4 times 13.8, then A equals 23.46 square yards. Step 6 says, \u201cCheck,\u201d in bold. Beside this is written, \u201cIs this answer reasonable? Yes. The area of the trapezoid is less than the area of a rectangle with a base of 8.2 yd. and height 3.4 yd., but more than the area of a rectangle with base 5.6 yd. and height 3.4 yd.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469647601\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_082_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of a trapezoid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">A<\/em> = the area<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td><span id=\"eip-id1168466277354\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_082_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272067215\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_082_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Step 6. <strong data-effect=\"bold\">Check:<\/strong> Is this answer reasonable?\nYes. The area of the trapezoid is less than the area of a rectangle with a base of 8.2 yd and height 3.4 yd, but more than the area of a rectangle with base 5.6 yd and height 3.4 yd.<span id=\"eip-id1168469711174\" data-type=\"media\" data-alt=\"This image is a table with two rows. the first row is split into three columns. The first column is the formula Area of a rectangle equals base times height. On the next line under this it has numbers plugged into the formula; the base, 8.2 in parentheses times the height 3.4 in parentheses. Under this is it has \u201cequals 27.88 yards squared\u201d. The centre column includes the formula of a trapezoid and says Area of a trapezoid equals one half times 3.5 yards in parentheses times 5.8 plus 8.2 in parentheses. Under this it has \u201cequals 23.46 yards squared\u201d. In the third column it it has the formula the area of a rectangle equals base times height. Under this it has equals 5.6 in parentheses times 3.4 in parentheses. Under this it has \u201cequals 19.04 yards squared.\u201d In the second row, centered from left to right it has \u201cArea of a rectangle\u201d and a \u201cgreater than\u201d sign, \u201cArea of a trapezoid\u201d and a greater than sign and \u201carea of a rectangle\u201d. Under Area of a rectangle it has 27.88, then 23.46 under \u201carea of a trapezoid\u201d, then 19.04 under \u201carea of a rectangle\u201d.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_066.jpg\" alt=\"This image is a table with two rows. the first row is split into three columns. The first column is the formula Area of a rectangle equals base times height. On the next line under this it has numbers plugged into the formula; the base, 8.2 in parentheses times the height 3.4 in parentheses. Under this is it has \u201cequals 27.88 yards squared\u201d. The centre column includes the formula of a trapezoid and says Area of a trapezoid equals one half times 3.5 yards in parentheses times 5.8 plus 8.2 in parentheses. Under this it has \u201cequals 23.46 yards squared\u201d. In the third column it it has the formula the area of a rectangle equals base times height. Under this it has equals 5.6 in parentheses times 3.4 in parentheses. Under this it has \u201cequals 19.04 yards squared.\u201d In the second row, centered from left to right it has \u201cArea of a rectangle\u201d and a \u201cgreater than\u201d sign, \u201cArea of a trapezoid\u201d and a greater than sign and \u201carea of a rectangle\u201d. Under Area of a rectangle it has 27.88, then 23.46 under \u201carea of a trapezoid\u201d, then 19.04 under \u201carea of a rectangle\u201d.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>Vinny has 23.46 square yards in which he can plan<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104090407\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1533455\" data-type=\"exercise\">\n<div id=\"fs-id1612307\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1685675\" data-type=\"problem\">\n<p id=\"fs-id1790946\">Lin wants to sod his lawn, which is shaped like a trapezoid. The bases are \\(10.8\\) yards and \\(6.7\\) yards, and the height is \\(4.6\\) yards. How many square yards of sod does he need?<\/p>\n\n<\/div>\n<div id=\"fs-id1534290\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1487468\">40.25 sq. yd<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id940652\" data-type=\"problem\">\n<p id=\"fs-id1386498\">Kira wants cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are \\(18\\) feet and \\(14\\) feet and whose height is \\(15\\) feet, how many square feet of pavers will he need?<\/p>\n\n<\/div>\n<div id=\"fs-id1171487564666\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171505120247\">240 sq. ft.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"eip-375\" class=\"links-to-literacy\" data-type=\"note\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Access Additional Online Resources<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1579336\">\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24perirect\">Perimeter of a Rectangle<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24arearect\">Area of a Rectangle<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24periareaform\">Perimeter and Area Formulas<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24areatri\">Area of a Triangle<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24areatrifract\">Area of a Triangle with Fractions<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24areatrap\">Area of a Trapezoid<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"eip-87\">\n \t<li><strong>Properties of Rectangles<\/strong>\n<ul id=\"eip-id1168921412515\">\n \t<li>Rectangles have four sides and four right (90\u00b0) angles.<\/li>\n \t<li>The lengths of opposite sides are equal.<\/li>\n \t<li>The perimeter, \\(P\\), of a rectangle is the sum of twice the length and twice the width.\n<ul id=\"eip-id1168933998684\">\n \t<li>\\(P=2L+2W\\)<\/li>\n<\/ul>\n<\/li>\n \t<li>The area, \\(A\\), of a rectangle is the length times the width.\n<ul id=\"eip-id5597402\">\n \t<li>\\(A=L\\cdot W\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Triangle Properties<\/strong>\n<ul id=\"eip-id7402430\">\n \t<li>For any triangle \\(\\Delta ABC\\), the sum of the measures of the angles is 180\u00b0.\n<ul id=\"eip-id1170244913551\">\n \t<li>\\(m\\angle A+m\\angle B+m\\angle C=180\\)\u00b0<\/li>\n<\/ul>\n<\/li>\n \t<li>The perimeter of a triangle is the sum of the lengths of the sides.\n<ul id=\"eip-id1170253352636\">\n \t<li>\\(P=a+b+c\\)<\/li>\n<\/ul>\n<\/li>\n \t<li>The area of a triangle is one-half the base, b, times the height, h.\n<ul id=\"eip-id1170239311614\">\n \t<li>\\(A=\\frac{1}{2}bh\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1927628\">\n \t<dt>area<\/dt>\n \t<dd id=\"fs-id1171505277192\">The area is a measure of the surface covered by a figure.<\/dd>\n<\/dl>\n<dl id=\"fs-id1933603\">\n \t<dt>equilateral triangle<\/dt>\n \t<dd id=\"fs-id1816092\">A triangle with all three sides of equal length is called an equilateral triangle.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171506988885\">\n \t<dt>isosceles triangle<\/dt>\n \t<dd id=\"fs-id1674082\">A triangle with two sides of equal length is called an isosceles triangle.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171497994973\">\n \t<dt>perimeter<\/dt>\n \t<dd id=\"fs-id1171505779039\">The perimeter is a measure of the distance around a figure.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171488172541\">\n \t<dt>rectangle<\/dt>\n \t<dd id=\"fs-id1922026\">A rectangle is a geometric figure that has four sides and four right angles.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171505990665\">\n \t<dt>trapezoid<\/dt>\n \t<dd id=\"fs-id2022585\">A trapezoid is four-sided figure, a quadrilateral, with two sides that are parallel and two sides that are not.<\/dd>\n<\/dl>\n<\/div>\n<h1 style=\"text-align: left;\" data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1171498001678\">Understand Linear, Square, and Cubic Measure<\/h2>\n<p id=\"eip-832\">In the following exercises, determine whether you would measure each item using linear, square, or cubic units.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. amount of water in a fish tank<\/td>\n<td style=\"width: 50%;\">2. length of dental floss<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. living area of an apartment<\/td>\n<td style=\"width: 50%;\">4. floor space of a bathroom tile<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. height of a doorway<\/td>\n<td style=\"width: 50%;\">6. capacity of a truck trailer<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1679789\">In the following exercises, find the a) perimeter and b) area of each figure. Assume each side of the square is \\(1\\) cm.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 258px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 160px;\">\n<td style=\"width: 50%; height: 160px;\"><span id=\"fs-id1557835\" data-type=\"media\" data-alt=\"A rectangle is shown comprised of 4 squares forming a horizontal line.\">7.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_201_img.jpg\" alt=\"A rectangle is shown comprised of 4 squares forming a horizontal line.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 160px;\"><span id=\"fs-id1747015\" data-type=\"media\" data-alt=\"A rectangle is shown comprised of 3 squares forming a vertical line.\">8.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_202_img.jpg\" alt=\"A rectangle is shown comprised of 3 squares forming a vertical line.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1577499\" data-type=\"media\" data-alt=\"Three squares are shown. There is one on the bottom left, one on the bottom right, and one on the top right.\">9.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_203_img.jpg\" alt=\"Three squares are shown. There is one on the bottom left, one on the bottom right, and one on the top right.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1171505618069\" data-type=\"media\" data-alt=\"Four squares are shown. Three form a horizontal line, and there is one above the centre square.\">10.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_204_img.jpg\" alt=\"Four squares are shown. Three form a horizontal line, and there is one above the centre square.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id2035119\" data-type=\"media\" data-alt=\"Five squares are shown. There are three forming a horizontal line across the top and two underneath the two on the right.\">11.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_205_img.jpg\" alt=\"Five squares are shown. There are three forming a horizontal line across the top and two underneath the two on the right.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1568260\" data-type=\"media\" data-alt=\"A square is shown. It is comprised of nine smaller squares.\">12.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_206_img.jpg\" alt=\"A square is shown. It is comprised of nine smaller squares.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1913911\" style=\"text-align: left;\">Use the Properties of Rectangles<\/h2>\n<p id=\"eip-919\">In the following exercises, find the a) perimeter and b) area of each rectangle.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">13. The length of a rectangle is \\(85\\) feet and the width is \\(45\\) feet.<\/td>\n<td style=\"width: 50%;\">14. The length of a rectangle is \\(26\\) inches and the width is \\(58\\) inches.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. A rectangular room is \\(15\\) feet wide by \\(14\\) feet long.<\/td>\n<td style=\"width: 50%;\">16. A driveway is in the shape of a rectangle \\(20\\) feet wide by \\(35\\) feet long.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1586793\">In the following exercises, solve.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 370px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">17. Find the length of a rectangle with perimeter \\(124\\) inches and width \\(38\\) inches.<\/td>\n<td style=\"width: 50%; height: 30px;\">18. Find the length of a rectangle with perimeter \\(20.2\\) yards and width of \\(7.8\\) yards.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">19. Find the width of a rectangle with perimeter \\(92\\) metres and length \\(19\\) metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">20. Find the width of a rectangle with perimeter \\(16.2\\) metres and length \\(3.2\\) metres.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">21. The area of a rectangle is \\(414\\) square metres. The length is \\(18\\) metres. What is the width?<\/td>\n<td style=\"width: 50%; height: 30px;\">22. The area of a rectangle is \\(782\\) square centimetres. The width is \\(17\\) centimetres. What is the length?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">23. The length of a rectangle is \\(9\\) inches more than the width. The perimeter is \\(46\\) inches. Find the length and the width.<\/td>\n<td style=\"width: 50%; height: 30px;\">24. The width of a rectangle is \\(8\\) inches more than the length. The perimeter is \\(52\\) inches. Find the length and the width.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">25. The perimeter of a rectangle is \\(58\\) metres. The width of the rectangle is \\(5\\) metres less than the length. Find the length and the width of the rectangle.<\/td>\n<td style=\"width: 50%; height: 46px;\">26. The perimeter of a rectangle is \\(62\\) feet. The width is \\(7\\) feet less than the length. Find the length and the width.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">27. The width of the rectangle is \\(0.7\\) metres less than the length. The perimeter of a rectangle is \\(52.6\\) metres. Find the dimensions of the rectangle.<\/td>\n<td style=\"width: 50%; height: 46px;\">28. The length of the rectangle is \\(1.1\\) metres less than the width. The perimeter of a rectangle is \\(49.4\\) metres. Find the dimensions of the rectangle.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">29. The perimeter of a rectangle of \\(150\\) feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.<\/td>\n<td style=\"width: 50%; height: 46px;\">30. The length of a rectangle is three times the width. The perimeter is \\(72\\) feet. Find the length and width of the rectangle.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. The length of a rectangle is \\(3\\) metres less than twice the width. The perimeter is \\(36\\) metres. Find the length and width.<\/td>\n<td style=\"width: 50%; height: 14px;\">32. The length of a rectangle is \\(5\\) inches more than twice the width. The perimeter is \\(34\\) inches. Find the length and width.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. The width of a rectangular window is \\(24\\) inches. The area is \\(624\\) square inches. What is the length?<\/td>\n<td style=\"width: 50%; height: 14px;\">34. The length of a rectangular poster is \\(28\\) inches. The area is \\(1316\\) square inches. What is the width?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35. The area of a rectangular roof is \\(2310\\) square metres. The length is \\(42\\) metres. What is the width?<\/td>\n<td style=\"width: 50%; height: 14px;\">36. The area of a rectangular tarp is \\(132\\) square feet. The width is \\(12\\) feet. What is the length?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">37. The perimeter of a rectangular courtyard is \\(160\\) feet. The length is \\(10\\) feet more than the width. Find the length and the width.<\/td>\n<td style=\"width: 50%; height: 14px;\">38. The perimeter of a rectangular painting is \\(306\\) centimetres. The length is \\(17\\) centimetres more than the width. Find the length and the width.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">39. The width of a rectangular window is \\(40\\) inches less than the height. The perimeter of the doorway is \\(224\\) inches. Find the length and the width.<\/td>\n<td style=\"width: 50%; height: 14px;\">40. The width of a rectangular playground is \\(7\\) metres less than the length. The perimeter of the playground is \\(46\\) metres. Find the length and the width.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1552808\">Use the Properties of Triangles<\/h2>\n<p id=\"eip-650\">In the following exercises, solve using the properties of triangles.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 222px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">41. Find the area of a triangle with base \\(12\\) inches and height \\(5\\) inches.<\/td>\n<td style=\"width: 50%; height: 30px;\">42. Find the area of a triangle with base \\(45\\) centimetres and height \\(30\\) centimetres.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">43. Find the area of a triangle with base \\(8.3\\) metres and height \\(6.1\\) metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">44. Find the area of a triangle with base \\(24.2\\) feet and height \\(20.5\\) feet.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">45. A triangular flag has base of \\(1\\) foot and height of \\(1.5\\) feet. What is its area?<\/td>\n<td style=\"width: 50%; height: 30px;\">46. A triangular window has base of \\(8\\) feet and height of \\(6\\) feet. What is its area?<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">47. If a triangle has sides of \\(6\\) feet and \\(9\\) feet and the perimeter is \\(23\\) feet, how long is the third side?<\/td>\n<td style=\"width: 50%; height: 46px;\">48. If a triangle has sides of \\(14\\) centimetres and \\(18\\) centimetres and the perimeter is \\(49\\) centimetres, how long is the third side?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">49. What is the base of a triangle with an area of \\(207\\) square inches and height of \\(18\\) inches?<\/td>\n<td style=\"width: 50%; height: 30px;\">50. What is the height of a triangle with an area of \\(893\\) square inches and base of \\(38\\) inches?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. The perimeter of a triangular reflecting pool is \\(36\\) yards. The lengths of two sides are \\(10\\) yards and \\(15\\) yards. How long is the third side?<\/td>\n<td style=\"width: 50%; height: 14px;\">52. A triangular courtyard has perimeter of \\(120\\) metres. The lengths of two sides are \\(30\\) metres and \\(50\\) metres. How long is the third side?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. An isosceles triangle has a base of \\(20\\) centimetres. If the perimeter is \\(76\\) centimetres, find the length of each of the other sides.<\/td>\n<td style=\"width: 50%; height: 14px;\">54. An isosceles triangle has a base of \\(25\\) inches. If the perimeter is \\(95\\) inches, find the length of each of the other sides.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. Find the length of each side of an equilateral triangle with a perimeter of \\(51\\) yards.<\/td>\n<td style=\"width: 50%; height: 14px;\">56. Find the length of each side of an equilateral triangle with a perimeter of \\(54\\) metres.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. The perimeter of an equilateral triangle is \\(18\\) metres. Find the length of each side.<\/td>\n<td style=\"width: 50%; height: 14px;\">58. The perimeter of an equilateral triangle is \\(42\\) miles. Find the length of each side.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">59. The perimeter of an isosceles triangle is \\(42\\) feet. The length of the shortest side is \\(12\\) feet. Find the length of the other two sides.<\/td>\n<td style=\"width: 50%;\">60. The perimeter of an isosceles triangle is \\(83\\) inches. The length of the shortest side is \\(24\\) inches. Find the length of the other two sides.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61. A dish is in the shape of an equilateral triangle. Each side is \\(8\\) inches long. Find the perimeter.<\/td>\n<td style=\"width: 50%;\">62. A floor tile is in the shape of an equilateral triangle. Each side is \\(1.5\\) feet long. Find the perimeter.