{"id":613,"date":"2020-08-21T19:41:17","date_gmt":"2020-08-21T23:41:17","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-geometry-applications-circles-and-irregular-figures\/"},"modified":"2021-03-24T10:53:47","modified_gmt":"2021-03-24T14:53:47","slug":"solve-geometry-applications-circles-and-irregular-figures","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-geometry-applications-circles-and-irregular-figures\/","title":{"raw":"3.4 Solve Geometry Applications: Circles and Irregular Figures","rendered":"3.4 Solve Geometry Applications: Circles and Irregular Figures"},"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>Use the properties of circles<\/li>\n \t<li>Find the area of irregular figures<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1171506645886\">In this section, we\u2019ll continue working with geometry applications. We will add several new formulas to our collection of formulas. To help you as you do the examples and exercises in this section, we will show 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\">Problem Solving Strategy for Geometry Applications<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168469784124\" class=\"stepwise\" type=\"1\">\n \t<li><strong>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>Identify <\/strong> what you are looking for.<\/li>\n \t<li><strong>Name <\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li><strong>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>Solve <\/strong> the equation using good algebra techniques.<\/li>\n \t<li><strong>Check <\/strong> the answer in the problem and make sure it makes sense.<\/li>\n \t<li><strong>Answer <\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Use the Properties of Circles<\/h1>\n<p id=\"fs-id1613325\">\u00a0We\u2019ll\u00a0 refer to the properties of circles as we use them to solve applications.<\/p>\n\n<div id=\"fs-id1171506663136\" 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 Circles<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n<span id=\"fs-id1365138\" data-type=\"media\" data-alt=\"An image of a circle is shown. There is a line drawn through the widest part at the centre of the circle with a red dot indicating the centre of the circle. The line is labeled d. The two segments from the centre of the circle to the outside of the circle are each labeled r.\"><img class=\"alignright\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_09_05_001.jpg\" alt=\"An image of a circle is shown. There is a line drawn through the widest part at the centre of the circle with a red dot indicating the centre of the circle. The line is labeled d. The two segments from the centre of the circle to the outside of the circle are each labeled r.\" data-media-type=\"image\/jpeg\"><\/span>\n<ul id=\"fs-id1489165\" data-bullet-style=\"bullet\">\n \t<li>\\(r\\) is the length of the radius<\/li>\n \t<li>\\(d\\) is the length of the diametre<\/li>\n \t<li>\\(d=2r\\)<\/li>\n \t<li>Circumference is the perimeter of a circle. The formula for circumference is\n<div id=\"fs-id1171105198477\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(C=2\\pi r\\)<\/div><\/li>\n \t<li>The formula for area of a circle is\n<div id=\"fs-id1171105180774\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(A=\\pi {r}^{2}\\)<\/div><\/li>\n<\/ul>\n<\/div>\n<\/div>\nRemember, that we approximate \\(\\pi \\) with \\(3.14\\) or \\(\\frac{22}{7}\\) depending on whether the radius of the circle is given as a decimal or a fraction. If you use the \\(\\pi \\) key on your calculator to do the calculations in this section, your answers will be slightly different from the answers shown. That is because the \\(\\pi \\) key uses more than two decimal places.\n\n<\/div>\n<\/div>\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-id1549320\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171513637241\" data-type=\"exercise\">\n<div id=\"fs-id1323804\" data-type=\"problem\">\n<div id=\"fs-id1171487568034\" data-type=\"problem\">\n<p id=\"fs-id1933138\">A circular sandbox has a radius of \\(2.5\\) feet. Find the a) circumference and b) area of the sandbox.<\/p>\n\n<\/div>\n<div id=\"fs-id1587329\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">a)<\/div>\n<table id=\"eip-id1168467555346\" 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 circle. The radius is labeled r equals 2.5 ft. 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 circumference of the circle.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is C equals 2 pi r. Below this is C equals 2 times pi times 2.5 ft., then C is approximately 2 times 3.14 times 2.5 ft. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is C is approximately 2 times 3.14 times 2.5, then C is approximately 15.7 feet. Step 6 says, \u201cCheck,\u201d in bold. Then, \u201cDoes this answer make sense? Yes. If we draw a square around the circle, its sides would be 5 ft. (twice the radius), so its perimeter would be 20 ft. This is slightly more than the circle's circumference, 15.7 ft. Beneath this is a picture of the circle with a red square drawn around it. Each side of the square is labeled 5 ft. The radius is labeled as r equals 2.5 ft. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe circumference of the sandbox is 15.7 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-id1168468498969\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_029_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 circumference of the circle<\/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> = circumference of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula\nSubstitute<\/td>\n<td>\\(C=2\\pi r\\)\n\\(C=2\\pi \\left(2.5\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td>\\(C\\approx 2\\left(3.14\\right)\\left(2.5\\right)\\)\n\\(C\\approx 15\\text{ft}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check.<\/strong> Does this answer make sense?\nYes. If we draw a square around the circle, its sides would be 5 ft (twice the radius), so its perimeter would be 20 ft. This is slightly more than the circle's circumference, 15.7 ft.<\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_029_img-02.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 circumference of the sandbox is 15.7 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n&nbsp;\n\nb)\n<table id=\"eip-id1168468253524\" class=\"unnumbered unstyled\" summary=\"Identify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of the circle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cA equals pi r squared.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals pi times r squared. Below this is A is approximately 3.14 times 2.5 ft. squared. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A is approximately 19.625 square feet. Step 6 says, \u201cCheck,\u201d in bold. Then, \u201cDoes this answer make sense? Yes. If we draw a square around the circle, its sides would be 5 ft., as shown in part a. So the area of the square would be 25 sq. ft. This is slightly more than the circle's area, 19.625 sq. ft. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe area of the circle is 19.625 square feet.\" 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-id1168467313672\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_029_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 circle<\/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 of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula\nSubstitute<\/td>\n<td>\\(A=\\pi{r}^{2}\\)\n\\(A=\\pi{\\left(2.5\\right)}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td>\\(A\\approx \\left(3.14\\right){\\left(2.5\\right)}^{2}\\)\n\\(A\\approx 19.625\\phantom{\\rule{0.2em}{0ex}}\\text{sq. ft}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check.<\/strong>\nYes. If we draw a square around the circle, its sides would be 5 ft, as shown in part a). So the area of the square would be 25 sq. ft. This is slightly more than the circle's area, 19.625 sq. ft.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The area of the circle is 19.625 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-id1549320\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171513637241\" data-type=\"exercise\">\n<div id=\"fs-id1323804\" data-type=\"problem\">\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-id1323804\" data-type=\"problem\">\n<p id=\"fs-id2146917\">A circular mirror has radius of \\(5\\) inches. Find the a) circumference and b) area of the mirror.<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168469728002\" class=\"circled\" type=\"a\">\n \t<li>31.4 in.<\/li>\n \t<li>78.5 sq. in.<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div 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-id1171505810220\" data-type=\"problem\">\n<p id=\"fs-id1665536\">A circular spa has radius of \\(4.5\\) feet. Find the a) circumference and b) area of the spa.<\/p>\n\n<\/div>\n<div id=\"fs-id1574843\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168469655844\" class=\"circled\" type=\"a\">\n \t<li>28.26 ft<\/li>\n \t<li>63.585 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\nWe usually see the formula for circumference in terms of the radius \\(r\\) of the circle:\n\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105527474\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(C=2\\pi r\\)<\/div>\n<p id=\"fs-id1685662\">But since the diametre of a circle is two times the radius, we could write the formula for the circumference in terms \\(\\text{of}\\phantom{\\rule{0.2em}{0ex}}d\\).<\/p>\n\n<div id=\"fs-id1171105202378\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}&amp; &amp; &amp; C=2\\pi r\\hfill \\\\ \\text{Using the commutative property, we get}\\hfill &amp; &amp; &amp; C=\\pi \\cdot2r\\hfill \\\\ \\text{Then substituting}\\phantom{\\rule{0.2em}{0ex}}d=2r\\hfill &amp; &amp; &amp; C=\\pi \\cdot\\text{d}\\hfill \\\\ \\text{So}\\hfill &amp; &amp; &amp; C=\\pi d\\hfill \\end{array}\\)<\/div>\n<p id=\"fs-id1567127\">We will use this form of the circumference when we\u2019re given the length of the diametre instead of the radius.<\/p>\n\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 data-type=\"problem\">\n\nA circular table has a diametre of four feet. What is the circumference of the table?\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-id1168467247251\" 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 circular table. The diametre is labeled d equals 4 ft. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this is \u201cthe circumference of the table.\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 circumference of the table.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is C equals pi d. Below this is C equals pi times 4. Step 5 says, \u201cSolve the equation, using 3.14 for pi.\u201d The word \u201csolve\u201d is in bold. Beside this is C is approximately 3.14 times 4, then C is approximately 12.56 feet. Step 6 says, \u201cCheck,\u201d in bold. Then, \u201cIf we put a square around the circle, its side would be 4. The perimeter would be 16. It makes sense that the circumference of the circle, 12.56, a little less than 16.\u201d Beneath this is a picture of the circle with a red square drawn around it. Each side of the square is labeled 4 ft. The diametre is labeled as d equals 4 ft. Step 7 says, \u201cAnswer the question\u201d in bold. The answer is given as \u201cThe diametre of the table is 12.56 square feet.\" 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-id1168467253483\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_032_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 circumference of the table<\/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 circumference of the table<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula for the situation.\nSubstitute.<\/td>\n<td>\\(C=\\pi d\\)\n\\(C=\\pi \\left(4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation, using 3.14 for \\(\\pi \\).<\/td>\n<td>\\(C\\approx \\left(3.14\\right)\\left(4\\right)\\)\n\\(C\\approx 12.56\\phantom{\\rule{0.2em}{0ex}}\\text{feet}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> If we put a square around the circle, its side would be 4.\nThe perimeter would be 16. It makes sense that the circumference of the circle, 12.56, is a little less than 16.<\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_032_img-02.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 diametre of the table is 12.56 square 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 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1553333\" data-type=\"problem\">\n<p id=\"fs-id1573443\">Find the circumference of a circular fire pit whose diametre is \\(5.5\\) feet.