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">63. A road sign in the shape of an isosceles triangle has a base of \\(36\\) inches. If the perimeter is \\(91\\) inches, find the length of each of the other sides.<\/td>\n<td style=\"width: 50%;\">64. A scarf in the shape of an isosceles triangle has a base of \\(0.75\\) metres. If the perimeter is \\(2\\) metres, find the length of each of the other sides.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. The perimeter of a triangle is \\(39\\) feet. One side of the triangle is \\(1\\) foot longer than the second side. The third side is \\(2\\) feet longer than the second side. Find the length of each side.<\/td>\n<td style=\"width: 50%;\">66. The perimeter of a triangle is \\(35\\) feet. One side of the triangle is \\(5\\) feet longer than the second side. The third side is \\(3\\) feet longer than the second side. Find the length of each side.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">67. One side of a triangle is twice the smallest side. The third side is \\(5\\) feet more than the shortest side. The perimeter is \\(17\\) feet. Find the lengths of all three sides.<\/td>\n<td style=\"width: 50%;\">68. One side of a triangle is three times the smallest side. The third side is \\(3\\) feet more than the shortest side. The perimeter is \\(13\\) feet. Find the lengths of all three sides.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1968347\">Use the Properties of Trapezoids<\/h2>\nIn the following exercises, solve using the properties of trapezoids.\n<table style=\"border-collapse: collapse; width: 100%; height: 176px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">69. The height of a trapezoid is \\(12\\) feet and the bases are \\(9\\) and \\(15\\) feet. What is the area?<\/td>\n<td style=\"width: 50%; height: 30px;\">70. The height of a trapezoid is \\(24\\) yards and the bases are \\(18\\) and \\(30\\) yards. What is the area?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">71. Find the area of a trapezoid with a height of \\(51\\) metres and bases of \\(43\\) and \\(67\\) metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">72. Find the area of a trapezoid with a height of \\(62\\) inches and bases of \\(58\\) and \\(75\\) inches.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">73. The height of a trapezoid is \\(15\\) centimetres and the bases are \\(12.5\\) and \\(18.3\\) centimetres. What is the area?<\/td>\n<td style=\"width: 50%; height: 30px;\">74. The height of a trapezoid is \\(48\\) feet and the bases are \\(38.6\\) and \\(60.2\\) feet. What is the area?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">75. Find the area of a trapezoid with a height of \\(4.2\\) metres and bases of \\(8.1\\) and \\(5.5\\) metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">76. Find the area of a trapezoid with a height of \\(32.5\\) centimetres and bases of \\(54.6\\) and \\(41.4\\) centimetres.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">77. Laurel is making a banner shaped like a trapezoid. The height of the banner is \\(3\\) feet and the bases are \\(4\\) and \\(5\\) feet. What is the area of the banner?<\/td>\n<td style=\"width: 50%; height: 14px;\">78. Niko wants to tile the floor of his bathroom. The floor is shaped like a trapezoid with width \\(5\\) feet and lengths \\(5\\) feet and \\(8\\) feet. What is the area of the floor?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">79. Theresa needs a new top for her kitchen counter. The counter is shaped like a trapezoid with width \\(18.5\\) inches and lengths \\(62\\) and \\(50\\) inches. What is the area of the counter?<\/td>\n<td style=\"width: 50%; height: 14px;\">80. Elena is knitting a scarf. The scarf will be shaped like a trapezoid with width \\(8\\) inches and lengths \\(48.2\\) inches and \\(56.2\\) inches. What is the area of the scarf?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%; height: 200px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 110px;\">\n<td style=\"width: 50%; height: 110px;\">81.<strong data-effect=\"bold\"> Fence<\/strong> Jose just removed the children\u2019s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a \\(50\\) foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be \\(10\\) feet. How long can he make the other side if he wants to use the entire roll of fence?<\/td>\n<td style=\"width: 50%; height: 110px;\">82.<strong data-effect=\"bold\"> Gardening<\/strong> Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take \\(48\\) feet of fencing to enclose the garden. Find the length and width of her garden.<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 50%; height: 62px;\">83.<strong data-effect=\"bold\"> Fence<\/strong> Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are \\(6\\) feet, \\(8\\) feet, and \\(10\\) feet. The fence costs \\(\\$10\\) per foot. How much will it cost for Christa to fence in her flowerbed?<\/td>\n<td style=\"width: 50%; height: 62px;\">\n<p id=\"fs-id1171505792377\">84.<strong data-effect=\"bold\"> Painting<\/strong> Caleb wants to paint one wall of his attic. The wall is shaped like a trapezoid with height \\(8\\) feet and bases \\(20\\) feet and \\(12\\) feet. The cost of the painting one square foot of wall is about \\(?0.05\\). About how much will it cost for Caleb to paint the attic wall?<\/p>\n<span id=\"fs-id1171505276350\" data-type=\"media\" data-alt=\"A right trapezoid is shown.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_207_img.jpg\" alt=\"A right trapezoid is shown.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">86. If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171487570514\">87. Look at the two figures.<\/p>\n<span id=\"fs-id2145050\" data-type=\"media\" data-alt=\"A rectangle is shown on the left. It is labeled as 2 by 8. A square is shown on the right. It is labeled as 4 by 4.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_208_img.jpg\" alt=\"A rectangle is shown on the left. It is labeled as 2 by 8. A square is shown on the right. It is labeled as 4 by 4.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171487189484\">a) Which figure looks like it has the larger area? Which looks like it has the larger perimeter?<\/p>\n<p id=\"fs-id1171505279391\">b) Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?<\/p>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171505780908\">88. The length of a rectangle is \\(5\\) feet more than the width. The area is \\(50\\) square feet. Find the length and the width.<\/p>\n<p id=\"fs-id1171488139794\">a) Write the equation you would use to solve the problem.<\/p>\n<p id=\"fs-id1482367\">b) Why can\u2019t you solve this equation with the methods you learned in the previous chapter?<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 350px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. cubic<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. square<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. linear<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">7.\n\na) 10 cm\n\nb) 4 sq. cm<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">9.\n\na) 8 cm\n\nb) 3 sq. cm<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">11.\n\na) 10 cm\n\nb) 5 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">13.\n\na) 260 ft\n\nb) 3825 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">15.\n\na) 58 ft\n\nb) 210 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">17. 24 inches<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. 27 metres<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. 23 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. 7 in., 16 in.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. 17 m, 12 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. 13.5 m, 12.8 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. 25 ft, 50 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. 7 m, 11 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. 26 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. 55 m<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. 35 ft, 45 ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. 76 in., 36 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41. 60 sq. in.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. 25.315 sq. m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45. 0.75 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">47. 8 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">49. 23 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">51. 11 ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">53. 28 cm<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">55. 17 ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">57. 6 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">59. 15 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">61. 24 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">63. 27.5 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">65. 12 ft, 13 ft, 14 ft<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. 3 ft, 6 ft, 8 ft<\/td>\n<td style=\"width: 33.3333%;\">69. 144 sq. ft<\/td>\n<td style=\"width: 33.3333%;\">71. 2805 sq. m<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">73. 231 sq. cm<\/td>\n<td style=\"width: 33.3333%;\">75. 28.56 sq. m<\/td>\n<td style=\"width: 33.3333%;\">77. 13.5 sq. ft<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">79.\u00a01036 sq. in.<\/td>\n<td style=\"width: 33.3333%;\">81. 15 ft<\/td>\n<td style=\"width: 33.3333%;\">83. \\$24<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">85. Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\">87.\u00a0Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cUse Properties of Rectangles, Triangles, and Trapezoids\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Understand linear, square, and cubic measure<\/li>\n<li>Use properties of rectangles<\/li>\n<li>Use properties of triangles<\/li>\n<li>Use properties of trapezoids<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Understand Linear, Square, and Cubic Measure<\/h1>\n<p id=\"fs-id1171505779061\">When you measure your height or the length of a garden hose, you use a ruler or tape measure <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_001\">(Figure.1)<\/a>. A tape measure might remind you of a line\u2014you use it for linear measure, which measures length. Inch, foot, yard, mile, centimetre and metre are units of linear measure.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_001\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">This tape measure measures inches along the top and centimetres along the bottom.<\/div>\n<figure style=\"width: 670px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_09_04_001.jpg\" alt=\"A picture of a portion of a tape measure is shown. The top shows the numbers 1 through 5. The portion from the beginning to the 1 has a red circle and an arrow to a picture from 0 to 1 inch, with 1 sixteenth, 1 eighth, 3 eighths, 1 half, and 3 fourths labeled. Above this, it is labeled \u201cStandard Measures.\u201d The bottom of the tape measure shows the numbers 1 through 10, then 1 and 2. The region from the edge to about 3 and a half has a red circle with an arrow pointing to a picture from 0 to 3.5. It is labeled 0, 1 cm, 1.7 cm, 2.3 cm and 3.5 cm. Above this, it is labeled \u201cMetric (S).\u201d\" width=\"670\" height=\"117\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.1<\/figcaption><\/figure>\n<p id=\"fs-id1467500\">When you want to know how much tile is needed to cover a floor, or the size of a wall to be painted, you need to know the area, a measure of the region needed to cover a surface. Area is measured is square units. We often use square inches, square feet, square centimetres, or square miles to measure area. A square centimetre is a square that is one centimetre (cm) on each side. A square inch is a square that is one inch on each side <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_002\">(Figure.2)<\/a>.<\/p>\n<p>Square measures have sides that are each <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> unit in length.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_002\" class=\"bc-figure figure\">\n<figure style=\"width: 556px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_002.jpg\" alt=\"Two squares are shown. The smaller one has sides labeled 1 cm and is 1 square centimetre. The larger one has sides labeled 1 inch and is 1 square inch.\" width=\"556\" height=\"124\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.2<\/figcaption><\/figure>\n<p id=\"fs-id1100308\"><a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_003\">(Figure.3)<\/a> shows a rectangular rug that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet long by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet wide. Each square is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> foot wide by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> foot long, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> square foot. The rug is made of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> squares. The area of the rug is<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> square feet.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_003\" class=\"bc-figure figure\">\n<div><\/div>\n<figure style=\"width: 212px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_003.jpg\" alt=\"A rectangle is shown. It has 3 squares across and 2 squares down, a total of 6 squares.\" width=\"212\" height=\"142\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 3 The rug contains six squares of 1 square foot each, so the total area of the rug is 6 square feet.<\/figcaption><\/figure>\n<p id=\"fs-id1588170\">When you measure how much it takes to fill a container, such as the amount of gasoline that can fit in a tank, or the amount of medicine in a syringe, you are measuring volume. Volume is measured in cubic units such as cubic inches or cubic centimetres. When measuring the volume of a rectangular solid, you measure how many cubes fill the container. We often use cubic centimetres, cubic inches, and cubic feet. A cubic centimetre is a cube that measures one centimetre on each side, while a cubic inch is a cube that measures one inch on each side <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_004\">(Figure.4)<\/a>.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_004\" class=\"bc-figure figure\">\n<figure style=\"width: 323px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_004.jpg\" alt=\"Two cubes are shown. The smaller one has sides labeled 1 cm and is labeled as 1 cubic centimetre. The larger one has sides labeled 1 inch and is labeled as 1 cubic inch.\" width=\"323\" height=\"253\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 4 Cubic measures have sides that are 1 unit in length.<\/figcaption><\/figure>\n<p id=\"fs-id1054320\">Suppose the cube in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_005\">(Figure.5)<\/a> measures <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches on each side and is cut on the lines shown. How many little cubes does it contain? If we were to take the big cube apart, we would find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7b50e6fd02515483149eb902ea18dfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> little cubes, with each one measuring one inch on all sides. So each little cube has a volume of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> cubic inch, and the volume of the big cube is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7b50e6fd02515483149eb902ea18dfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> cubic inches.<\/p>\n<p>A cube that measures 3 inches on each side is made up of 27 one-inch cubes, or 27 cubic inches.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_005\" class=\"bc-figure figure\">\n<figure style=\"width: 97px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_005.jpg\" alt=\"A cube is shown, comprised of smaller cubes. Each side of the cube has 3 smaller cubes across, for a total of 27 smaller cubes.\" width=\"97\" height=\"81\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.5<\/figcaption><\/figure>\n<\/div>\n<div data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505120904\" data-type=\"problem\">\n<p id=\"fs-id2147044\">For each item, state whether you would use linear, square, or cubic measure:<\/p>\n<p id=\"fs-id1171505279541\">a) amount of carpeting needed in a room<\/p>\n<p id=\"fs-id1171505781802\">b) extension cord length<\/p>\n<p id=\"fs-id1600939\">c) amount of sand in a sandbox<\/p>\n<p id=\"fs-id962051\">d) length of a curtain rod<\/p>\n<p id=\"fs-id2166824\">e) amount of flour in a canister<\/p>\n<p id=\"fs-id1161888\">f) size of the roof of a doghouse.<\/p>\n<\/div>\n<div id=\"fs-id1447944\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-104\" class=\"unnumbered unstyled\" summary=\"...\" data-label=\"\">\n<tbody>\n<tr>\n<td>a) You are measuring how much surface the carpet covers, which is the area.<\/td>\n<td>square measure<\/td>\n<\/tr>\n<tr>\n<td>b) You are measuring how long the extension cord is, which is the length.<\/td>\n<td>linear measure<\/td>\n<\/tr>\n<tr>\n<td>c) You are measuring the volume of the sand.<\/td>\n<td>cubic measure<\/td>\n<\/tr>\n<tr>\n<td>d) You are measuring the length of the curtain rod.<\/td>\n<td>linear measure<\/td>\n<\/tr>\n<tr>\n<td>e) You are measuring the volume of the flour.<\/td>\n<td>cubic measure<\/td>\n<\/tr>\n<tr>\n<td>f) You are measuring the area of the roof.<\/td>\n<td>square measure<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1481876\" data-type=\"problem\">\n<p id=\"fs-id1935428\">Determine whether you would use linear, square, or cubic measure for each item.<\/p>\n<p id=\"fs-id1954512\">a) amount of paint in a can b) height of a tree c) floor of your bedroom d) diametre of bike wheel e) size of a piece of sod f) amount of water in a swimming pool<\/p>\n<\/div>\n<div id=\"fs-id1807421\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168467254475\" class=\"circled\" type=\"a\">\n<li>cubic<\/li>\n<li>linear<\/li>\n<li>square<\/li>\n<li>linear<\/li>\n<li>square<\/li>\n<li>cubic<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171505547635\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1772635\" data-type=\"exercise\">\n<div id=\"fs-id1807421\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171513624342\" data-type=\"problem\">\n<p id=\"fs-id1362401\">Determine whether you would use linear, square, or cubic measure for each item.<\/p>\n<p id=\"fs-id1895627\">a) volume of a packing box b) size of patio c) amount of medicine in a syringe d) length of a piece of yarn e) size of housing lot f) height of a flagpole<\/p>\n<\/div>\n<div id=\"fs-id1161229\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168468780837\" class=\"circled\" type=\"a\">\n<li>cubic<\/li>\n<li>square<\/li>\n<li>cubic<\/li>\n<li>linear<\/li>\n<li>square<\/li>\n<li>linear<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1171505778736\">Many geometry applications will involve finding the perimeter or the area of a figure. There are also many applications of perimeter and area in everyday life, so it is important to make sure you understand what they each mean.<\/p>\n<p id=\"fs-id958752\">Picture a room that needs new floor tiles. The tiles come in squares that are a foot on each side\u2014one square foot. How many of those squares are needed to cover the floor? This is the area of the floor.<\/p>\n<p id=\"fs-id1171511544941\">Next, think about putting new baseboard around the room, once the tiles have been laid. To figure out how many strips are needed, you must know the distance around the room. You would use a tape measure to measure the number of feet around the room. This distance is the perimeter.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Perimeter and Area<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1858719\">The perimeter is a measure of the distance around a figure.<\/p>\n<p id=\"fs-id1171499420654\">The area is a measure of the surface covered by a figure.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1922361\"><a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_006\">(Figure. 6)<\/a> shows a square tile that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> inch on each side. If an ant walked around the edge of the tile, it would walk <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> inches. This distance is the perimeter of the tile.<\/p>\n<p id=\"fs-id1171488172599\">Since the tile is a square that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> inch on each side, its area is one square inch. The area of a shape is measured by determining how many square units cover the shape.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6192de45f38c25e3e88a4a9f8d952ea6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#101;&#114;&#105;&#109;&#101;&#116;&#101;&#114;&#125;&#61;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#110;&#99;&#104;&#101;&#115;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#114;&#101;&#97;&#125;&#61;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#113;&#117;&#97;&#114;&#101;&#32;&#105;&#110;&#99;&#104;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"161\" style=\"vertical-align: -14px;\" \/><\/p>\n<div id=\"CNX_BMath_Figure_09_04_006\" class=\"bc-figure figure\">\n<figure style=\"width: 229px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_006.jpg\" alt=\"A 5 square by 5 square checkerboard is shown with each side labeled 1 inch. An image of an ant is shown on the top left square.\" width=\"229\" height=\"178\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure 6 When the ant walks completely around the tile on its edge, it is tracing the perimeter of the tile. The area of the tile is 1 square inch.<\/figcaption><\/figure>\n<div data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1490358\" data-type=\"problem\">\n<p id=\"fs-id1594194\">Each of two square tiles is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> square inch. Two tiles are shown together.<\/p>\n<p id=\"fs-id1877892\">a) What is the perimeter of the figure?<\/p>\n<p id=\"fs-id1711457\">b) What is the area?<\/p>\n<p><span id=\"fs-id1879440\" data-type=\"media\" data-alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_007.jpg\" alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id2110859\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1327911\">a) The perimeter is the distance around the figure. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches.<\/p>\n<p id=\"fs-id1690172\">b) The area is the surface covered by the figure. There are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> square inch tiles so the area is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> square inches.<\/p>\n<p><span id=\"fs-id1171505480664\" data-type=\"media\" data-alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side. The top and bottom each have two adjacent 1 inch labels across, the sides have 1 inch labels.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_008.jpg\" alt=\"A checkerboard is shown. It has 10 squares across the top and 5 down the side. The top and bottom each have two adjacent 1 inch labels across, the sides have 1 inch labels.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487500930\" data-type=\"problem\">\n<p id=\"fs-id1044430\">Find the a) perimeter and b) area of the figure:<\/p>\n<p><span data-type=\"media\" data-alt=\"A rectangle is shown comprised of 3 squares.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_009_img.jpg\" alt=\"A rectangle is shown comprised of 3 squares.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168469834117\" class=\"circled\" type=\"a\">\n<li>8 inches<\/li>\n<li>3 sq. inches<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1915814\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1931650\" data-type=\"exercise\">\n<div id=\"fs-id1171487500930\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1875231\" data-type=\"problem\">\n<p id=\"fs-id974965\">Find the a) perimeter and b) area of the figure:<\/p>\n<p><span id=\"fs-id1171513624489\" data-type=\"media\" data-alt=\"A square is shown comprised of 4 smaller squares.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_010_img.jpg\" alt=\"A square is shown comprised of 4 smaller squares.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1171498004127\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168468326099\" class=\"circled\" type=\"a\">\n<li>8 centimetres<\/li>\n<li>4 sq. centimetres<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use the Properties of Rectangles<\/h1>\n<p id=\"fs-id1556861\">A rectangle has four sides and four right angles. The opposite sides of a rectangle are the same length. We refer to one side of the rectangle as the length, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>, and the adjacent side as the width, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4caed22919a1780df1b6310b338b904e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_012\">(Figure.7)<\/a>.<\/p>\n<p>A rectangle has four sides, and four right angles. The sides are labeled L for length and W for width.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_012\" class=\"bc-figure figure\">\n<figure style=\"width: 189px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_012.jpg\" alt=\"A rectangle is shown. Each angle is marked with a square. The top and bottom are labeled L, the sides are labeled W.\" width=\"189\" height=\"123\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.7<\/figcaption><\/figure>\n<p id=\"fs-id1171505275854\">The perimeter, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, of the rectangle is the distance around the rectangle. If you started at one corner and walked around the rectangle, you would walk <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-19b5e1ec9b734d1f5b7d80a5ad911fd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;&#43;&#87;&#43;&#76;&#43;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"127\" style=\"vertical-align: -2px;\" \/> units, or two lengths and two widths. The perimeter then is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f916ea5a35c31f93efd72ec87a39ac05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#80;&#61;&#76;&#43;&#87;&#43;&#76;&#43;&#87;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#114;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#80;&#61;&#50;&#76;&#43;&#50;&#87;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"165\" style=\"vertical-align: -24px;\" \/><\/p>\n<p id=\"fs-id1753081\">What about the area of a rectangle? Remember the rectangular rug from the beginning of this section. It was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet long by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet wide, and its area was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> square feet. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_013\">(Figure.8)<\/a>. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e34735f665d1c170260bfb124efc027f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"68\" style=\"vertical-align: 0px;\" \/>, we see that the area, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/>, is the length, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>, times the width, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4caed22919a1780df1b6310b338b904e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>, so the area of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c142b3dc533df153f0e13657f12c7f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#76;&#92;&#99;&#100;&#111;&#116;&#32;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"81\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p>The area of this rectangular rug is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> square feet, its length times its width.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_013\" class=\"bc-figure figure\">\n<figure style=\"width: 241px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_013.jpg\" alt=\"A rectangle is shown. It is made up of 6 squares. The bottom is 2 squares across and marked as 2, the side is 3 squares long and marked as 3.\" width=\"241\" height=\"178\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.8<\/figcaption><\/figure>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Rectangles<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1171497076758\" data-bullet-style=\"bullet\">\n<li>Rectangles have four sides and four right <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7f59684a5fb9bbd4ebb9b2323f0aa17f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"30\" style=\"vertical-align: -5px;\" \/>\u00b0 angles.<\/li>\n<li>The lengths of opposite sides are equal.<\/li>\n<li>The perimeter, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, of a rectangle is the sum of twice the length and twice the width. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_012\">(Figure 8)<\/a>.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd41d005b7610a456dc9e5dc6ad9fd67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#76;&#43;&#50;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -2px;\" \/><\/li>\n<\/ul>\n<ul>\n<li>The area, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/>, of a rectangle is the length times the width.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c142b3dc533df153f0e13657f12c7f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#76;&#92;&#99;&#100;&#111;&#116;&#32;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"81\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1908419\">For easy reference as we work the examples in this section, we will state the Problem Solving Strategy for Geometry Applications here.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Use a Problem Solving Strategy for Geometry Applications<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1170325029073\" class=\"stepwise\" type=\"1\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1558949\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1549060\" data-type=\"exercise\">\n<div id=\"fs-id1931478\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1764703\" data-type=\"problem\">\n<p id=\"fs-id1171507005201\">The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> metres and the width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres. Find a) the perimeter, and b) the area.<\/p>\n<\/div>\n<div id=\"fs-id1171498003823\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468455627\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. There is an image of a rectangle. The top and bottom are labeled 32 m and the sides are labeled 20 m. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe perimeter of a rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cLet P equal the perimeter.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W, then P equals 2 times 32 plus 2 times 20. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is P equals 64 plus 40, then P equals 104. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P followed by an equal sign with a question mark, then 104. Then 20 plus 32 plus 20 plus 32 followed by an equal sign with a question mark, then 104. Then 104 equals 104. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe perimeter of the rectangle is 104 metres.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468395600\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the perimeter of a rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">P<\/em> = the perimeter<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><span id=\"eip-id1168467174763\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168469507351\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_067_img_MW-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The perimeter of the rectangle is 104 metres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467114806\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. There is an image of a rectangle. The top and bottom are labeled 32 m and the sides are labeled 20 m. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cLet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals L times W, then A equals 32 m times 20 m. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals 640. Step 6 says, \u201cCheck,\u201d in bold. Beside this is A followed by an equal sign with a question mark, then 640. Then 32 times 20 followed by an equal sign with a question mark, then 640. Then 640 equals 640, followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe area of the rectangle is 640 square metres.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468499149\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of a rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">A<\/em> = the area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><span id=\"eip-id1168468460104\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168469785286\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_068_img_MW-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The area of the rectangle is 60 square metres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1931478\" data-type=\"problem\">\n<p id=\"fs-id1602689\">The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-454fa4f8a22c90ab5a5245afd540f8f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> yards and the width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> yards. Find a) the perimeter and b) the area.<\/p>\n<\/div>\n<div id=\"fs-id1786251\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168467174146\" class=\"circled\" type=\"a\">\n<li>340 yd<\/li>\n<li>6000 sq. yd<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1786251\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171511544945\" data-type=\"problem\">\n<p id=\"fs-id1904165\">The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e608b19de1bcf92fa9559aac92a66de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet and the width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f11c6e846ac2fe8cea2c6e472ea6458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet. Find a) the perimeter and b) the area.<\/p>\n<\/div>\n<div id=\"fs-id1562413\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168469773073\" class=\"circled\" type=\"a\">\n<li>220 ft<\/li>\n<li>2976 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1564306\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1507197\" data-type=\"exercise\">\n<div id=\"fs-id1562413\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505275626\" data-type=\"problem\">\n<p id=\"fs-id1489861\">Find the length of a rectangle with perimeter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches and width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id1717808\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469470101\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. There is an image of a rectangle. The top and bottom are labeled L and the sides are labeled 10 in. Below the rectangle is P equals 50 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length of the rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cLet L equal the length.\u201d Step 4 says, \u201cTranslate. Write the formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W. Below P is 50 in, below 2L is 2L, and below 2W is 2 times 10 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 50 minus a red 20 equals 2L plus 20 minus a red 20, then 30 equals 2L with both sides over a red 2, then 15 equals L. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals 50, then 15 plus 10 plus 15 plus 10 followed by an equal sign with a question mark, then 500. Then 50 equals 50, followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length is 15 inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469784173\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length of the rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">L<\/em> = the length<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><span id=\"eip-id1168466229487\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168466483065\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_069_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length is 15 inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1392754\" data-type=\"problem\">\n<p id=\"fs-id1580362\">Find the length of a rectangle with a perimeter of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85d2fe3dc632ffa22ca593406cbf160d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches and width of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd40a7f142c1fc4152e724db5432f76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id1776151\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1934174\">15 in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1478584\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1548995\" data-type=\"exercise\">\n<div id=\"fs-id1776151\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505482456\" data-type=\"problem\">\n<p id=\"fs-id1747478\">Find the length of a rectangle with a perimeter of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> yards and width of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> yards.<\/p>\n<\/div>\n<div id=\"fs-id1406132\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171498421216\">9 yd<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1394303\">In the next example, the width is defined in terms of the length. We\u2019ll wait to draw the figure until we write an expression for the width so that we can label one side with that expression.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1954612\" data-type=\"problem\">\n<p id=\"fs-id1862284\">The width of a rectangle is two inches less than the length. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30352d66e4a511eedaaaf1c7497a30c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1550204\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466427903\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem.\u201d The word \u201cread\u201d is in bold. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length and width of the rectangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cSince the width is defined in terms of the length, we let L equal length. The width is two feet less than the length, so we let L minus 2 equal width. Now we can draw a figure using these expressions for the length and width.\u201d An image of a rectangle is shown. The top and bottom are labeled L minus 2, the sides are labeled L. Beneath the rectangle is P equals 52 in. Step 4 says, \u201cTranslate. Write the appropriate formula. The formula for the perimeter of a rectangle relates all the information. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W. Below that is 52 equals 2L plus 2 times L minus 2. Step 5 says, \u201cSolve the equation. Combine like terms. Add 4 to each side. Divide by 4.\u201d The word \u201csolve\u201d is in bold. Beside this is 52 equals 2L plus 2L minus 4, then 52 equals 4L minus 4, then 56 equals 4L, then 56 over 4 equals 4L over 4, then 14 equals L. The length is 14 inches. The next part reads, \u201cNow we need to find the width. The width is L minus 2.\u201d Beside this is L minus 2, then a red 14 minus 2, then 12. The width is 12 inches. Step 6 says, \u201cCheck,\u201d in bold. Beside this is \u201csince 14 plus 12 plus 14 plus 12 equals 52, this works!\u201d Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length is 14 inches and the width is 12 inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width of the rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/p>\n<p>Now we can draw a figure using these expressions for the length and width.<\/td>\n<td>Since the width is defined in terms of the length, we let <em data-effect=\"italics\">L<\/em> = length. The width is two feet less that the length, so we let <em data-effect=\"italics\">L<\/em> \u2212 2 = width<br \/>\n<span id=\"eip-id1168466319758\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_070_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula. The formula for the perimeter of a rectangle relates all the information.