<\/p>\n\n<\/div>\n<div id=\"fs-id1171505794101\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171506644144\">17.27 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1864175\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1867339\" data-type=\"exercise\">\n<div id=\"fs-id1553333\" 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 data-type=\"problem\">\n\nIf the diametre of a circular trampoline is \\(12\\) feet, what is its circumference?\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>37.68 ft\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1349580\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1610347\" data-type=\"exercise\">\n<div data-type=\"solution\">\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-id1683811\" data-type=\"problem\">\n<p id=\"fs-id1498081\">Find the diametre of a circle with a circumference of \\(47.1\\) centimetres.<\/p>\n\n<\/div>\n<div id=\"fs-id1418161\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468767882\" 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 circle. The diametre is labeled d. Below this is C equals 47.1 cm. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this is \u201cthe diametre of the circle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet d equal the diametre of the circle.\u201d Step 4 says, \u201cTranslate. Write the formula. Substitute, using 3.14 to approximate pi.\u201d The word \u201ctranslate\u201d is in bold. Beside this is C equals pi times d. Below this is 47.1 cm. is approximately 3.14 times d. Step 5 says \u201csolve\u201d in bold. Beside this is 47.1 over 3.14 is approximately 3.14d over 3.14, then 15 is approximately d. Step 6 says, \u201cCheck,\u201d in bold. Beside this is C equals pi times d, then 47.1 followed by an equal sign with a question mark, then 3.14 times 15. Below this is 47.1 equals 47.1, followed by a check mark. Step 7 says, \u201cAnswer the question\u201d in bold. The answer is given as \u201cThe diametre of the circle is approximately 15 centimetres.\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-id1168467257979\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_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 diametre of the circle<\/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\">d<\/em> = the diametre of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the formula.\nSubstitute, using 3.14 to approximate \\(\\pi \\).<\/td>\n<td><span id=\"eip-id1168467143388\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168468597734\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-03.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><\/td>\n<td><span id=\"eip-id1168467258996\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span>\n<span id=\"eip-id1168467173423\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong>\n\\(47.1\\stackrel{?}{=}\\left(3.14\\right)\\left(15\\right)\\)\n\\(47.1=47.1\\)\u2713<\/td>\n<td><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-06.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer the question.<\/strong><\/td>\n<td>The diametre of the circle is approximately 15 centimetres.<\/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-id1171505481386\" data-type=\"problem\">\n<p id=\"fs-id1171498370892\">Find the diametre of a circle with circumference of \\(94.2\\) centimetres.<\/p>\n\n<\/div>\n<div id=\"fs-id2063819\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id2032181\">30 cm<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1713306\" data-type=\"exercise\">\n<div id=\"fs-id2063819\" 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-id1347320\" data-type=\"problem\">\n<p id=\"fs-id1171505977370\">Find the diametre of a circle with circumference of \\(345.4\\) feet.<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1798736\">110 ft<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Area of Irregular Figures<\/h1>\n<p id=\"fs-id1171487154912\">So far, we have found area for rectangles, triangles, trapezoids, and circles. An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas. But some irregular figures are made up of two or more standard geometric shapes. To find the area of one of these irregular figures, we can split it into figures whose formulas we know and then add the areas of the figures.<\/p>\n\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-id1867154\" data-type=\"problem\">\n<p id=\"fs-id1580231\">Find the area of the shaded region.<\/p>\n<strong><span id=\"fs-id1686212\" data-type=\"media\" data-alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_012_img.jpg\" alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\" data-media-type=\"image\/jpeg\"><\/span><\/strong>\n\n<\/div>\n<div id=\"fs-id1885059\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1868264\">The given figure is irregular, but we can break it into two rectangles. The area of the shaded region will be the sum of the areas of both rectangles.<\/p>\n<span data-type=\"media\" data-alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_013_img.jpg\" alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1474787\">The blue rectangle has a width of \\(12\\) and a length of \\(4\\). The red rectangle has a width of \\(2\\), but its length is not labeled. The right side of the figure is the length of the red rectangle plus the length of the blue rectangle. Since the right side of the blue rectangle is \\(4\\) units long, the length of the red rectangle must be \\(6\\) units.<\/p>\n<span id=\"fs-id1183456\" data-type=\"media\" data-alt=\"An image of a blue horizontal rectangle attached to a red vertical rectangle is shown. The top is labeled 12, the side of the blue rectangle is labeled 4. The whole side is labeled 10, the blue portion is labeled 4 and the red portion is labeled 6. The width of the red rectangle is labeled 2.\"><img class=\"alignnone aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_014_img.jpg\" alt=\"An image of a blue horizontal rectangle attached to a red vertical rectangle is shown. The top is labeled 12, the side of the blue rectangle is labeled 4. The whole side is labeled 10, the blue portion is labeled 4 and the red portion is labeled 6. The width of the red rectangle is labeled 2.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1446904\" data-type=\"media\" data-alt=\"The first line says A sub figure equals A sub rectangle plus A sub red rectangle. Below this is A sub figure equals bh plus red bh. Below this is A sub figure equals 12 times 4 plus red 2 times 6. Below this is A sub figure equals 48 plus red 12. Below this is A sub figure equals 60.\"><img class=\"alignnone aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_015_img.jpg\" alt=\"The first line says A sub figure equals A sub rectangle plus A sub red rectangle. Below this is A sub figure equals bh plus red bh. Below this is A sub figure equals 12 times 4 plus red 2 times 6. Below this is A sub figure equals 48 plus red 12. Below this is A sub figure equals 60.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171492752505\">The area of the figure is \\(60\\) square units.<\/p>\n<p id=\"fs-id1171505957472\">Is there another way to split this figure into two rectangles? Try it, and make sure you get the same area.<\/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 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1498168\" data-type=\"problem\">\n<p id=\"fs-id1587990\">Find the area of each shaded region:<\/p>\n<span id=\"fs-id1490086\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 8, the width of the horizontal rectangle is labeled as 2. The side is labeled as 6, the width of the vertical rectangle is labeled as 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_016_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 8, the width of the horizontal rectangle is labeled as 2. The side is labeled as 6, the width of the vertical rectangle is labeled as 3.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id2146187\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id967326\">28 sq. units<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1818370\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1933534\" data-type=\"exercise\">\n<div id=\"fs-id2146187\" 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 data-type=\"problem\">\n<p id=\"fs-id1747927\">Find the area of each shaded region:<\/p>\n<span id=\"fs-id1804616\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 14, the width of the horizontal rectangle is labeled as 5. The side is labeled as 10, the width of the missing space is labeled as 6.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_017_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 14, the width of the horizontal rectangle is labeled as 5. The side is labeled as 10, the width of the missing space is labeled as 6.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1934441\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171487146210\">110 sq. units<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1711806\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1565897\" data-type=\"exercise\">\n<div data-type=\"problem\">\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-id1171505780832\" data-type=\"problem\">\n<p id=\"fs-id1536095\">Find the area of the shaded region.<\/p>\n<span data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_018_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1581693\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1798630\">We can break this irregular figure into a triangle and rectangle. The area of the figure will be the sum of the areas of triangle and rectangle.<\/p>\n<p id=\"fs-id1778236\">The rectangle has a length of \\(8\\) units and a width of \\(4\\) units.<\/p>\n<p id=\"fs-id1171507039432\">We need to find the base and height of the triangle.<\/p>\n<p id=\"fs-id1928038\">Since both sides of the rectangle are \\(4\\), the vertical side of the triangle is \\(3\\), which is \\(7-4\\).<\/p>\n<p id=\"fs-id1703479\">The length of the rectangle is \\(8\\), so the base of the triangle will be \\(3\\), which is \\(8-4\\).<\/p>\n<span data-type=\"media\" data-alt=\"A geometric shape is shown. It is a blue rectangle with a red triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7. The right side of the rectangle is labeled 4. The right side and bottom of the triangle are labeled 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_019_img.jpg\" alt=\"A geometric shape is shown. It is a blue rectangle with a red triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7. The right side of the rectangle is labeled 4. The right side and bottom of the triangle are labeled 3.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1427689\">Now we can add the areas to find the area of the irregular figure.<\/p>\n<span id=\"fs-id1613556\" data-type=\"media\" data-alt=\"The top line reads A sub figure equals A sub rectangle plus A sub red triangle. The second line reads A sub figure equals lw plus one-half red bh. The next line says A sub figure equals 8 times 4 plus one-half times red 3 times red 3. The next line reads A sub figure equals 32 plus red 4.5. The last line says A sub figure equals 36.5 sq. units.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_020_img.jpg\" alt=\"The top line reads A sub figure equals A sub rectangle plus A sub red triangle. The second line reads A sub figure equals lw plus one-half red bh. The next line says A sub figure equals 8 times 4 plus one-half times red 3 times red 3. The next line reads A sub figure equals 32 plus red 4.5. The last line says A sub figure equals 36.5 sq. units.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1801421\">The area of the figure is \\(36.5\\) square units.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1934441\" data-type=\"solution\">\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-id1171498388257\" data-type=\"problem\">\n\nFind the area of each shaded region.\n\n<span id=\"fs-id1222516\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the lower right side. The base of the rectangle is labeled 8, the height of the rectangle is labeled 4. The distance from the top of the rectangle to where the triangle begins is labeled 3, the top of the triangle is labeled 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_021_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the lower right side. The base of the rectangle is labeled 8, the height of the rectangle is labeled 4. The distance from the top of the rectangle to where the triangle begins is labeled 3, the top of the triangle is labeled 3.