<br \/>\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168466644630\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_070_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70584946b31b45f5172bf4ef822e70b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;&#61;&#50;&#76;&#43;&#50;&#76;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"136\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cecdfa000c544b8deafa3586e29bf1b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;&#61;&#52;&#76;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"93\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add 4 to each side.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-219551089c8af812d997365d7801dc7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;&#61;&#52;&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide by 4.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8c04a24df60ff5c8afcb247b82c67063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#54;&#125;&#123;&#52;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#76;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-685f140d79a23e8493789ed30518ac1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#61;&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The length is 14 inches.<\/td>\n<\/tr>\n<tr>\n<td>Now we need to find the width.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The width is <em data-effect=\"italics\">L<\/em> \u2212 2.<\/td>\n<td data-align=\"left\"><span id=\"eip-id1168466200890\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_070_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\nThe width is 12 inches.<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><br \/>\nSince <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ab4887185848f4fb46e54f1351c6cc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#43;&#49;&#50;&#43;&#49;&#52;&#43;&#49;&#50;&#61;&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"176\" style=\"vertical-align: -2px;\" \/>, this works!<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length is 14 feet and the width is 12 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1932001\" data-type=\"problem\">\n<p id=\"fs-id1863871\">The width of a rectangle is seven metres less than the length. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c04d88fcf64566a852d0a051ac00e70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1805128\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1377421\">18 m, 11 m<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171512117622\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1684704\" data-type=\"exercise\">\n<div id=\"fs-id1932001\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2052069\" data-type=\"problem\">\n<p id=\"fs-id1915314\">The length of a rectangle is eight feet more than the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7029ea134aa43ac5ffd9f780e196307d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1171497978496\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171487568509\">11 ft , 19 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1932001\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1414483\">The length of a rectangle is four centimetres more than twice the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22882aef9be2977d31de3bdcd09db94c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> centimetres. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1171487493999\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468670350\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem.\u201d The word \u201cread\u201d is in bold. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length and the width.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet w equal width. The length is four more than twice the width. 2w plus 4 equals length.\u201d An image of a rectangle is shown. The top and bottom are labeled 2W plus 4, the sides are labeled W. Beneath the rectangle is P equals 32 cm. Step 4 says, \u201cTranslate. Write the appropriate formula and substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W. Below that is 32 equals 2 times 2W plus 4 plus 2W. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 32 equals 4W plus 8 plus 2W, then 32 equals 6W plus 8, then 24 equals 6W, then 4 equals W width, then 2W plus 4 length, then 2 times a red 4 plus 4, then 12, followed by \u201cThe length is 12 cm.\u201d Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals 2L plus 2W, then 32 followed by an equal sign with a question mark, then 2 times 12 plus 2 times 4, then 32 equals 32 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length is 12 cm and the width is 4 cm.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">W<\/em> = width<br \/>\nThe length is four more than twice the width.<br \/>\n2<em data-effect=\"italics\">w<\/em> + 4 = length<br \/>\n<span id=\"eip-id1168468261144\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula and substitute in the given information.<\/td>\n<td><span id=\"eip-id1168467318309\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164271792878\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_071_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length is 12 cm and the width is 4 cm.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1805128\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1929348\" data-type=\"problem\">\n<p id=\"fs-id1668277\">The length of a rectangle is eight more than twice the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de25eb06760758d2c59eb63fca270413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1171487568155\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1535645\">8 ft, 24 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1532320\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1715140\" data-type=\"exercise\">\n<div id=\"fs-id1171487568155\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1915022\" data-type=\"problem\">\n<p id=\"fs-id1776454\">The width of a rectangle is six less than twice the length. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1759344\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171505974580\">5 cm, 4 cm<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1673589\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id907273\" data-type=\"exercise\">\n<div id=\"fs-id1759344\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547656\" data-type=\"problem\">\n<p id=\"fs-id1901758\">The area of a rectangular room is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a50dc763c28880470e0beb1ebdb119a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> square feet. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet. What is the width?<\/p>\n<\/div>\n<div id=\"fs-id1171487189498\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466072798\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a rectangle. The bottom is labeled 14 ft. and the side is labeled W. Beside the rectangle is Area equals 168 ft. squared. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe width of a rectangular room.\u201d Step 3 says, \u201cName. Choose a variable to represent the width.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet w equal width.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula and substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals LW followed by 168 equals 14 times W. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 168 over 14 equals 14W over 14, then 12 equals W.\u201d Step 6 says, \u201cCheck,\u201d in bold. Beside this is A equals LW, then 168 followed by an equal sign with a question mark, then 14 times 12. Below this is 168 equals 168 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe width of the room is 12 feet.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem.<\/td>\n<td><span id=\"eip-id1168466262188\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the width of a rectangular room<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">W<\/em> = width<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula and substitute in the given information.<\/td>\n<td><span id=\"eip-id1164270730310\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164270730332\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_083_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The width of the room is 12 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1257520\" data-type=\"problem\">\n<p>The area of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22f4cdcb94ef0166337b09771c21d8fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#57;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\" \/> square feet. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e554ca92166de4bd98acfbef8f678cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet. What is the width?<\/p>\n<\/div>\n<div id=\"fs-id1593194\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1685301\">26 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1471916\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171512117693\" data-type=\"exercise\">\n<div id=\"fs-id1257520\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1394027\" data-type=\"problem\">\n<p id=\"fs-id1171505779962\">The width of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b44aa122f73c22d86f2d764af01f919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> metres. The area is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f30cefb4e3914c561cf75e0a1f0ee660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/> square metres. What is the length?<\/p>\n<\/div>\n<div id=\"fs-id1715331\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1550525\">29 m<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1593194\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487569847\" data-type=\"problem\">\n<p id=\"fs-id1171487569639\">The perimeter of a rectangular swimming pool is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-74a92b6c533b233c6f544c969f0e81fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: -1px;\" \/> feet. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet more than the width. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1586798\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469520954\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a rectangle. The sides are labeled w and the top and bottom are labeled w plus 15. Below the rectangle is P equals 150 ft. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length and width of the pool.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet w equal width.\u201d Then, \u201cthe length is 15 feet more than the width,\u201d and w plus 15 equals length. Step 4 says, \u201cTranslate. Write the appropriate formula and substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals 2L plus 2W, then 150 ft. equals 2 times w plus 15 ft. plus 2W. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 150 equals 2W plus 30 plus 2W, then 150 equals 4W plus 30, then 120 equals 4W. Below this is 30 equals W the width of the pool. Next is W plus 15 length of the pool, followed by a red 30 plus 15, then 45. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals 2L plus 2W, then 150 followed by an equal sign with a question mark, then 2 times 45 plus 2 times 30. Below this is 150 equals 150 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe length of the pool is 45 feet and the width of the pool is 30 feet.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469562861\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072.img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width of the pool<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<br \/>\nThe length is 15 feet more than the width.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-814c047f0331200a35d71aac0d390cd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#105;&#100;&#116;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"88\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a928bc07f8503337a0c90dad29e0144c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;&#43;&#49;&#53;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#110;&#103;&#116;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"131\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula and substitute.<\/td>\n<td><span id=\"eip-id1168466467969\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1168466463591\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_072_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The length of the pool is 45 feet and the width is 30 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104048697\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1715331\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487565544\" data-type=\"problem\">\n<p id=\"fs-id1171487566798\">The perimeter of a rectangular swimming pool is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-150ffdc5b0bfec3eb42a9f6ea45a11e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/> feet. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-89bc2c119dcafc9b555c6b2841530d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet more than the width. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1527584\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1837003\">30 ft, 70 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1772056\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2239997\" data-type=\"exercise\">\n<div id=\"fs-id1171487565544\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id962062\" data-type=\"problem\">\n<p id=\"fs-id1765272\">The length of a rectangular garden is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> yards more than the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd1f95d8d580ca7e0a22581555ffd7b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/> yards. Find the length and width.<\/p>\n<\/div>\n<div id=\"fs-id1559124\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>60 yd, 90 yd<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use the Properties of Triangles<\/h1>\n<p id=\"fs-id1571656\">We now know how to find the area of a rectangle. We can use this fact to help us visualize the formula for the area of a triangle. In the rectangle in <a class=\"autogenerated-content\" href=\"#fs-id1901874\">(Figure.9)<\/a>, we\u2019ve labeled the length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and the width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>, so it\u2019s area is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8a9e1c9d57f61d255b2410c13baad5cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p>The area of a rectangle is the base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, times the height, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_035\" class=\"bc-figure figure\">\n<figure style=\"width: 151px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_035.jpg\" alt=\"A rectangle is shown. The side is labeled h and the bottom is labeled b. The centre says A equals bh.\" width=\"151\" height=\"89\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.9<\/figcaption><\/figure>\n<p id=\"fs-id1171505624044\">We can divide this rectangle into two congruent triangles <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_036\">(Figure.10)<\/a>. Triangles that are congruent have identical side lengths and angles, and so their areas are equal. The area of each triangle is one-half the area of the rectangle, or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c65f514d7fad4f3e5b7763e8019b4e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"27\" style=\"vertical-align: -6px;\" \/>. This example helps us see why the formula for the area of a triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b372c8f17c232fb83c5e06a24bf6fd73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p>A rectangle can be divided into two triangles of equal area. The area of each triangle is one-half the area of the rectangle.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_036\" class=\"bc-figure figure\">\n<figure style=\"width: 323px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_036.jpg\" alt=\"A rectangle is shown. A diagonal line is drawn from the upper left corner to the bottom right corner. The side of the rectangle is labeled h and the bottom is labeled b. Each triangle says one-half bh. To the right of the rectangle, it says \u201cArea of each triangle,\u201d and shows the equation A equals one-half bh.\" width=\"323\" height=\"107\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.10<\/figcaption><\/figure>\n<p id=\"fs-id1171505925447\">The formula for the area of a triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b372c8f17c232fb83c5e06a24bf6fd73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> is the base and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> is the height.<\/p>\n<p id=\"fs-id1486748\">To find the area of the triangle, you need to know its base and height. The base is the length of one side of the triangle, usually the side at the bottom. The height is the length of the line that connects the base to the opposite vertex, and makes a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc16a99348931a3823eff3764a961940_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>\u00b0 angle with the base. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_037\">(Figure.11)<\/a> shows three triangles with the base and height of each marked.<\/p>\n<p>The height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> of a triangle is the length of a line segment that connects the the base to the opposite vertex and makes a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dc16a99348931a3823eff3764a961940_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/>\u00b0 angle with the base.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_037\" class=\"bc-figure figure\">\n<figure style=\"width: 563px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_037.jpg\" alt=\"Three triangles are shown. The triangle on the left is a right triangle. The bottom is labeled b and the side is labeled h. The middle triangle is an acute triangle. The bottom is labeled b. There is a dotted line from the top vertex to the base of the triangle, forming a right angle with the base. That line is labeled h. The triangle on the right is an obtuse triangle. The bottom of the triangle is labeled b. The base has a dotted line extended out and forms a right angle with a dotted line to the top of the triangle. The vertical line is labeled h.\" width=\"563\" height=\"107\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.11<\/figcaption><\/figure>\n<div id=\"fs-id1802095\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Triangle Properties<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1752354\">For any triangle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23f00feef91cb9ba3057f9e15d82ff39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#65;&#66;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/>, the sum of the measures of the angles is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1371cfb17a414d739b40e633931613a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/>\u00b0.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-88e2dad49ec6bc160c882e0577bbcf78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#65;&#43;&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#66;&#43;&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#67;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#56;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"221\" style=\"vertical-align: -2px;\" \/>\u00b0<\/p>\n<p id=\"fs-id1928592\">The perimeter of a triangle is the sum of the lengths of the sides.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4abea6f02f4ab78a43a4d9118ea2b19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/p>\n<p>The area of a triangle is one-half the base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, times the height, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7226ce5bb8385dfb537ea25d92656ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"67\" style=\"vertical-align: -6px;\" \/><\/p>\n<p><span id=\"fs-id1930696\" data-type=\"media\" data-alt=\"A triangle is shown. The vertices are labeled A, B, and C. The sides are labeled a, b, and c. There is a vertical dotted line from vertex B at the top of the triangle to the base of the triangle, meeting the base at a right angle. The dotted line is labeled h.