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1595102\">36.5 sq. units<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1226083\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1874428\" data-type=\"exercise\">\n<div data-type=\"solution\">\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-id1800675\" data-type=\"problem\">\n<p id=\"fs-id1010201\">Find the area of each shaded region.<\/p>\n<span id=\"fs-id1818716\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with an equilateral triangle attached to the top. The base of the rectangle is labeled 12, each side is labeled 5. The base of the triangle is split into two pieces, each labeled 2.5.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_022_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with an equilateral triangle attached to the top. The base of the rectangle is labeled 12, each side is labeled 5. The base of the triangle is split into two pieces, each labeled 2.5.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1662331\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id2036916\">70 sq. units<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1486786\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2025833\" data-type=\"exercise\">\n<div id=\"fs-id1800675\" 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 id=\"fs-id1800675\" data-type=\"problem\">\n<div id=\"fs-id1856919\" data-type=\"problem\">\n<p id=\"fs-id1426894\">A high school track is shaped like a rectangle with a semi-circle (half a circle) on each end. The rectangle has length \\(105\\) metres and width \\(68\\) metres. Find the area enclosed by the track. Round your answer to the nearest hundredth.<\/p>\n<span id=\"fs-id1171498469825\" data-type=\"media\" data-alt=\"A track is shown, shaped like a rectangle with a semi-circle attached to each side.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_023.jpg\" alt=\"A track is shown, shaped like a rectangle with a semi-circle attached to each side.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1171509233619\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1171508048284\">We will break the figure into a rectangle and two semi-circles. The area of the figure will be the sum of the areas of the rectangle and the semicircles.<\/p>\n<span id=\"fs-id1560025\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with a semi-circle attached to each side. The base of the rectangle is labeled 105 m. The height of the rectangle and diametre of the circle on the left is labeled 68 m.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_024_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with a semi-circle attached to each side. The base of the rectangle is labeled 105 m. The height of the rectangle and diametre of the circle on the left is labeled 68 m.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1960367\">The rectangle has a length of \\(105\\) m and a width of \\(68\\) m. The semi-circles have a diametre of \\(68\\) m, so each has a radius of \\(34\\) m.<\/p>\n<span id=\"fs-id1349676\" data-type=\"media\" data-alt=\"The top line reads A sub figure equals A sub rectangle plus A sub semicircles. The second line reads A sub figure equals bh plus red 2 times (in parentheses) red 1\/2pi times r squared. The next line says A sub figure approximately equals 105 times 68 plus red 2 times (in parentheses) red 1\/2 times 3.14 times 34 squared. The next line reads A sub figure approximately equals 7140 plus red 3629.84. The last line says A sub figure approximately equals 10,769.84 square metres.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_030_img.jpg\" alt=\"The top line reads A sub figure equals A sub rectangle plus A sub semicircles. The second line reads A sub figure equals bh plus red 2 times (in parentheses) red 1\/2pi times r squared. The next line says A sub figure approximately equals 105 times 68 plus red 2 times (in parentheses) red 1\/2 times 3.14 times 34 squared. The next line reads A sub figure approximately equals 7140 plus red 3629.84. The last line says A sub figure approximately equals 10,769.84 square metres.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1662331\" 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-id1912783\" data-type=\"problem\">\n\nFind the area:\n\n<span id=\"fs-id1591392\" data-type=\"media\" data-alt=\"A shape is shown. It is a blue rectangle with a portion of the rectangle missing. There is a red circle the same height as the rectangle attached to the missing side of the rectangle. The top of the rectangle is labeled 15, the height is labeled 9.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_026_img.jpg\" alt=\"A shape is shown. It is a blue rectangle with a portion of the rectangle missing. There is a red circle the same height as the rectangle attached to the missing side of the rectangle. The top of the rectangle is labeled 15, the height is labeled 9.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1704279\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1555644\">103.2 sq. units<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1613271\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171505627162\" data-type=\"exercise\">\n<div id=\"fs-id1912783\" data-type=\"problem\">\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-id1766793\" data-type=\"problem\">\n<p id=\"fs-id1563626\">Find the area:<\/p>\n<span id=\"fs-id1559326\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It appears to be two trapezoids with a semicircle at the top. The base of the semicircle is labeled 5.2. The height of the trapezoids is labeled 6.5. The combined base of the trapezoids is labeled 3.3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_027_img.jpg\" alt=\"A blue geometric shape is shown. It appears to be two trapezoids with a semicircle at the top. The base of the semicircle is labeled 5.2. The height of the trapezoids is labeled 6.5. The combined base of the trapezoids is labeled 3.3.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<div id=\"fs-id1815364\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1171498405063\">38.24 sq. units<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1704279\" data-type=\"solution\">\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-id1171505622228\">\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24circumcircle\">Circumference of a Circle<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24areacircle\">Area of a Circle<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24areaLpoly\">Area of an L-shaped polygon<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24areaLpolyd\">Area of an L-shaped polygon with Decimals<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24perirectcirc\">Perimeter Involving a Rectangle and Circle<\/a><\/li>\n \t<li><a href=\"http:\/\/www.openstax.org\/l\/24arearectcirc\">Area Involving a Rectangle and Circle<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1869131\" class=\"media-2\" data-type=\"note\">\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"eip-557\">\n \t<li><strong>Problem Solving Strategy for Geometry Applications<\/strong>\n<ol id=\"eip-id1167297880352\" class=\"stepwise\" type=\"1\">\n \t<li>Read 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>Identify what you are looking for.<\/li>\n \t<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li>Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n \t<li>Solve the equation using good algebra techniques.<\/li>\n \t<li>Check the answer in the problem and make sure it makes sense.<\/li>\n \t<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong>Properties of Circles<\/strong>\n<span id=\"eip-id1165866546210\" data-type=\"media\" data-alt=\".\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_227_img.jpg\" alt=\".\" data-media-type=\"image\/jpg\"><\/span><\/li>\n<\/ul>\n<ul id=\"eip-id1168176888451\">\n \t<li>\\(d=2r\\)<\/li>\n \t<li><strong>Circumference:<\/strong>\\(C=2\\pi r\\) or \\(C=\\pi d\\)<\/li>\n \t<li><strong>Area:<\/strong>\\(A=\\pi {r}^{2}\\)<\/li>\n<\/ul>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1713352\">\n \t<dt>irregular figure<\/dt>\n \t<dd>An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1785546\">Use the Properties of Circles<\/h2>\n<p id=\"eip-772\">In the following exercises, solve using the properties of circles.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. The lid of a paint bucket is a circle with radius \\(7\\) inches. Find the a) circumference and b) area of the lid.<\/td>\n<td style=\"width: 50%;\">2. An extra-large pizza is a circle with radius \\(8\\) inches. Find the a) circumference and b) area of the pizza.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. A farm sprinkler spreads water in a circle with radius of \\(8.5\\) feet. Find the a) circumference and b) area of the watered circle.<\/td>\n<td style=\"width: 50%;\">4. A circular rug has radius of \\(3.5\\) feet. Find the a) circumference and b) area of the rug.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. A reflecting pool is in the shape of a circle with diametre of \\(20\\) feet. What is the circumference of the pool?<\/td>\n<td style=\"width: 50%;\">6. A turntable is a circle with diametre of \\(10\\) inches. What is the circumference of the turntable?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. A circular saw has a diametre of \\(12\\) inches. What is the circumference of the saw?<\/td>\n<td style=\"width: 50%;\">8. A round coin has a diametre of \\(3\\) centimetres. What is the circumference of the coin?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">9. A barbecue grill is a circle with a diametre of \\(2.2\\) feet. What is the circumference of the grill?<\/td>\n<td style=\"width: 50%;\">10. The top of a pie tin is a circle with a diametre of \\(9.5\\) inches. What is the circumference of the top?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. A circle has a circumference of \\(163.28\\) inches. Find the diametre.<\/td>\n<td style=\"width: 50%;\">12. A circle has a circumference of \\(59.66\\) feet. Find the diametre.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. A circle has a circumference of \\(17.27\\) metres. Find the diametre.<\/td>\n<td style=\"width: 50%;\">14. A circle has a circumference of \\(80.07\\) centimetres. Find the diametre.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nIn the following exercises, find the radius of the circle with given circumference.\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. A circle has a circumference of \\(150.72\\) feet.<\/td>\n<td style=\"width: 50%;\">16. A circle has a circumference of \\(251.2\\) centimetres.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. A circle has a circumference of \\(40.82\\) miles.<\/td>\n<td style=\"width: 50%;\">18. A circle has a circumference of \\(78.5\\) inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1683577\">Find the Area of Irregular Figures<\/h2>\nIn the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.\n<table style=\"border-collapse: collapse; width: 100%; height: 1595px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 130px;\">\n<td style=\"width: 50%; height: 130px;\"><span id=\"fs-id1529752\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a horizontal rectangle attached to a vertical rectangle. The top is labeled 6, the height of the horizontal rectangle is labeled 2, the distance from the edge of the horizontal rectangle to the start of the vertical rectangle is 4, the base of the vertical rectangle is 2, the right side of the shape is 4.\">19.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_201_img.jpg\" alt=\"A geometric shape is shown. It is a horizontal rectangle attached to a vertical rectangle. The top is labeled 6, the height of the horizontal rectangle is labeled 2, the distance from the edge of the horizontal rectangle to the start of the vertical rectangle is 4, the base of the vertical rectangle is 2, the right side of the shape is 4.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 130px;\"><span id=\"fs-id1171505779757\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is an L-shape. The base is labeled 10, the right side 1, the top and left side are each labeled 4.\">20.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_202_img.jpg\" alt=\"A geometric shape is shown. It is an L-shape. The base is labeled 10, the right side 1, the top and left side are each labeled 4.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 134px;\">\n<td style=\"width: 50%; height: 134px;\"><span id=\"fs-id1528128\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a sideways U-shape. The top is labeled 6, the left side is labeled 6. An inside horizontal piece is labeled 3. Each of the vertical pieces on the right are labeled 2.\">21.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_203_img.jpg\" alt=\"A geometric shape is shown. It is a sideways U-shape. The top is labeled 6, the left side is labeled 6. An inside horizontal piece is labeled 3. Each of the vertical pieces on the right are labeled 2.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 134px;\"><span id=\"fs-id956782\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a U-shape. The base is labeled 7. The right side is labeled 5. The two horizontal lines at the top and the vertical line on the inside are all labeled 3.\">22.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_204_img.jpg\" alt=\"A geometric shape is shown. It is a U-shape. The base is labeled 7. The right side is labeled 5. The two horizontal lines at the top and the vertical line on the inside are all labeled 3.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 224px;\">\n<td style=\"width: 50%; height: 224px;\"><span id=\"fs-id1171497978499\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the bottom left side. The top is labeled 4. The right side is labeled 10. The base is labeled 9. The vertical line from the top of the triangle to the top of the rectangle is labeled 3.\">23.\u00a0<img class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_205_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the bottom left side. The top is labeled 4. The right side is labeled 10. The base is labeled 9. The vertical line from the top of the triangle to the top of the rectangle is labeled 3.\" width=\"178\" height=\"222\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 224px;\"><span id=\"fs-id1909808\" data-type=\"media\" data-alt=\"A trapezoid is shown. The bases are labeled 5 and 10, the height is 5.\">24.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_206_img.jpg\" alt=\"A trapezoid is shown. The bases are labeled 5 and 10, the height is 5.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 214px;\">\n<td style=\"width: 50%; height: 214px;\"><span id=\"fs-id1651331\" data-type=\"media\" data-alt=\"Two triangles are shown. They appear to be right triangles. The bases are labeled 3, the heights 4, and the longest sides 5.\">25.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_207_img.jpg\" alt=\"Two triangles are shown. They appear to be right triangles. The bases are labeled 3, the heights 4, and the longest sides 5.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 214px;\"><span id=\"fs-id1171496188721\" data-type=\"media\" data-alt=\"A geometric shape is shown. It appears to be composed of two triangles. The shared base of both triangles is 8, the heights are both labeled 6.\">26.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_208_img.jpg\" alt=\"A geometric shape is shown. It appears to be composed of two triangles. The shared base of both triangles is 8, the heights are both labeled 6.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 193px;\">\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1767054\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is composed of two trapezoids. The base is labeled 10. The height of one trapezoid is 2. The horizontal and vertical sides are all labeled 5.\">27.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_209_img.jpg\" alt=\"A geometric shape is shown. It is composed of two trapezoids. The base is labeled 10. The height of one trapezoid is 2. The horizontal and vertical sides are all labeled 5.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1439058\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a trapezoid attached to a triangle. The base of the triangle is labeled 6, the height is labeled 5. The height of the trapezoid is 6, one base is 3.\">28.\u00a0<img class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_210_img.jpg\" alt=\"A geometric shape is shown. It is a trapezoid attached to a triangle. The base of the triangle is labeled 6, the height is labeled 5. The height of the trapezoid is 6, one base is 3.\" width=\"184\" height=\"192\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 286px;\">\n<td style=\"width: 50%; height: 286px;\"><span data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 8, the bottom is 8, the right side is 13, and the width of the smaller rectangle is 2.\">29.\u00a0<img class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_211_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 8, the bottom is 8, the right side is 13, and the width of the smaller rectangle is 2.\" width=\"187\" height=\"286\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 286px;\"><span id=\"fs-id1691446\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 12, the right side 7, the base 6. The width of the smaller rectangle is labeled 1.\">30.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_212_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 12, the right side 7, the base 6. The width of the smaller rectangle is labeled 1.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 193px;\">\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\">31.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_213_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\">32.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_214_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 165px;\">\n<td style=\"width: 50%; height: 165px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\"><span id=\"fs-id1684566\" data-type=\"media\" data-alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The base of the triangle is labeled 4. The height of the triangle and the diametre of the circle are 8.\">33.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_215_img.jpg\" alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The base of the triangle is labeled 4. The height of the triangle and the diametre of the circle are 8.\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<td style=\"width: 50%; height: 165px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\"><span id=\"fs-id1026279\" data-type=\"media\" data-alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The height of the triangle is labeled 4. The base of the triangle, also the diametre of the semi-circle, is labeled 4.\">34.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_216_img.jpg\" alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The height of the triangle is labeled 4. The base of the triangle, also the diametre of the semi-circle, is labeled 4.\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\"><span id=\"fs-id1110047\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\">35.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_217_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\"><span id=\"fs-id1171487155290\" data-type=\"media\" data-alt=\"A geometric shape is shown. A trapezoid is shown with a semi-circle attached to the top. The diametre of the circle, which is also the top of the trapezoid, is labeled 8. The height of the trapezoid is 6. The bottom of the trapezoid is 13.\">36.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_218_img.jpg\" alt=\"A geometric shape is shown. A trapezoid is shown with a semi-circle attached to the top. The diametre of the circle, which is also the top of the trapezoid, is labeled 8. The height of the trapezoid is 6. The bottom of the trapezoid is 13.\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\"><span id=\"fs-id1968285\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the top on the left side and a circle attached to the top right corner. The diametre of the circle is labeled 5. The height of the triangle is labeled 5, the base is labeled 4. The height of the rectangle is labeled 6, the base 11.\">37.\u00a0<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_219_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the top on the left side and a circle attached to the top right corner. The diametre of the circle is labeled 5. The height of the triangle is labeled 5, the base is labeled 4. The height of the rectangle is labeled 6, the base 11.\" data-media-type=\"image\/jpeg\"><\/span><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\"><span id=\"fs-id1783446\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a trapezoid with a triangle attached to the top, and a circle attached to the triangle. The diametre of the circle is 4. The height of the triangle is 5, the base of the triangle, which is also the top of the trapezoid, is 6. The bottom of the trapezoid is 9. The height of the trapezoid is 7.\">38.\u00a0<img class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_220_img.jpg\" alt=\"A geometric shape is shown. It is a trapezoid with a triangle attached to the top, and a circle attached to the triangle. The diametre of the circle is 4. The height of the triangle is 5, the base of the triangle, which is also the top of the trapezoid, is 6. The bottom of the trapezoid is 9. The height of the trapezoid is 7.\" width=\"182\" height=\"326\" data-media-type=\"image\/jpeg\">\u00a0<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1349800\">In the following exercises, solve.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id2021160\">39. A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides \\(250\\) feet long, and the triangles are isosceles right triangles. Find the area of the park.<\/p>\n<span id=\"fs-id1593422\" data-type=\"media\" data-alt=\"A square is shown with four triangles coming off each side.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_221_img.jpg\" alt=\"A square is shown with four triangles coming off each side.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%;\">40. A gift box will be made from a rectangular piece of cardboard measuring \\(12\\) inches by \\(20\\) inches, with squares cut out of the corners of the sides, as shown. The sides of the squares are \\(3\\) inches. Find the area of the cardboard after the corners are cut out.\n\n<span id=\"fs-id1723514\" data-type=\"media\" data-alt=\"A rectangle is shown. Each corner has a gray shaded square. There are dotted lines drawn across the side of each square attached to the next square.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_222_img.jpg\" alt=\"A rectangle is shown. Each corner has a gray shaded square. There are dotted lines drawn across the side of each square attached to the next square.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1578705\">41. Perry needs to put in a new lawn. His lot is a rectangle with a length of \\(120\\) feet and a width of \\(100\\) feet. The house is rectangular and measures \\(50\\) feet by \\(40\\) feet. His driveway is rectangular and measures \\(20\\) feet by \\(30\\) feet, as shown. Find the area of Perry\u2019s lawn.<\/p>\n<span id=\"fs-id1364316\" data-type=\"media\" data-alt=\"A rectangular lot is shown. In it is a home shaped like a rectangle attached to a rectangular driveway.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_223_img.jpg\" alt=\"A rectangular lot is shown. In it is a home shaped like a rectangle attached to a rectangular driveway.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1747055\">42. Denise is planning to put a deck in her back yard. The deck will be a \\(\\text{20-ft}\\) by \\(\\text{12-ft}\\) rectangle with a semicircle of diametre \\(6\\) feet, as shown below. Find the area of the deck.<\/p>\n<span id=\"fs-id1909803\" data-type=\"media\" data-alt=\"A picture of a deck is shown. It is shaped like a rectangle with a semi-circle attached to the top on the left side.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_224_img.jpg\" alt=\"A picture of a deck is shown. It is shaped like a rectangle with a semi-circle attached to the top on the left side.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171505622498\">43. <strong data-effect=\"bold\">Area of a Tabletop<\/strong> Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a \\(\\text{1-ft}\\) by \\(\\text{3-ft}\\) rectangle with a semicircle at each end, as shown. a) Find the area of the table with one leaf up. b) Find the area of the table with both leaves up.<\/p>\n<span id=\"fs-id2057237\" data-type=\"media\" data-alt=\"An image of a table is shown. There is a rectangular portion attached to a semi-circular portion. There is another semi-circular leaf folded down on the other side of the rectangle.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_225_img.jpg\" alt=\"An image of a table is shown. There is a rectangular portion attached to a semi-circular portion. There is another semi-circular leaf folded down on the other side of the rectangle.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%;\">44.