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_038_img.jpg\" alt=\"A triangle is shown. The vertices are labeled A, B, and C. The sides are labeled a, b, and c. There is a vertical dotted line from vertex B at the top of the triangle to the base of the triangle, meeting the base at a right angle. The dotted line is labeled h.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1602784\" data-type=\"problem\">\n<p id=\"fs-id1799270\">Find the area of a triangle whose base is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba90047eec6a05e400b16dfb86d7f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> inches and whose height is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id1418466\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468457178\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a triangle. The base of the triangle is labeled 11 in and the height of the triangle is labeled 8 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of the triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal area of the triangle.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times b times h. Below this is A equals one-half times 11 in. times 8 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals 44 square inches. Step 6 says, \u201cCheck,\u201d in bold. Beside this is A equals one-half bh, then 44 followed by an equal sign with a question mark, then one-half times 11 times 8, then 44 equals 44 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe area is 44 square inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468388397\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of the triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">A<\/em> = area of the triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><span id=\"eip-id1168468357737\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272169003\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_073_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The area is 44 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171488156140\" data-type=\"problem\">\n<p id=\"fs-id1171498388066\">Find the area of a triangle with base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-837d0d6b05c238eddf106b68ec9dcfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id1748718\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1498105\">13 sq. in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1924824\" data-type=\"problem\">\n<p id=\"fs-id1171496946102\">Find the area of a triangle with base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id1171487146402\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1882186\">49 sq. in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id16795130\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1423184\" data-type=\"exercise\">\n<div id=\"fs-id1171488156140\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1562031\" data-type=\"problem\">\n<p id=\"fs-id1559945\">The perimeter of a triangular garden is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet. The lengths of two sides are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet. How long is the third side?<\/p>\n<\/div>\n<div id=\"fs-id1171487511856\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466081900\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a triangle. The sides of the triangle are labeled 4 ft., 9 ft., and c. Below the triangle is P equals 24 ft. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201clength of the third side of the triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet c equal the third side.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals a plus b plus c. Below this is 24 ft. equals 4 ft. plus 9 ft. plus c. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 24 equals 13 plus c, then 11 equals c. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals a plus b plus c, then 24 followed by an equal sign with a question mark, then 4 plus 9 plus 11, then 24 equals 24 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe third side is 11 ft. long.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469745372\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>length of the third side of a triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">c<\/em> = the third side<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168466112852\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272066645\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_074_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The third side is 11 feet long.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1748718\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id972955\" data-type=\"problem\">\n<p id=\"fs-id1481576\">The perimeter of a triangular garden is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet. The lengths of two sides are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01cb55a185cee9b8f0aa311ce70a4b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet. How long is the third side?<\/p>\n<\/div>\n<div id=\"fs-id1656452\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171505940975\">8 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171505481383\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1790476\" data-type=\"exercise\">\n<div id=\"fs-id972955\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1547798\" data-type=\"problem\">\n<p id=\"fs-id1171506186890\">The lengths of two sides of a triangular window are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet. How long is the third side?<\/p>\n<\/div>\n<div id=\"fs-id1171498403869\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1793391\">6 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1656452\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1915793\" data-type=\"problem\">\n<p id=\"fs-id1712158\">The area of a triangular church window is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b5f1c3a0e1ca514e4e63519e4d0c016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> square metres. The base of the window is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> metres. What is the window\u2019s height?<\/p>\n<\/div>\n<div id=\"fs-id1376811\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467155173\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a triangle. The base of the triangle is labeled 15 m and the height of the triangle is labeled h. Below the triangle is A equals 90 m squared. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cheight of a triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet h equal the height.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times b times h. Below this is 90 m squared equals one-half times 15 m times h. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 90 equals 15 over 2 times h, then 12 equals h. Step 6 says, \u201cCheck,\u201d in bold. Beside this is A equals one-half bh, then 90 followed by an equal sign with a question mark, then one-half times 15 times 12, then 90 equals 90 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe height of the triangle is 12 metres.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468303076\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>height of a triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">h<\/em> = the height<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168468653388\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164271013482\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_075_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The height of the triangle is 12 metres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1435066\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1448113\" data-type=\"exercise\">\n<div id=\"fs-id1171498403869\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1914206\" data-type=\"problem\">\n<p id=\"fs-id1481654\">The area of a triangular painting is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d56c7a77e8b254cd18ace0d2874456b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> square inches. The base is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches. What is the height?<\/p>\n<\/div>\n<div id=\"fs-id1778473\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1328179\">14 in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171506203651\" data-type=\"problem\">\n<p id=\"fs-id1711674\">A triangular tent door has an area of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> square feet. The height is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet. What is the base?<\/p>\n<\/div>\n<div id=\"fs-id1545334\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1587349\">6 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Isosceles and Equilateral Triangles<\/h1>\n<p id=\"fs-id1482074\">Besides the right triangle, some other triangles have special names. A triangle with two sides of equal length is called an isosceles triangle. A triangle that has three sides of equal length is called an equilateral triangle. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_045\">(Figure.12)<\/a> shows both types of triangles.<\/p>\n<p>In an isosceles triangle, two sides have the same length, and the third side is the base. In an equilateral triangle, all three sides have the same length.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_045\" class=\"bc-figure figure\">\n<figure style=\"width: 367px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_045.jpg\" alt=\"Two triangles are shown. All three sides of the triangle on the left are labeled s. It is labeled \u201cequilateral triangle\u201d. Two sides of the triangle on the right are labeled s. It is labeled \u201cisosceles triangle\u201d.\" width=\"367\" height=\"231\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.12<\/figcaption><\/figure>\n<div id=\"fs-id1662237\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Isosceles and Equilateral Triangles<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id2037850\">An <strong data-effect=\"bold\">isosceles<\/strong> triangle has two sides the same length.<\/p>\n<p>An <strong data-effect=\"bold\">equilateral<\/strong> triangle has three sides of equal length.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"title\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1888433\" data-type=\"problem\">\n<p id=\"fs-id1171505548057\">The perimeter of an equilateral triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7d4f86f5d9fad5ef5c0c16ea6db8147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches. Find the length of each side.<\/p>\n<\/div>\n<div id=\"fs-id1549131\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468574026\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of an equilateral triangle. Each side of the triangle is labeled s. Below the triangle is Perimeter equals 93 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe length of the sides of an equilateral triangle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet s equal length of each side.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals a plus b plus c. Below this is 93 in equals s plus s plus s. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 93 equals 3s, then 31 equals s. Step 6 says, \u201cCheck,\u201d in bold. Beside this is an image of an equilateral triangle. Each side is labeled 31. Below the triangle is 93 followed by an equal sign with a question mark, then 31 plus 31 plus 31, then 93 equals 93 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cEach side is 31 inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468738268\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\nPerimeter = 93 in.<\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>length of the sides of an equilateral triangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">s<\/em> = length of each side<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><span id=\"eip-id1168468576504\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272060705\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_076_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>Each side is 31 inches<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1530946\" data-type=\"problem\">\n<p id=\"fs-id1171506666626\">Find the length of each side of an equilateral triangle with perimeter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3db773b3fb1c245f782b7a601d70917_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id1595728\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171488073207\">13 in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1937636\" data-type=\"problem\">\n<p id=\"fs-id1786746\">Find the length of each side of an equilateral triangle with perimeter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-deb4bebaec9fe47ccd035848be13a879_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres.<\/p>\n<\/div>\n<div id=\"fs-id1501535\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1798725\">17 cm<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1786620\" data-type=\"exercise\">\n<div id=\"fs-id1530946\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2167088\" data-type=\"problem\">\n<p id=\"fs-id1171498011638\">Arianna has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e22b7bfb3808305d8efb9d3458e02044_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: -1px;\" \/> inches of beading to use as trim around a scarf. The scarf will be an isosceles triangle with a base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7029ea134aa43ac5ffd9f780e196307d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches. How long can she make the two equal sides?<\/p>\n<\/div>\n<div id=\"fs-id1171488105757\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168466073183\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of an isosceles triangle. Two sides of the triangle are labeled s. The base of the triangle is labeled 60 in. Below the triangle is Perimeter equals 156 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe lengths of the two equal sides.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet s equal the length of each side.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute in the given information.\u201d The word \u201ctranslate\u201d is in bold. Beside this is P equals a plus b plus c. Below this is 156 in equals s plus 60 in plus s. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is 156 equals 2s plus 60, then 96 equals 2s, then 48 equals s. Step 6 says, \u201cCheck,\u201d in bold. Beside this is P equals a plus b plus c, then 156 followed by an equal sign with a question mark, then 48 plus 60 plus 48, then 156 equals 156 followed by a check mark. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cAriana can make each of the two equal sides 48 inches long.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168466315318\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<em data-effect=\"italics\">P<\/em> = 156 in.<\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the lengths of the two equal sides<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">s<\/em> = the length of each side<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute in the given information.<\/td>\n<td><span id=\"eip-id1168469876808\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272069623\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_077_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>Arianna can make each of the two equal sides 48 inches l<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1595728\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1575241\" data-type=\"problem\">\n<p id=\"fs-id1171506203395\">A backyard deck is in the shape of an isosceles triangle with a base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet. The perimeter of the deck is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f11c6e846ac2fe8cea2c6e472ea6458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet. How long is each of the equal sides of the deck?<\/p>\n<\/div>\n<div id=\"fs-id1776706\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171505478153\">14 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1786077\" data-type=\"problem\">\n<p id=\"fs-id1783120\">A boat\u2019s sail is an isosceles triangle with base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> metres. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01cb55a185cee9b8f0aa311ce70a4b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> metres. How long is each of the equal sides of the sail?<\/p>\n<\/div>\n<div id=\"fs-id1171498469951\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1784277\">7 m<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Use the Properties of Trapezoids<\/h1>\n<p id=\"fs-id1064389\">A trapezoid is four-sided figure, a <em data-effect=\"italics\">quadrilateral<\/em>, with two sides that are parallel and two sides that are not. The parallel sides are called the bases. We call the length of the smaller base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>, and the length of the bigger base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>. The height, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>, of a trapezoid is the distance between the two bases as shown in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_052\">(Figure.13)<\/a>.<\/p>\n<p>A trapezoid has a larger base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, and a smaller base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/>. The height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> is the distance between the bases.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_052\" class=\"bc-figure figure\">\n<figure style=\"width: 291px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_052.jpg\" alt=\"A trapezoid is shown. The top is labeled b and marked as the smaller base. The bottom is labeled B and marked as the larger base. A vertical line forms a right angle with both bases and is marked as h.\" width=\"291\" height=\"129\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.13<\/figcaption><\/figure>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Formula for the A<span class=\"no-emphasis\" data-type=\"term\">rea of a Trapezoid<\/span><\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-113cb576c7585fed8d482ba4fda70ec4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#114;&#101;&#97;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#114;&#97;&#112;&#101;&#122;&#111;&#105;&#100;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#66;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"198\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1501788\">Splitting the trapezoid into two triangles may help us understand the formula. The area of the trapezoid is the sum of the areas of the two triangles. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_053\">(Figure.14)<\/a>.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_053\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Splitting a trapezoid into two triangles may help you understand the formula for its area.<\/div>\n<figure style=\"width: 179px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_053.jpg\" alt=\"An image of a trapezoid is shown. The top is labeled with a small b, the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner.\" width=\"179\" height=\"123\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.14<\/figcaption><\/figure>\n<p id=\"fs-id1888313\">The height of the trapezoid is also the height of each of the two triangles. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_078\">(Figure.15)<\/a>.