<strong data-effect=\"bold\"> Painting<\/strong> Leora wants to paint the nursery in her house. The nursery is an \\(\\text{8-ft}\\) by \\(\\text{10-ft}\\) rectangle, and the ceiling is \\(8\\) feet tall. There is a \\(\\text{3-ft}\\) by \\(\\text{6.5-ft}\\) door on one wall, a \\(\\text{3-ft}\\) by \\(\\text{6.5-ft}\\) closet door on another wall, and one \\(\\text{4-ft}\\) by \\(\\text{3.5-ft}\\) window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?<\/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%;\">45. Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.\n\n<span id=\"fs-id1759532\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a vertical rectangle attached to a horizontal rectangle. The width of the vertical rectangle is 3, the left side is labeled 6, the bottom is labeled 9, and the width of the horizontal rectangle is labeled 3. The top of the horizontal rectangle is labeled 6, and the distance from the top of that rectangle to the top of the other rectangle is labeled 3.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_226_img.jpg\" alt=\"A geometric shape is shown. It is a vertical rectangle attached to a horizontal rectangle. The width of the vertical rectangle is 3, the left side is labeled 6, the bottom is labeled 9, and the width of the horizontal rectangle is labeled 3. The top of the horizontal rectangle is labeled 6, and the distance from the top of that rectangle to the top of the other rectangle is labeled 3.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%;\">46. A circle has a diametre of \\(14\\) feet. Find the area of the circle a) using \\(3.14\\) for \\(\\pi \\) b) using \\(\\frac{22}{7}\\) for \\(\\pi\\). c) Which calculation to do prefer? Why?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 style=\"text-align: left;\">Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 91.3242%; height: 226px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 103px;\">\n<td style=\"width: 36.9863%;\">1.\n\na) 43.96 in.\n\nb) 153.86 sq. in.<\/td>\n<td style=\"width: 27.245%;\">3.\n\na) 53.38 ft\n\nb) 226.865 sq. ft<\/td>\n<td style=\"width: 27.0167%;\">5. 62.8 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">7. 37.68 in.<\/td>\n<td style=\"width: 27.245%;\">9. 6.908 ft<\/td>\n<td style=\"width: 27.0167%;\">11. 52 in.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">13. 5.5 m<\/td>\n<td style=\"width: 27.245%;\">15. 24 ft<\/td>\n<td style=\"width: 27.0167%;\">17. 6.5 mi<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">19. 16 sq. units<\/td>\n<td style=\"width: 27.245%;\">21. 30 sq. units<\/td>\n<td style=\"width: 27.0167%;\">23. 57.5 sq. units<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">25. 12 sq. units<\/td>\n<td style=\"width: 27.245%;\">27. 67.5 sq. units<\/td>\n<td style=\"width: 27.0167%;\">29. 89 sq. units<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">31. 44.81 sq. units<\/td>\n<td style=\"width: 27.245%;\">33. 41.12 sq. units<\/td>\n<td style=\"width: 27.0167%;\">35. 35.13 sq. units<\/td>\n<\/tr>\n<tr style=\"height: 10px;\">\n<td style=\"width: 36.9863%;\">37. 95.625 sq. units<\/td>\n<td style=\"width: 27.245%;\">39. 187,500 sq. ft<\/td>\n<td style=\"width: 27.0167%;\">41. 9400 sq. ft<\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"width: 36.9863%;\">43. a) 6.5325 sq. ft\u00a0 b) 10.065 sq. ft<\/td>\n<td style=\"width: 27.245%;\">45.\u00a0Answers will vary.<\/td>\n<td style=\"width: 27.0167%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cSolve Geometry Applications: Circles and Irregular Figures\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>Use the properties of circles<\/li>\n<li>Find the area of irregular figures<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1171506645886\">In this section, we\u2019ll continue working with geometry applications. We will add several new formulas to our collection of formulas. To help you as you do the examples and exercises in this section, we will show 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\">Problem Solving Strategy for Geometry Applications<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"eip-id1168469784124\" class=\"stepwise\" type=\"1\">\n<li><strong>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>Identify <\/strong> what you are looking for.<\/li>\n<li><strong>Name <\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong>Translate <\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong>Solve <\/strong> the equation using good algebra techniques.<\/li>\n<li><strong>Check <\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong>Answer <\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1>Use the Properties of Circles<\/h1>\n<p id=\"fs-id1613325\">\u00a0We\u2019ll\u00a0 refer to the properties of circles as we use them to solve applications.<\/p>\n<div id=\"fs-id1171506663136\" 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 Circles<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><span id=\"fs-id1365138\" data-type=\"media\" data-alt=\"An image of a circle is shown. There is a line drawn through the widest part at the centre of the circle with a red dot indicating the centre of the circle. The line is labeled d. The two segments from the centre of the circle to the outside of the circle are each labeled r.\"><img decoding=\"async\" class=\"alignright\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_09_05_001.jpg\" alt=\"An image of a circle is shown. There is a line drawn through the widest part at the centre of the circle with a red dot indicating the centre of the circle. The line is labeled d. The two segments from the centre of the circle to the outside of the circle are each labeled r.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<ul id=\"fs-id1489165\" data-bullet-style=\"bullet\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> is the length of the radius<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e8716946f6a868f015e0d62f28bc540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> is the length of the diametre<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8555898f6852f975d8aa259fdbfa726b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#50;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/li>\n<li>Circumference is the perimeter of a circle. The formula for circumference is\n<div id=\"fs-id1171105198477\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-767e9ce0b2254f27d4d47053aaa6d025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#50;&#92;&#112;&#105;&#32;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" style=\"vertical-align: 0px;\" \/><\/div>\n<\/li>\n<li>The formula for area of a circle is\n<div id=\"fs-id1171105180774\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f1af377446d8cedd8e9b8ffe9159a0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: 0px;\" \/><\/div>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p>Remember, that we approximate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-980f77b67737a79200c69c26bf9f365c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da5064f8df8d52c5cf0c9150d7a271ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> depending on whether the radius of the circle is given as a decimal or a fraction. If you use the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> key on your calculator to do the calculations in this section, your answers will be slightly different from the answers shown. That is because the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> key uses more than two decimal places.<\/p>\n<\/div>\n<\/div>\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-id1549320\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171513637241\" data-type=\"exercise\">\n<div id=\"fs-id1323804\" data-type=\"problem\">\n<div id=\"fs-id1171487568034\" data-type=\"problem\">\n<p id=\"fs-id1933138\">A circular sandbox has a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet. Find the a) circumference and b) area of the sandbox.<\/p>\n<\/div>\n<div id=\"fs-id1587329\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">a)<\/div>\n<table id=\"eip-id1168467555346\" 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 circle. The radius is labeled r equals 2.5 ft. 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 circumference of the circle.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is C equals 2 pi r. Below this is C equals 2 times pi times 2.5 ft., then C is approximately 2 times 3.14 times 2.5 ft. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is C is approximately 2 times 3.14 times 2.5, then C is approximately 15.7 feet. Step 6 says, \u201cCheck,\u201d in bold. Then, \u201cDoes this answer make sense? Yes. If we draw a square around the circle, its sides would be 5 ft. (twice the radius), so its perimeter would be 20 ft. This is slightly more than the circle's circumference, 15.7 ft. Beneath this is a picture of the circle with a red square drawn around it. Each side of the square is labeled 5 ft. The radius is labeled as r equals 2.5 ft. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe circumference of the sandbox is 15.7 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-id1168468498969\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_029_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 circumference of the circle<\/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> = circumference of the circle<\/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><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-767e9ce0b2254f27d4d47053aaa6d025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#50;&#92;&#112;&#105;&#32;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-24cd31901070fd2a84d53461d1a6ee37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#50;&#92;&#112;&#105;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">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-fac1f11301c7fc3f7e084fa7c898ede1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"134\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d14dc68c8ca0fec54bd6069d8ab6c606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#49;&#53;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"67\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check.<\/strong> Does this answer make sense?<br \/>\nYes. If we draw a square around the circle, its sides would be 5 ft (twice the radius), so its perimeter would be 20 ft. This is slightly more than the circle&#8217;s circumference, 15.7 ft.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_029_img-02.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 circumference of the sandbox is 15.7 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>b)<\/p>\n<table id=\"eip-id1168468253524\" class=\"unnumbered unstyled\" summary=\"Identify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe area of the circle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201cA equals pi r squared.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is A equals pi times r squared. Below this is A is approximately 3.14 times 2.5 ft. squared. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is A is approximately 19.625 square feet. Step 6 says, \u201cCheck,\u201d in bold. Then, \u201cDoes this answer make sense? Yes. If we draw a square around the circle, its sides would be 5 ft., as shown in part a. So the area of the square would be 25 sq. ft. This is slightly more than the circle's area, 19.625 sq. ft. Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe area of the circle is 19.625 square feet.\" 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-id1168467313672\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_029_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 circle<\/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 of the circle<\/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><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38ff99c5998e7053c90da9adc6494d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#112;&#105;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7cc5cf11d9c4f5b362450ac473091fac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#112;&#105;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"91\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td data-valign=\"top\">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-deba3da67c297270e9fbd16bbc5bc73f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"129\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c64d4ce5ac25cfc9746747d0c197190_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#49;&#57;&#46;&#54;&#50;&#53;&#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;&#46;&#32;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"130\" style=\"vertical-align: -3px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check.