<\/p>\n<div id=\"CNX_BMath_Figure_09_04_078\" class=\"bc-figure figure\">\n<figure style=\"width: 193px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_078.jpg\" alt=\"An image of a trapezoid is shown. The top is labeled with a small b, the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner. There is an arrow pointing to a second trapezoid. The upper right-hand side of the trapezoid forms a blue triangle, with the height of the trapezoid drawn in as a dotted line. The lower left-hand side of the trapezoid forms a red triangle, with the height of the trapezoid drawn in as a dotted line.\" width=\"193\" height=\"122\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.15<\/figcaption><\/figure>\n<\/div>\n<p id=\"fs-id1786318\">The formula for the area of a trapezoid is<\/p>\n<p><span id=\"fs-id1344340\" data-type=\"media\" data-alt=\"This image shows the formula for the area of a trapezoid and says \u201carea of trapezoid equals one-half h times smaller base b plus larger base B).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_056_img.jpg\" alt=\"This image shows the formula for the area of a trapezoid and says \u201carea of trapezoid equals one-half h times smaller base b plus larger base B).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1864567\">If we distribute, we get,<\/p>\n<p><span id=\"fs-id1477452\" data-type=\"media\" data-alt=\"The top line says area of trapezoid equals one-half times blue little b times h plus one-half times red big B times h. Below this is area of trapezoid equals A sub blue triangle plus A sub red triangle.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_079_img.jpg\" alt=\"The top line says area of trapezoid equals one-half times blue little b times h plus one-half times red big B times h. Below this is area of trapezoid equals A sub blue triangle plus A sub red triangle.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div id=\"fs-id1791445\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Trapezoids<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1429217\" data-bullet-style=\"bullet\">\n<li>A trapezoid has four sides. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_04_052\">(Figure.13)<\/a>.<\/li>\n<li>Two of its sides are parallel and two sides are not.<\/li>\n<li>The area, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/>, of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e4136008b989c5f8248fbb08b5139ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#66;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"117\" style=\"vertical-align: -6px;\" \/>.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1433391\" data-type=\"problem\">\n<p id=\"fs-id1454196\">Find the area of a trapezoid whose height is 6 inches and whose bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba90047eec6a05e400b16dfb86d7f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id962767\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468452905\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a trapezoid. The larger base at the top of the trapezoid is labeled 14 in, the smaller base at the bottom is labeled 11 in, the height is shown by a dotted line and is labeled 6 in. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a trapezoid.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times h times parentheses little b plus big B. Below this is A equals one-half times 6 in times parentheses 11 in plus 14 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals one-half times 6 times 25, then A equals 3 times 25, then A equals 75 square inches. Step 6 says, \u201cCheck,\u201d in bold. Beside this is written, \u201cIs this answer reasonable?\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168468774032\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_080_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of the trapezoid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6c7942252bd47fb9b58200b0c8d9cc61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#97;&#114;&#101;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"100\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><span id=\"eip-id1168467200978\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_080_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272216853\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_080_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1402808\">If we draw a rectangle around the trapezoid that has the same big base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> and a height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>, its area should be greater than that of the trapezoid.<\/p>\n<p id=\"fs-id1904190\">If we draw a rectangle inside the trapezoid that has the same little base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> and a height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>, its area should be smaller than that of the trapezoid.<\/p>\n<p><span data-type=\"media\" data-alt=\"A table is shown with 3 columns and 4 rows. The first column has an image of a trapezoid with a rectangle drawn around it in red. The larger base of the trapezoid is labeled 14 and is the same as the base of the rectangle. The height of the trapezoid is labeled 6 and is the same as the height of the rectangle. The smaller base of the trapezoid is labeled 11. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 14 times 6. Below is A sub rectangle equals 84 square inches. The second column has an image of a trapezoid. The larger base is labeled 14, the smaller base is labeled 11, and the height is labeled 6. Below this is A sub trapezoid equals one-half times h times parentheses little b plus big B. Below this is A sub trapezoid equals one-half times 6 times parentheses 11 plus 14. Below this is A sub trapezoid equals 75 square inches. The third column has an image of a trapezoid with a red rectangle drawn inside of it. The height is labeled 6. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 11 times 6. Below is A sub rectangle equals 66 square inches.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_060.jpg\" alt=\"A table is shown with 3 columns and 4 rows. The first column has an image of a trapezoid with a rectangle drawn around it in red. The larger base of the trapezoid is labeled 14 and is the same as the base of the rectangle. The height of the trapezoid is labeled 6 and is the same as the height of the rectangle. The smaller base of the trapezoid is labeled 11. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 14 times 6. Below is A sub rectangle equals 84 square inches. The second column has an image of a trapezoid. The larger base is labeled 14, the smaller base is labeled 11, and the height is labeled 6. Below this is A sub trapezoid equals one-half times h times parentheses little b plus big B. Below this is A sub trapezoid equals one-half times 6 times parentheses 11 plus 14. Below this is A sub trapezoid equals 75 square inches. The third column has an image of a trapezoid with a red rectangle drawn inside of it. The height is labeled 6. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 11 times 6. Below is A sub rectangle equals 66 square inches.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171496188733\">The area of the larger rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2044c4aefe2adfc3b277146852400fd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> square inches and the area of the smaller rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ea33956dc54e5d69c0bdc4ec3467097_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> square inches. So it makes sense that the area of the trapezoid is between <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2044c4aefe2adfc3b277146852400fd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ea33956dc54e5d69c0bdc4ec3467097_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> square inches<\/p>\n<p id=\"fs-id1439870\">Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question. The area of the trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da7843edb510e285d79daaeecac66b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> square inches.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1870546\" data-type=\"problem\">\n<p id=\"fs-id1358434\">The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> yards and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dde8d4cade60a4f3ca0e779512b974c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> yards. What is the area?<\/p>\n<\/div>\n<div id=\"fs-id1793537\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>161 sq. yd<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1580621\">The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> centimetres. What is the area?<\/p>\n<\/div>\n<div id=\"fs-id1171505941020\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1784487\">225 sq. cm<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1914969\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id781068\" data-type=\"exercise\">\n<div id=\"fs-id1793537\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505120215\" data-type=\"problem\">\n<p id=\"fs-id2064937\">Find the area of a trapezoid whose height is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet and whose bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f8f34f6a017ea88bcd2de6a269681f0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da1717c95c8532237f3fd4f1da700a7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"31\" style=\"vertical-align: -1px;\" \/> feet.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469577474\" class=\"unnumbered unstyled has-images\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a trapezoid. The smaller base at the top of the trapezoid is labeled 10.3 ft, the larger base at the bottom is labeled 13.7 ft, the height is shown by a dotted line and is labeled h. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a trapezoid.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times h times parentheses little b plus big B. Below this is A equals one-half times 5 ft times parentheses 10.3 ft plus 13.7 ft. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals one-half times 5 times 24, then A equals 12 times 5, then A equals 60 square feet. Step 6 says, \u201cCheck,\u201d in bold. Beside this is written, \u201cIs this answer reasonable? The area of the trapezoid should be less than the area of a rectangle with base 13.7 and height 5, but more than the area of a rectangle with base 10.3 and height 5.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 328.867px;\">Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1168469468737\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_081_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 284.333px;\">the area of the trapezoid<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td style=\"width: 284.333px;\">Let <em data-effect=\"italics\">A<\/em> = the area<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1168469565101\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_081_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\" data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1164272204164\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_081_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 6. <strong data-effect=\"bold\">Check:<\/strong> Is this answer reasonable?<br \/>\nThe area of the trapezoid should be less than the area of a rectangle with base 13.7 and height 5, but more than the area of a rectangle with base 10.3 and height 5.<\/td>\n<td style=\"width: 284.333px;\"><span id=\"eip-id1168466684076\" data-type=\"media\" data-alt=\"An image of a trapezoid is shown with a red rectangle drawn around it. The larger base of the trapezoid is labeled 13.7 ft. and is the same as the base of the rectangle. The height of both the trapezoid and the rectangle is 5 ft. Next to this is an image of a trapezoid with a black rectangle drawn inside it. The smaller base of the trapezoid is labeled 10.3 ft. and is the same as the base of the rectangle. Below the images is A sub red rectangle is greater than A sub trapezoid is greater than A sub rectangle. Below this is 68.5, 60, and 51.5.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_063.jpg\" alt=\"An image of a trapezoid is shown with a red rectangle drawn around it. The larger base of the trapezoid is labeled 13.7 ft. and is the same as the base of the rectangle. The height of both the trapezoid and the rectangle is 5 ft. Next to this is an image of a trapezoid with a black rectangle drawn inside it. The smaller base of the trapezoid is labeled 10.3 ft. and is the same as the base of the rectangle. Below the images is A sub red rectangle is greater than A sub trapezoid is greater than A sub rectangle. Below this is 68.5, 60, and 51.5.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 328.867px;\">Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td style=\"width: 284.333px;\">The area of the trapezoid is 60 square feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171487575864\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id1171505941020\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1550216\">The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> centimetres and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d602dc11ea561e346780b09ed5d5d87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9db75e381fdfe3988f363c206b4b5da2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"23\" style=\"vertical-align: -1px;\" \/> centimetres. What is the area?<\/p>\n<\/div>\n<div id=\"fs-id1361907\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1804038\">42 sq. cm<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171506138038\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1712277\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1350237\" data-type=\"problem\">\n<p id=\"fs-id1767992\">The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> metres and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9aa7e60892eca3e2f717a7a0e5dd2966_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6578adc4c7ff8a4a5147446911541c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/> metres. What is the area?<\/p>\n<\/div>\n<div id=\"fs-id1612307\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1931241\">63 sq. m<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1361907\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1433882\" data-type=\"problem\">\n<p id=\"fs-id1656994\">Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1605f75320ddc984a1418c7acf8d1a2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: -1px;\" \/> yards and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17f9334def3aeb2025134bd752d0dea3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21e879270cb90c5cf68e32b1602d2f41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/> yards. How many square yards will be available to plant?<\/p>\n<\/div>\n<div id=\"fs-id1598220\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469766721\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a trapezoid. The smaller base at the top of the trapezoid is labeled 5.6 yd., the larger base at the bottom is labeled 8.2 yd., the height is shown by a dotted line and is labeled 3.4 yd. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of a trapezoid.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet A equal the area.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals one-half times h times parentheses little b plus big B. Below this is A equals one-half times 3.4 yd. times parentheses 5.6 yd. plus 8.2 yd. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A equals one-half times 3.4 times 13.8, then A equals 23.46 square yards. Step 6 says, \u201cCheck,\u201d in bold. Beside this is written, \u201cIs this answer reasonable? Yes. The area of the trapezoid is less than the area of a rectangle with a base of 8.2 yd. and height 3.4 yd., but more than the area of a rectangle with base 5.6 yd. and height 3.4 yd.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><span id=\"eip-id1168469647601\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_082_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the area of a trapezoid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em data-effect=\"italics\">A<\/em> = the area<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><span id=\"eip-id1168466277354\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_082_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><span id=\"eip-id1164272067215\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_082_img-03.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Step 6. <strong data-effect=\"bold\">Check:<\/strong> Is this answer reasonable?<br \/>\nYes. The area of the trapezoid is less than the area of a rectangle with a base of 8.2 yd and height 3.4 yd, but more than the area of a rectangle with base 5.6 yd and height 3.4 yd.<span id=\"eip-id1168469711174\" data-type=\"media\" data-alt=\"This image is a table with two rows. the first row is split into three columns. The first column is the formula Area of a rectangle equals base times height. On the next line under this it has numbers plugged into the formula; the base, 8.2 in parentheses times the height 3.4 in parentheses. Under this is it has \u201cequals 27.88 yards squared\u201d. The centre column includes the formula of a trapezoid and says Area of a trapezoid equals one half times 3.5 yards in parentheses times 5.8 plus 8.2 in parentheses. Under this it has \u201cequals 23.46 yards squared\u201d. In the third column it it has the formula the area of a rectangle equals base times height. Under this it has equals 5.6 in parentheses times 3.4 in parentheses. Under this it has \u201cequals 19.04 yards squared.\u201d In the second row, centered from left to right it has \u201cArea of a rectangle\u201d and a \u201cgreater than\u201d sign, \u201cArea of a trapezoid\u201d and a greater than sign and \u201carea of a rectangle\u201d. Under Area of a rectangle it has 27.88, then 23.46 under \u201carea of a trapezoid\u201d, then 19.04 under \u201carea of a rectangle\u201d.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_066.jpg\" alt=\"This image is a table with two rows. the first row is split into three columns. The first column is the formula Area of a rectangle equals base times height. On the next line under this it has numbers plugged into the formula; the base, 8.2 in parentheses times the height 3.4 in parentheses. Under this is it has \u201cequals 27.88 yards squared\u201d. The centre column includes the formula of a trapezoid and says Area of a trapezoid equals one half times 3.5 yards in parentheses times 5.8 plus 8.2 in parentheses. Under this it has \u201cequals 23.46 yards squared\u201d. In the third column it it has the formula the area of a rectangle equals base times height. Under this it has equals 5.6 in parentheses times 3.4 in parentheses. Under this it has \u201cequals 19.04 yards squared.\u201d In the second row, centered from left to right it has \u201cArea of a rectangle\u201d and a \u201cgreater than\u201d sign, \u201cArea of a trapezoid\u201d and a greater than sign and \u201carea of a rectangle\u201d. Under Area of a rectangle it has 27.88, then 23.46 under \u201carea of a trapezoid\u201d, then 19.04 under \u201carea of a rectangle\u201d.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>Vinny has 23.46 square yards in which he can plan<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171104090407\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1533455\" data-type=\"exercise\">\n<div id=\"fs-id1612307\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1685675\" data-type=\"problem\">\n<p id=\"fs-id1790946\">Lin wants to sod his lawn, which is shaped like a trapezoid. The bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7693633ed2bfbf8f357552701025c079_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> yards and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-980582f622e2f0d52267dfc2f85f642d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/> yards, and the height is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d602dc11ea561e346780b09ed5d5d87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: -1px;\" \/> yards. How many square yards of sod does he need?