<\/strong><br \/>\nYes. If we draw a square around the circle, its sides would be 5 ft, as shown in part a). So the area of the square would be 25 sq. ft. This is slightly more than the circle&#8217;s area, 19.625 sq. ft.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The area of the circle is 19.625 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-id1549320\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171513637241\" data-type=\"exercise\">\n<div id=\"fs-id1323804\" data-type=\"problem\">\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-id1323804\" data-type=\"problem\">\n<p id=\"fs-id2146917\">A circular mirror has radius of <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. Find the a) circumference and b) area of the mirror.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168469728002\" class=\"circled\" type=\"a\">\n<li>31.4 in.<\/li>\n<li>78.5 sq. in.<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div 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-id1171505810220\" data-type=\"problem\">\n<p id=\"fs-id1665536\">A circular spa has radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8fac357af10206befdb463e651007c5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"22\" style=\"vertical-align: -1px;\" \/> feet. Find the a) circumference and b) area of the spa.<\/p>\n<\/div>\n<div id=\"fs-id1574843\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168469655844\" class=\"circled\" type=\"a\">\n<li>28.26 ft<\/li>\n<li>63.585 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>We usually see the formula for circumference in terms of the radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> of the circle:<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171105527474\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-767e9ce0b2254f27d4d47053aaa6d025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#50;&#92;&#112;&#105;&#32;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" style=\"vertical-align: 0px;\" \/><\/div>\n<p id=\"fs-id1685662\">But since the diametre of a circle is two times the radius, we could write the formula for the circumference in terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72b97db2a6174b5343eb5364cff1e44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#125;&#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;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"28\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1171105202378\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-760e15765fe01c530a651b5fcaa93e26_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;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#67;&#61;&#50;&#92;&#112;&#105;&#32;&#114;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#115;&#105;&#110;&#103;&#32;&#116;&#104;&#101;&#32;&#99;&#111;&#109;&#109;&#117;&#116;&#97;&#116;&#105;&#118;&#101;&#32;&#112;&#114;&#111;&#112;&#101;&#114;&#116;&#121;&#44;&#32;&#119;&#101;&#32;&#103;&#101;&#116;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#67;&#61;&#92;&#112;&#105;&#32;&#92;&#99;&#100;&#111;&#116;&#50;&#114;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#110;&#32;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#105;&#110;&#103;&#125;&#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;&#100;&#61;&#50;&#114;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#67;&#61;&#92;&#112;&#105;&#32;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#111;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#67;&#61;&#92;&#112;&#105;&#32;&#100;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"439\" style=\"vertical-align: -33px;\" \/><\/div>\n<p id=\"fs-id1567127\">We will use this form of the circumference when we\u2019re given the length of the diametre instead of the radius.<\/p>\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 data-type=\"problem\">\n<p>A circular table has a diametre of four feet. What is the circumference of the table?<\/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-id1168467247251\" 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 circular table. The diametre is labeled d equals 4 ft. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this is \u201cthe circumference of the table.\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 circumference of the table.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute.\u201d The word \u201ctranslate\u201d is in bold. Beside this is C equals pi d. Below this is C equals pi times 4. Step 5 says, \u201cSolve the equation, using 3.14 for pi.\u201d The word \u201csolve\u201d is in bold. Beside this is C is approximately 3.14 times 4, then C is approximately 12.56 feet. Step 6 says, \u201cCheck,\u201d in bold. Then, \u201cIf we put a square around the circle, its side would be 4. The perimeter would be 16. It makes sense that the circumference of the circle, 12.56, a little less than 16.\u201d Beneath this is a picture of the circle with a red square drawn around it. Each side of the square is labeled 4 ft. The diametre is labeled as d equals 4 ft. Step 7 says, \u201cAnswer the question\u201d in bold. The answer is given as \u201cThe diametre of the table is 12.56 square feet.\" 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-id1168467253483\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_032_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 circumference of the table<\/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 circumference of the table<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula for the situation.<br \/>\nSubstitute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d53af99f4271505ce26601a2fb3edbbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#112;&#105;&#32;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-388607ca41c7989e1dd866a7a9c3badd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#112;&#105;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation, using 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f9d7dd3ceffb07c7f8e4135095f0f3c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-653c383f36200cb790624469e5ba3f03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#49;&#50;&#46;&#53;&#54;&#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;&#102;&#101;&#101;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"109\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> If we put a square around the circle, its side would be 4.<br \/>\nThe perimeter would be 16. It makes sense that the circumference of the circle, 12.56, is a little less than 16.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_032_img-02.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 diametre of the table is 12.56 square 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 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1553333\" data-type=\"problem\">\n<p id=\"fs-id1573443\">Find the circumference of a circular fire pit whose diametre is <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;\" \/> feet.<\/p>\n<\/div>\n<div id=\"fs-id1171505794101\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171506644144\">17.27 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1864175\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1867339\" data-type=\"exercise\">\n<div id=\"fs-id1553333\" 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 data-type=\"problem\">\n<p>If the diametre of a circular trampoline 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 its circumference?<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>37.68 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1349580\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1610347\" data-type=\"exercise\">\n<div data-type=\"solution\">\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-id1683811\" data-type=\"problem\">\n<p id=\"fs-id1498081\">Find the diametre of a circle with a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49a1b169e870f0551a79d79fffc8cf99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#55;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"31\" style=\"vertical-align: -1px;\" \/> centimetres.<\/p>\n<\/div>\n<div id=\"fs-id1418161\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468767882\" 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 circle. The diametre is labeled d. Below this is C equals 47.1 cm. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this is \u201cthe diametre of the circle.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet d equal the diametre of the circle.\u201d Step 4 says, \u201cTranslate. Write the formula. Substitute, using 3.14 to approximate pi.\u201d The word \u201ctranslate\u201d is in bold. Beside this is C equals pi times d. Below this is 47.1 cm. is approximately 3.14 times d. Step 5 says \u201csolve\u201d in bold. Beside this is 47.1 over 3.14 is approximately 3.14d over 3.14, then 15 is approximately d. Step 6 says, \u201cCheck,\u201d in bold. Beside this is C equals pi times d, then 47.1 followed by an equal sign with a question mark, then 3.14 times 15. Below this is 47.1 equals 47.1, followed by a check mark. Step 7 says, \u201cAnswer the question\u201d in bold. The answer is given as \u201cThe diametre of the circle is approximately 15 centimetres.\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-id1168467257979\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_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 diametre of the circle<\/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\">d<\/em> = the diametre of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the formula.<br \/>\nSubstitute, using 3.14 to approximate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td><span id=\"eip-id1168467143388\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-02.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168468597734\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-03.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><\/td>\n<td><span id=\"eip-id1168467258996\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-04.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><br \/>\n<span id=\"eip-id1168467173423\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-05.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-809ebbd5e8a5859d79c90b2700e76c90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#55;&#46;&#49;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"134\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e87f44c1c5515636998c9bdae52755b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#55;&#46;&#49;&#61;&#52;&#55;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"86\" style=\"vertical-align: 0px;\" \/>\u2713<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_033_img-06.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer the question.<\/strong><\/td>\n<td>The diametre of the circle is approximately 15 centimetres.<\/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-id1171505481386\" data-type=\"problem\">\n<p id=\"fs-id1171498370892\">Find the diametre of a circle with circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15df659da93720bd83c6148c70d49198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#52;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> centimetres.<\/p>\n<\/div>\n<div id=\"fs-id2063819\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id2032181\">30 cm<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1713306\" data-type=\"exercise\">\n<div id=\"fs-id2063819\" 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-id1347320\" data-type=\"problem\">\n<p id=\"fs-id1171505977370\">Find the diametre of a circle with circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-51fcf0e1395f508c0f219cda19444332_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#52;&#53;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"41\" style=\"vertical-align: -1px;\" \/> feet.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1798736\">110 ft<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Area of Irregular Figures<\/h1>\n<p id=\"fs-id1171487154912\">So far, we have found area for rectangles, triangles, trapezoids, and circles. An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas. But some irregular figures are made up of two or more standard geometric shapes. To find the area of one of these irregular figures, we can split it into figures whose formulas we know and then add the areas of the figures.<\/p>\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-id1867154\" data-type=\"problem\">\n<p id=\"fs-id1580231\">Find the area of the shaded region.<\/p>\n<p><strong><span id=\"fs-id1686212\" data-type=\"media\" data-alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_012_img.jpg\" alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\" data-media-type=\"image\/jpeg\" \/><\/span><\/strong><\/p>\n<\/div>\n<div id=\"fs-id1885059\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1868264\">The given figure is irregular, but we can break it into two rectangles. The area of the shaded region will be the sum of the areas of both rectangles.<\/p>\n<p><span data-type=\"media\" data-alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_013_img.jpg\" alt=\"An image of an attached horizontal rectangle and a vertical rectangle is shown. The top is labeled 12, the side of the horizontal rectangle is labeled 4. The side is labeled 10, the width of the vertical rectangle is labeled 2.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1474787\">The blue rectangle has a width of <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;\" \/> and a length of <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;\" \/>. The red rectangle has a width of <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;\" \/>, but its length is not labeled. The right side of the figure is the length of the red rectangle plus the length of the blue rectangle. Since the right side of the blue rectangle is <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;\" \/> units long, the length of the red rectangle must be <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;\" \/> units.<\/p>\n<p><span id=\"fs-id1183456\" data-type=\"media\" data-alt=\"An image of a blue horizontal rectangle attached to a red vertical rectangle is shown. The top is labeled 12, the side of the blue rectangle is labeled 4. The whole side is labeled 10, the blue portion is labeled 4 and the red portion is labeled 6. The width of the red rectangle is labeled 2.\"><img decoding=\"async\" class=\"alignnone aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_014_img.jpg\" alt=\"An image of a blue horizontal rectangle attached to a red vertical rectangle is shown. The top is labeled 12, the side of the blue rectangle is labeled 4. The whole side is labeled 10, the blue portion is labeled 4 and the red portion is labeled 6. The width of the red rectangle is labeled 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1446904\" data-type=\"media\" data-alt=\"The first line says A sub figure equals A sub rectangle plus A sub red rectangle. Below this is A sub figure equals bh plus red bh. Below this is A sub figure equals 12 times 4 plus red 2 times 6. Below this is A sub figure equals 48 plus red 12. Below this is A sub figure equals 60.\"><img decoding=\"async\" class=\"alignnone aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_015_img.jpg\" alt=\"The first line says A sub figure equals A sub rectangle plus A sub red rectangle. Below this is A sub figure equals bh plus red bh. Below this is A sub figure equals 12 times 4 plus red 2 times 6. Below this is A sub figure equals 48 plus red 12. Below this is A sub figure equals 60.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171492752505\">The area of the figure 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;\" \/> square units.<\/p>\n<p id=\"fs-id1171505957472\">Is there another way to split this figure into two rectangles? Try it, and make sure you get the same area.<\/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 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1498168\" data-type=\"problem\">\n<p id=\"fs-id1587990\">Find the area of each shaded region:<\/p>\n<p><span id=\"fs-id1490086\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 8, the width of the horizontal rectangle is labeled as 2. The side is labeled as 6, the width of the vertical rectangle is labeled as 3.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_016_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 8, the width of the horizontal rectangle is labeled as 2. The side is labeled as 6, the width of the vertical rectangle is labeled as 3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id2146187\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id967326\">28 sq. units<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1818370\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1933534\" data-type=\"exercise\">\n<div id=\"fs-id2146187\" 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 data-type=\"problem\">\n<p id=\"fs-id1747927\">Find the area of each shaded region:<\/p>\n<p><span id=\"fs-id1804616\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 14, the width of the horizontal rectangle is labeled as 5. The side is labeled as 10, the width of the missing space is labeled as 6.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_017_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a horizontal rectangle attached to a vertical rectangle. The top is labeled as 14, the width of the horizontal rectangle is labeled as 5. The side is labeled as 10, the width of the missing space is labeled as 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1934441\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171487146210\">110 sq. units<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1711806\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1565897\" data-type=\"exercise\">\n<div data-type=\"problem\">\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-id1171505780832\" data-type=\"problem\">\n<p id=\"fs-id1536095\">Find the area of the shaded region.<\/p>\n<p><span data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_018_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1581693\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1798630\">We can break this irregular figure into a triangle and rectangle. The area of the figure will be the sum of the areas of triangle and rectangle.<\/p>\n<p id=\"fs-id1778236\">The rectangle has a length 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;\" \/> units and a width of <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;\" \/> units.<\/p>\n<p id=\"fs-id1171507039432\">We need to find the base and height of the triangle.<\/p>\n<p id=\"fs-id1928038\">Since both sides of the rectangle 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;\" \/>, the vertical side of the triangle 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;\" \/>, which is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ad08e565aed640d068767233478786cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"fs-id1703479\">The length of the 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;\" \/>, so the base of the triangle will be <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;\" \/>, which is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-71cc0e8882553a4a50f89b54e6a19aea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p><span data-type=\"media\" data-alt=\"A geometric shape is shown. It is a blue rectangle with a red triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7. The right side of the rectangle is labeled 4. The right side and bottom of the triangle are labeled 3.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_019_img.jpg\" alt=\"A geometric shape is shown. It is a blue rectangle with a red triangle attached to the top on the right side. The left side is labeled 4, the top 5, the bottom 8, the right side 7. The right side of the rectangle is labeled 4. The right side and bottom of the triangle are labeled 3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1427689\">Now we can add the areas to find the area of the irregular figure.<\/p>\n<p><span id=\"fs-id1613556\" data-type=\"media\" data-alt=\"The top line reads A sub figure equals A sub rectangle plus A sub red triangle. The second line reads A sub figure equals lw plus one-half red bh. The next line says A sub figure equals 8 times 4 plus one-half times red 3 times red 3. The next line reads A sub figure equals 32 plus red 4.5. The last line says A sub figure equals 36.5 sq. units.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_020_img.jpg\" alt=\"The top line reads A sub figure equals A sub rectangle plus A sub red triangle. The second line reads A sub figure equals lw plus one-half red bh. The next line says A sub figure equals 8 times 4 plus one-half times red 3 times red 3. The next line reads A sub figure equals 32 plus red 4.5. The last line says A sub figure equals 36.5 sq. units.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1801421\">The area of the figure is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d4b3af9422fbd469cebb4e9bf1299df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> square units.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1934441\" data-type=\"solution\">\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-id1171498388257\" data-type=\"problem\">\n<p>Find the area of each shaded region.<\/p>\n<p><span id=\"fs-id1222516\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the lower right side. The base of the rectangle is labeled 8, the height of the rectangle is labeled 4. The distance from the top of the rectangle to where the triangle begins is labeled 3, the top of the triangle is labeled 3.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_021_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with a triangle attached to the lower right side. The base of the rectangle is labeled 8, the height of the rectangle is labeled 4. The distance from the top of the rectangle to where the triangle begins is labeled 3, the top of the triangle is labeled 3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1595102\">36.5 sq. units<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1226083\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1874428\" data-type=\"exercise\">\n<div data-type=\"solution\">\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-id1800675\" data-type=\"problem\">\n<p id=\"fs-id1010201\">Find the area of each shaded region.<\/p>\n<p><span id=\"fs-id1818716\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with an equilateral triangle attached to the top. The base of the rectangle is labeled 12, each side is labeled 5. The base of the triangle is split into two pieces, each labeled 2.5.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_022_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with an equilateral triangle attached to the top. The base of the rectangle is labeled 12, each side is labeled 5. The base of the triangle is split into two pieces, each labeled 2.5.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1662331\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id2036916\">70 sq. units<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1486786\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2025833\" data-type=\"exercise\">\n<div id=\"fs-id1800675\" 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 id=\"fs-id1800675\" data-type=\"problem\">\n<div id=\"fs-id1856919\" data-type=\"problem\">\n<p id=\"fs-id1426894\">A high school track is shaped like a rectangle with a semi-circle (half a circle) on each end. The rectangle has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-077994c193e366e731b386b8503f548d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"25\" style=\"vertical-align: -1px;\" \/> metres and width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e3b92253edc96beb52811ed30fc440d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres. Find the area enclosed by the track. Round your answer to the nearest hundredth.<\/p>\n<p><span id=\"fs-id1171498469825\" data-type=\"media\" data-alt=\"A track is shown, shaped like a rectangle with a semi-circle attached to each side.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_023.jpg\" alt=\"A track is shown, shaped like a rectangle with a semi-circle attached to each side.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1171509233619\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1171508048284\">We will break the figure into a rectangle and two semi-circles. The area of the figure will be the sum of the areas of the rectangle and the semicircles.<\/p>\n<p><span id=\"fs-id1560025\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It looks like a rectangle with a semi-circle attached to each side. The base of the rectangle is labeled 105 m. The height of the rectangle and diametre of the circle on the left is labeled 68 m.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_024_img.jpg\" alt=\"A blue geometric shape is shown. It looks like a rectangle with a semi-circle attached to each side. The base of the rectangle is labeled 105 m. The height of the rectangle and diametre of the circle on the left is labeled 68 m.