<\/p>\n<\/div>\n<div id=\"fs-id1534290\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1487468\">40.25 sq. yd<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id940652\" data-type=\"problem\">\n<p id=\"fs-id1386498\">Kira wants cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet and whose height is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet, how many square feet of pavers will he need?<\/p>\n<\/div>\n<div id=\"fs-id1171487564666\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171505120247\">240 sq. ft.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"eip-375\" class=\"links-to-literacy\" data-type=\"note\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Access Additional Online Resources<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul id=\"fs-id1579336\">\n<li><a href=\"http:\/\/www.openstax.org\/l\/24perirect\">Perimeter of a Rectangle<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24arearect\">Area of a Rectangle<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24periareaform\">Perimeter and Area Formulas<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24areatri\">Area of a Triangle<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24areatrifract\">Area of a Triangle with Fractions<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24areatrap\">Area of a Trapezoid<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"eip-87\">\n<li><strong>Properties of Rectangles<\/strong>\n<ul id=\"eip-id1168921412515\">\n<li>Rectangles have four sides and four right (90\u00b0) angles.<\/li>\n<li>The lengths of opposite sides are equal.<\/li>\n<li>The perimeter, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, of a rectangle is the sum of twice the length and twice the width.\n<ul id=\"eip-id1168933998684\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fd41d005b7610a456dc9e5dc6ad9fd67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#50;&#76;&#43;&#50;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -2px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li>The area, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/>, of a rectangle is the length times the width.\n<ul id=\"eip-id5597402\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c142b3dc533df153f0e13657f12c7f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#76;&#92;&#99;&#100;&#111;&#116;&#32;&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"81\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li><strong>Triangle Properties<\/strong>\n<ul id=\"eip-id7402430\">\n<li>For any triangle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23f00feef91cb9ba3057f9e15d82ff39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#65;&#66;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/>, the sum of the measures of the angles is 180\u00b0.\n<ul id=\"eip-id1170244913551\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18edfbb1b7b9c6d260dce772378c97a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#65;&#43;&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#66;&#43;&#109;&#92;&#97;&#110;&#103;&#108;&#101;&#32;&#67;&#61;&#49;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"221\" style=\"vertical-align: -2px;\" \/>\u00b0<\/li>\n<\/ul>\n<\/li>\n<li>The perimeter of a triangle is the sum of the lengths of the sides.\n<ul id=\"eip-id1170253352636\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4abea6f02f4ab78a43a4d9118ea2b19d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#61;&#97;&#43;&#98;&#43;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li>The area of a triangle is one-half the base, b, times the height, h.\n<ul id=\"eip-id1170239311614\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b372c8f17c232fb83c5e06a24bf6fd73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#98;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1927628\">\n<dt>area<\/dt>\n<dd id=\"fs-id1171505277192\">The area is a measure of the surface covered by a figure.<\/dd>\n<\/dl>\n<dl id=\"fs-id1933603\">\n<dt>equilateral triangle<\/dt>\n<dd id=\"fs-id1816092\">A triangle with all three sides of equal length is called an equilateral triangle.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171506988885\">\n<dt>isosceles triangle<\/dt>\n<dd id=\"fs-id1674082\">A triangle with two sides of equal length is called an isosceles triangle.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171497994973\">\n<dt>perimeter<\/dt>\n<dd id=\"fs-id1171505779039\">The perimeter is a measure of the distance around a figure.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171488172541\">\n<dt>rectangle<\/dt>\n<dd id=\"fs-id1922026\">A rectangle is a geometric figure that has four sides and four right angles.<\/dd>\n<\/dl>\n<dl id=\"fs-id1171505990665\">\n<dt>trapezoid<\/dt>\n<dd id=\"fs-id2022585\">A trapezoid is four-sided figure, a quadrilateral, with two sides that are parallel and two sides that are not.<\/dd>\n<\/dl>\n<\/div>\n<h1 style=\"text-align: left;\" data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1171498001678\">Understand Linear, Square, and Cubic Measure<\/h2>\n<p id=\"eip-832\">In the following exercises, determine whether you would measure each item using linear, square, or cubic units.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. amount of water in a fish tank<\/td>\n<td style=\"width: 50%;\">2. length of dental floss<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. living area of an apartment<\/td>\n<td style=\"width: 50%;\">4. floor space of a bathroom tile<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. height of a doorway<\/td>\n<td style=\"width: 50%;\">6. capacity of a truck trailer<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1679789\">In the following exercises, find the a) perimeter and b) area of each figure. Assume each side of the square is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> cm.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 258px;\">\n<tbody>\n<tr style=\"height: 160px;\">\n<td style=\"width: 50%; height: 160px;\"><span id=\"fs-id1557835\" data-type=\"media\" data-alt=\"A rectangle is shown comprised of 4 squares forming a horizontal line.\">7.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_201_img.jpg\" alt=\"A rectangle is shown comprised of 4 squares forming a horizontal line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 160px;\"><span id=\"fs-id1747015\" data-type=\"media\" data-alt=\"A rectangle is shown comprised of 3 squares forming a vertical line.\">8.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_202_img.jpg\" alt=\"A rectangle is shown comprised of 3 squares forming a vertical line.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1577499\" data-type=\"media\" data-alt=\"Three squares are shown. There is one on the bottom left, one on the bottom right, and one on the top right.\">9.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_203_img.jpg\" alt=\"Three squares are shown. There is one on the bottom left, one on the bottom right, and one on the top right.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1171505618069\" data-type=\"media\" data-alt=\"Four squares are shown. Three form a horizontal line, and there is one above the centre square.\">10.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_204_img.jpg\" alt=\"Four squares are shown. Three form a horizontal line, and there is one above the centre square.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id2035119\" data-type=\"media\" data-alt=\"Five squares are shown. There are three forming a horizontal line across the top and two underneath the two on the right.\">11.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_205_img.jpg\" alt=\"Five squares are shown. There are three forming a horizontal line across the top and two underneath the two on the right.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1568260\" data-type=\"media\" data-alt=\"A square is shown. It is comprised of nine smaller squares.\">12.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_206_img.jpg\" alt=\"A square is shown. It is comprised of nine smaller squares.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1913911\" style=\"text-align: left;\">Use the Properties of Rectangles<\/h2>\n<p id=\"eip-919\">In the following exercises, find the a) perimeter and b) area of each rectangle.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">13. The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-93bab3e1e2449c9eb7d50303281fbada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet and the width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a494309aca1bdc45eb593f8e8497226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet.<\/td>\n<td style=\"width: 50%;\">14. The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc1c5ee273f78a117868c9594082c74b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches and the width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c04d88fcf64566a852d0a051ac00e70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. A rectangular room is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet wide by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet long.<\/td>\n<td style=\"width: 50%;\">16. A driveway is in the shape of a rectangle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet wide by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bff01d8c87d130da6950c561718ce13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet long.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1586793\">In the following exercises, solve.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 370px;\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">17. Find the length of a rectangle with perimeter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0763ae919089a8912670c5eb26c45969_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> inches and width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d761d015714dab15099f98dec9a6f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches.<\/td>\n<td style=\"width: 50%; height: 30px;\">18. Find the length of a rectangle with perimeter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-498ff2a745163c5d754a38abc63a6087_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> yards and width of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6578adc4c7ff8a4a5147446911541c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/> yards.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">19. Find the width of a rectangle with perimeter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3f71c71feea69aeaf91fa405e3d64a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> metres and length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23ae1c0b89342725f5c66b11294f8bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">20. Find the width of a rectangle with perimeter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-181aba053893ad1a31a8a08adcc75e2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: -1px;\" \/> metres and length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-78de7a68f0d9d8f64a233f74be4f6f87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> metres.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">21. The area of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-391334df04732f2470adde62943504de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> square metres. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> metres. What is the width?<\/td>\n<td style=\"width: 50%; height: 30px;\">22. The area of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7495da430dd03eaa7fc43b0f5bcd862_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#56;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\" \/> square centimetres. The width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres. What is the length?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">23. The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches more than the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d1b2be35527597b3ccb8db32048b384_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> inches. Find the length and the width.<\/td>\n<td style=\"width: 50%; height: 30px;\">24. The width of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches more than the length. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30352d66e4a511eedaaaf1c7497a30c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches. Find the length and the width.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">25. The perimeter of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c04d88fcf64566a852d0a051ac00e70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres. The width of the rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> metres less than the length. Find the length and the width of the rectangle.<\/td>\n<td style=\"width: 50%; height: 46px;\">26. The perimeter of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e608b19de1bcf92fa9559aac92a66de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet. The width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet less than the length. Find the length and the width.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">27. The width of the rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dce05b6a62893de03d6e74ce9452fa4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\" \/> metres less than the length. The perimeter of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7a17dcefb9a98ff261eab257f480ffb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: 0px;\" \/> metres. Find the dimensions of the rectangle.<\/td>\n<td style=\"width: 50%; height: 46px;\">28. The length of the rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-98101774293057575fc483ff69d41ff8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> metres less than the width. The perimeter of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-252c65ee952dc2cac0d6c78f45a587d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#57;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> metres. Find the dimensions of the rectangle.<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">29. The perimeter of a rectangle of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-74a92b6c533b233c6f544c969f0e81fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: -1px;\" \/> feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.<\/td>\n<td style=\"width: 50%; height: 46px;\">30. The length of a rectangle is three times the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c7bef200c216bbe8be23cd2a2c1371d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet. Find the length and width of the rectangle.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> metres less than twice the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres. Find the length and width.<\/td>\n<td style=\"width: 50%; height: 14px;\">32. The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches more than twice the width. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b71d4a39e9b05df9f1fe4834c0955ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> inches. Find the length and width.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. The width of a rectangular window is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> inches. The area is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f90afc9bdfdeb600a979744e3d589e6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> square inches. What is the length?<\/td>\n<td style=\"width: 50%; height: 14px;\">34. The length of a rectangular poster is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80588c2af70b499bde2614a130c98b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches. The area is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9fa1763373c0af744f4819aacafa7b54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: -1px;\" \/> square inches. What is the width?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35. The area of a rectangular roof is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d3e4a31466b7dfa749aba63d8cabc2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"36\" style=\"vertical-align: -1px;\" \/> square metres. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-663d228316bfd115aace82901fc82ec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> metres. What is the width?<\/td>\n<td style=\"width: 50%; height: 14px;\">36. The area of a rectangular tarp is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b48d58730d30099e43155dc1c2257b07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"25\" style=\"vertical-align: -1px;\" \/> square feet. The width is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet. What is the length?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">37. The perimeter of a rectangular courtyard is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-21b40b26dcd5c46e571710b78f863a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> feet. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet more than the width. Find the length and the width.<\/td>\n<td style=\"width: 50%; height: 14px;\">38. The perimeter of a rectangular painting is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f858a27c6d32a16871e9b7895b27a921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/> centimetres. The length is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres more than the width. Find the length and the width.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">39. The width of a rectangular window is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-89bc2c119dcafc9b555c6b2841530d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> inches less than the height. The perimeter of the doorway is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af2e910759227221f4ba10dddf072bcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: -1px;\" \/> inches. Find the length and the width.<\/td>\n<td style=\"width: 50%; height: 14px;\">40. The width of a rectangular playground is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> metres less than the length. The perimeter of the playground is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d1b2be35527597b3ccb8db32048b384_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> metres. Find the length and the width.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1552808\">Use the Properties of Triangles<\/h2>\n<p id=\"eip-650\">In the following exercises, solve using the properties of triangles.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 222px;\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">41. Find the area of a triangle with base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> inches and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches.<\/td>\n<td style=\"width: 50%; height: 30px;\">42. Find the area of a triangle with base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a494309aca1bdc45eb593f8e8497226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> centimetres.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">43. Find the area of a triangle with base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9767724a131e9fe12f88a4fb817671a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> metres and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-33fc1df0f7ee605b381e6d35441e3bcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">44. Find the area of a triangle with base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1fc1f662d642114a283afc56742cedb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> feet and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4e87ddf16702d6c6ea09b5a80e4bcfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> feet.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">45. A triangular flag has base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> foot and height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b2514947ef7a7471f9fcd9c60117cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"21\" style=\"vertical-align: -1px;\" \/> feet. What is its area?<\/td>\n<td style=\"width: 50%; height: 30px;\">46. A triangular window has base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet. What is its area?<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">47. If a triangle has sides of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and the perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e554ca92166de4bd98acfbef8f678cd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet, how long is the third side?<\/td>\n<td style=\"width: 50%; height: 46px;\">48. If a triangle has sides of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres and the perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c99f2a2d6b0972a936697151a4970a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> centimetres, how long is the third side?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">49. What is the base of a triangle with an area of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5e07b23537adc695fc5b12e20e0ef74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\" \/> square inches and height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches?<\/td>\n<td style=\"width: 50%; height: 30px;\">50. What is the height of a triangle with an area of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-938d3a0d31bb727fa4733276d003234a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#57;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/> square inches and base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d761d015714dab15099f98dec9a6f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. The perimeter of a triangular reflecting pool is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> yards. The lengths of two sides are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> yards and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> yards. How long is the third side?<\/td>\n<td style=\"width: 50%; height: 14px;\">52. A triangular courtyard has perimeter of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-454fa4f8a22c90ab5a5245afd540f8f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> metres. The lengths of two sides are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres. How long is the third side?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. An isosceles triangle has a base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> centimetres. If the perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12b818a990fee7373006af5f0935f243_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> centimetres, find the length of each of the other sides.<\/td>\n<td style=\"width: 50%; height: 14px;\">54. An isosceles triangle has a base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd40a7f142c1fc4152e724db5432f76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches. If the perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffb4dcee510557d85b10c85d699e726c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches, find the length of each of the other sides.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. Find the length of each side of an equilateral triangle with a perimeter of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-deb4bebaec9fe47ccd035848be13a879_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> yards.<\/td>\n<td style=\"width: 50%; height: 14px;\">56. Find the length of each side of an equilateral triangle with a perimeter of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66ceeedc341151a1adecf7dd22c17553_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -1px;\" \/> metres.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. The perimeter of an equilateral triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> metres. Find the length of each side.<\/td>\n<td style=\"width: 50%; height: 14px;\">58. The perimeter of an equilateral triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-663d228316bfd115aace82901fc82ec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> miles. Find the length of each side.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">59. The perimeter of an isosceles triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-663d228316bfd115aace82901fc82ec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet. The length of the shortest side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet. Find the length of the other two sides.<\/td>\n<td style=\"width: 50%;\">60. The perimeter of an isosceles triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-37c9486c23c8660d4383d35aeb048770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches. The length of the shortest side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> inches. Find the length of the other two sides.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">61. A dish is in the shape of an equilateral triangle. Each side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches long. Find the perimeter.<\/td>\n<td style=\"width: 50%;\">62. A floor tile is in the shape of an equilateral triangle. Each side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b2514947ef7a7471f9fcd9c60117cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"21\" style=\"vertical-align: -1px;\" \/> feet long. Find the perimeter.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">63. A road sign in the shape of an isosceles triangle has a base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches. If the perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5bf280819b34f8f3fe2b3ed476b3886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches, find the length of each of the other sides.<\/td>\n<td style=\"width: 50%;\">64. A scarf in the shape of an isosceles triangle has a base of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4190de69324b6881e1d1d3cccda23e9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> metres. If the perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> metres, find the length of each of the other sides.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">65. The perimeter of a triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a3db773b3fb1c245f782b7a601d70917_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet. One side of the triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> foot longer than the second side. The third side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet longer than the second side. Find the length of each side.<\/td>\n<td style=\"width: 50%;\">66. The perimeter of a triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bff01d8c87d130da6950c561718ce13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> feet. One side of the triangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet longer than the second side. The third side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet longer than the second side. Find the length of each side.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">67. One side of a triangle is twice the smallest side. The third side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet more than the shortest side. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet. Find the lengths of all three sides.<\/td>\n<td style=\"width: 50%;\">68. One side of a triangle is three times the smallest side. The third side is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet more than the shortest side. The perimeter is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-837d0d6b05c238eddf106b68ec9dcfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet. Find the lengths of all three sides.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1968347\">Use the Properties of Trapezoids<\/h2>\n<p>In the following exercises, solve using the properties of trapezoids.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 176px;\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">69. The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet. What is the area?<\/td>\n<td style=\"width: 50%; height: 30px;\">70. The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> yards and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> yards. What is the area?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">71. Find the area of a trapezoid with a height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-deb4bebaec9fe47ccd035848be13a879_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> metres and bases of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec0b6e7f7e46f16db27054b3329cf224_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-caba4236867d706d697ac624ed9bdbfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">72. Find the area of a trapezoid with a height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e608b19de1bcf92fa9559aac92a66de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches and bases of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c04d88fcf64566a852d0a051ac00e70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da7843edb510e285d79daaeecac66b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches.<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">73. The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> centimetres and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0154243e4669a75b5cdfd1ed3f8759ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a7add496f9669101fa684afceb10c4bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> centimetres. What is the area?<\/td>\n<td style=\"width: 50%; height: 30px;\">74. The height of a trapezoid is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f11c6e846ac2fe8cea2c6e472ea6458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f2afff81e80da5494a34ebae209ce29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#56;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec240a54e91eaa4d227b2cf8b2ac8929_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#48;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> feet. What is the area?<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">75. Find the area of a trapezoid with a height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b51aa9707a66a85997f31501edc50c65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> metres and bases of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9a2938478249a117e5c06416e10206d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e477cf46a48880ac1d21f91b0eaedde2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> metres.<\/td>\n<td style=\"width: 50%; height: 30px;\">76. Find the area of a trapezoid with a height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c55c29e2c47a8ac00588b5dc38a5d50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> centimetres and bases of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5bd79d9ef891e01effc53abaa54b1974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#52;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"32\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a257bf736c9ad796444af48ec53c8d52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> centimetres.<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">77. Laurel is making a banner shaped like a trapezoid. The height of the banner is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and the bases are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet. What is the area of the banner?<\/td>\n<td style=\"width: 50%; height: 14px;\">78. Niko wants to tile the floor of his bathroom. The floor is shaped like a trapezoid with width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet and lengths <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet. What is the area of the floor?<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">79. Theresa needs a new top for her kitchen counter. The counter is shaped like a trapezoid with width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-67ce592f083a0c9983c01c61481ba8a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/> inches and lengths <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e608b19de1bcf92fa9559aac92a66de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches. What is the area of the counter?<\/td>\n<td style=\"width: 50%; height: 14px;\">80. Elena is knitting a scarf. The scarf will be shaped like a trapezoid with width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches and lengths <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e1f88194253071060a3c7a8358b7c03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> inches and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffd701a380d8b7c09d0e6bf5fbc942e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#54;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> inches. What is the area of the scarf?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%; height: 200px;\">\n<tbody>\n<tr style=\"height: 110px;\">\n<td style=\"width: 50%; height: 110px;\">81.<strong data-effect=\"bold\"> Fence<\/strong> Jose just removed the children\u2019s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet. How long can he make the other side if he wants to use the entire roll of fence?<\/td>\n<td style=\"width: 50%; height: 110px;\">82.<strong data-effect=\"bold\"> Gardening<\/strong> Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1f11c6e846ac2fe8cea2c6e472ea6458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet of fencing to enclose the garden. Find the length and width of her garden.<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 50%; height: 62px;\">83.<strong data-effect=\"bold\"> Fence<\/strong> Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet. The fence costs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-463608914c9381f72b4976416be657cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#36;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: -1px;\" \/> per foot. How much will it cost for Christa to fence in her flowerbed?<\/td>\n<td style=\"width: 50%; height: 62px;\">\n<p id=\"fs-id1171505792377\">84.<strong data-effect=\"bold\"> Painting<\/strong> Caleb wants to paint one wall of his attic. The wall is shaped like a trapezoid with height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and bases <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet. The cost of the painting one square foot of wall is about <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad376a68ecc2a5e5be8186d609f3a1eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#63;&#48;&#46;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/>. About how much will it cost for Caleb to paint the attic wall?<\/p>\n<p><span id=\"fs-id1171505276350\" data-type=\"media\" data-alt=\"A right trapezoid is shown.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_207_img.jpg\" alt=\"A right trapezoid is shown.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">86. If you need to put a fence around your backyard, do you need to know the perimeter or the area of the backyard? Explain your reasoning.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171487570514\">87. Look at the two figures.<\/p>\n<p><span id=\"fs-id2145050\" data-type=\"media\" data-alt=\"A rectangle is shown on the left. It is labeled as 2 by 8. A square is shown on the right. It is labeled as 4 by 4.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_04_208_img.jpg\" alt=\"A rectangle is shown on the left. It is labeled as 2 by 8. A square is shown on the right. It is labeled as 4 by 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171487189484\">a) Which figure looks like it has the larger area? Which looks like it has the larger perimeter?<\/p>\n<p id=\"fs-id1171505279391\">b) Now calculate the area and perimeter of each figure. Which has the larger area? Which has the larger perimeter?<\/p>\n<\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171505780908\">88. The length of a rectangle is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet more than the width. The area is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> square feet. Find the length and the width.<\/p>\n<p id=\"fs-id1171488139794\">a) Write the equation you would use to solve the problem.<\/p>\n<p id=\"fs-id1482367\">b) Why can\u2019t you solve this equation with the methods you learned in the previous chapter?<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 350px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. cubic<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. square<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. linear<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">7.<\/p>\n<p>a) 10 cm<\/p>\n<p>b) 4 sq. cm<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">9.<\/p>\n<p>a) 8 cm<\/p>\n<p>b) 3 sq. cm<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">11.<\/p>\n<p>a) 10 cm<\/p>\n<p>b) 5 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">13.<\/p>\n<p>a) 260 ft<\/p>\n<p>b) 3825 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">15.<\/p>\n<p>a) 58 ft<\/p>\n<p>b) 210 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">17. 24 inches<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. 27 metres<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. 23 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. 7 in., 16 in.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. 17 m, 12 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. 13.5 m, 12.8 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. 25 ft, 50 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. 7 m, 11 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. 26 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. 55 m<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. 35 ft, 45 ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. 76 in., 36 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41. 60 sq. in.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. 25.315 sq. m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45. 0.75 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">47. 8 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">49. 23 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">51. 11 ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">53. 28 cm<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">55. 17 ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">57. 6 m<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">59. 15 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">61. 24 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">63. 27.5 in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">65. 12 ft, 13 ft, 14 ft<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">67. 3 ft, 6 ft, 8 ft<\/td>\n<td style=\"width: 33.3333%;\">69. 144 sq. ft<\/td>\n<td style=\"width: 33.3333%;\">71. 2805 sq. m<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">73. 231 sq. cm<\/td>\n<td style=\"width: 33.3333%;\">75. 28.56 sq. m<\/td>\n<td style=\"width: 33.3333%;\">77. 13.5 sq. ft<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">79.\u00a01036 sq. in.<\/td>\n<td style=\"width: 33.3333%;\">81. 15 ft<\/td>\n<td style=\"width: 33.3333%;\">83. &#36;24<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">85. Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\">87.\u00a0Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse Properties of Rectangles, Triangles, and Trapezoids\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n","protected":false},"author":90,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-524","chapter","type-chapter","status-publish","hentry"],"part":398,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/524","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/524\/revisions"}],"predecessor-version":[{"id":525,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/524\/revisions\/525"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/398"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/524\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=524"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=524"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=524"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}