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1960367\">The rectangle has a length of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-077994c193e366e731b386b8503f548d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"25\" style=\"vertical-align: -1px;\" \/> m and a width of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e3b92253edc96beb52811ed30fc440d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> m. The semi-circles have a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e3b92253edc96beb52811ed30fc440d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> m, so each has a radius of <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;\" \/> m.<\/p>\n<p><span id=\"fs-id1349676\" data-type=\"media\" data-alt=\"The top line reads A sub figure equals A sub rectangle plus A sub semicircles. The second line reads A sub figure equals bh plus red 2 times (in parentheses) red 1\/2pi times r squared. The next line says A sub figure approximately equals 105 times 68 plus red 2 times (in parentheses) red 1\/2 times 3.14 times 34 squared. The next line reads A sub figure approximately equals 7140 plus red 3629.84. The last line says A sub figure approximately equals 10,769.84 square metres.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_030_img.jpg\" alt=\"The top line reads A sub figure equals A sub rectangle plus A sub semicircles. The second line reads A sub figure equals bh plus red 2 times (in parentheses) red 1\/2pi times r squared. The next line says A sub figure approximately equals 105 times 68 plus red 2 times (in parentheses) red 1\/2 times 3.14 times 34 squared. The next line reads A sub figure approximately equals 7140 plus red 3629.84. The last line says A sub figure approximately equals 10,769.84 square metres.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1662331\" 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-id1912783\" data-type=\"problem\">\n<p>Find the area:<\/p>\n<p><span id=\"fs-id1591392\" data-type=\"media\" data-alt=\"A shape is shown. It is a blue rectangle with a portion of the rectangle missing. There is a red circle the same height as the rectangle attached to the missing side of the rectangle. The top of the rectangle is labeled 15, the height is labeled 9.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_026_img.jpg\" alt=\"A shape is shown. It is a blue rectangle with a portion of the rectangle missing. There is a red circle the same height as the rectangle attached to the missing side of the rectangle. The top of the rectangle is labeled 15, the height is labeled 9.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1704279\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1555644\">103.2 sq. units<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1613271\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171505627162\" data-type=\"exercise\">\n<div id=\"fs-id1912783\" data-type=\"problem\">\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-id1766793\" data-type=\"problem\">\n<p id=\"fs-id1563626\">Find the area:<\/p>\n<p><span id=\"fs-id1559326\" data-type=\"media\" data-alt=\"A blue geometric shape is shown. It appears to be two trapezoids with a semicircle at the top. The base of the semicircle is labeled 5.2. The height of the trapezoids is labeled 6.5. The combined base of the trapezoids is labeled 3.3.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_027_img.jpg\" alt=\"A blue geometric shape is shown. It appears to be two trapezoids with a semicircle at the top. The base of the semicircle is labeled 5.2. The height of the trapezoids is labeled 6.5. The combined base of the trapezoids is labeled 3.3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<div id=\"fs-id1815364\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1171498405063\">38.24 sq. units<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1704279\" data-type=\"solution\">\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-id1171505622228\">\n<li><a href=\"http:\/\/www.openstax.org\/l\/24circumcircle\">Circumference of a Circle<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24areacircle\">Area of a Circle<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24areaLpoly\">Area of an L-shaped polygon<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24areaLpolyd\">Area of an L-shaped polygon with Decimals<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24perirectcirc\">Perimeter Involving a Rectangle and Circle<\/a><\/li>\n<li><a href=\"http:\/\/www.openstax.org\/l\/24arearectcirc\">Area Involving a Rectangle and Circle<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1869131\" class=\"media-2\" data-type=\"note\">\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"eip-557\">\n<li><strong>Problem Solving Strategy for Geometry Applications<\/strong>\n<ol id=\"eip-id1167297880352\" class=\"stepwise\" type=\"1\">\n<li>Read 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>Identify what you are looking for.<\/li>\n<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li>Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li>Solve the equation using good algebra techniques.<\/li>\n<li>Check the answer in the problem and make sure it makes sense.<\/li>\n<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Properties of Circles<\/strong><br \/>\n<span id=\"eip-id1165866546210\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_227_img.jpg\" alt=\".\" data-media-type=\"image\/jpg\" \/><\/span><\/li>\n<\/ul>\n<ul id=\"eip-id1168176888451\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8555898f6852f975d8aa259fdbfa726b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#50;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><strong>Circumference:<\/strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-767e9ce0b2254f27d4d47053aaa6d025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#50;&#92;&#112;&#105;&#32;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"65\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d53af99f4271505ce26601a2fb3edbbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#61;&#92;&#112;&#105;&#32;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><strong>Area:<\/strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f1af377446d8cedd8e9b8ffe9159a0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#61;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1713352\">\n<dt>irregular figure<\/dt>\n<dd>An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1785546\">Use the Properties of Circles<\/h2>\n<p id=\"eip-772\">In the following exercises, solve using the properties of circles.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. The lid of a paint bucket is a circle with radius <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. Find the a) circumference and b) area of the lid.<\/td>\n<td style=\"width: 50%;\">2. An extra-large pizza is a circle with radius <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. Find the a) circumference and b) area of the pizza.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. A farm sprinkler spreads water in a circle with radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18a69ce801ebb07a7893aeb4b5b8b4d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet. Find the a) circumference and b) area of the watered circle.<\/td>\n<td style=\"width: 50%;\">4. A circular rug has radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a880aa3dee267fff1a375dd7cfcaa389_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet. Find the a) circumference and b) area of the rug.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. A reflecting pool is in the shape of a circle with diametre 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. What is the circumference of the pool?<\/td>\n<td style=\"width: 50%;\">6. A turntable is a circle with diametre of <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. What is the circumference of the turntable?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. A circular saw has a diametre of <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. What is the circumference of the saw?<\/td>\n<td style=\"width: 50%;\">8. A round coin has a diametre of <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;\" \/> centimetres. What is the circumference of the coin?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">9. A barbecue grill is a circle with a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f660b802d2f7d82d22e350fcb188c68d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet. What is the circumference of the grill?<\/td>\n<td style=\"width: 50%;\">10. The top of a pie tin is a circle with a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4ab482df63d7cab1dd10b6fc001025ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> inches. What is the circumference of the top?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5495c7255e7c83e47e9e5974e68b0362_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#51;&#46;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: -1px;\" \/> inches. Find the diametre.<\/td>\n<td style=\"width: 50%;\">12. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e5893cbf3d461bfdec9288dbba7e9b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#57;&#46;&#54;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/> feet. Find the diametre.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e54ebf9a8eba18f8847ec9c5fffc060_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#46;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> metres. Find the diametre.<\/td>\n<td style=\"width: 50%;\">14. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f4a62b07e885995377520cf75061ea3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#48;&#46;&#48;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"41\" style=\"vertical-align: 0px;\" \/> centimetres. Find the diametre.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In the following exercises, find the radius of the circle with given circumference.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">15. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a8fcf451bba2977e1d4dd0972c3d132_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#48;&#46;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -1px;\" \/> feet.<\/td>\n<td style=\"width: 50%;\">16. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d08ec7f14150996d79ab152c2b82e7c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#49;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> centimetres.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cebc4690335951c04f8622ee919a8be8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;&#46;&#56;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> miles.<\/td>\n<td style=\"width: 50%;\">18. A circle has a circumference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5abcf4ad2aaa337a8c1e30f4f301708d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#56;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1683577\">Find the Area of Irregular Figures<\/h2>\n<p>In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 1595px;\">\n<tbody>\n<tr style=\"height: 130px;\">\n<td style=\"width: 50%; height: 130px;\"><span id=\"fs-id1529752\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a horizontal rectangle attached to a vertical rectangle. The top is labeled 6, the height of the horizontal rectangle is labeled 2, the distance from the edge of the horizontal rectangle to the start of the vertical rectangle is 4, the base of the vertical rectangle is 2, the right side of the shape is 4.\">19.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_201_img.jpg\" alt=\"A geometric shape is shown. It is a horizontal rectangle attached to a vertical rectangle. The top is labeled 6, the height of the horizontal rectangle is labeled 2, the distance from the edge of the horizontal rectangle to the start of the vertical rectangle is 4, the base of the vertical rectangle is 2, the right side of the shape is 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 130px;\"><span id=\"fs-id1171505779757\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is an L-shape. The base is labeled 10, the right side 1, the top and left side are each labeled 4.\">20.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_202_img.jpg\" alt=\"A geometric shape is shown. It is an L-shape. The base is labeled 10, the right side 1, the top and left side are each labeled 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 134px;\">\n<td style=\"width: 50%; height: 134px;\"><span id=\"fs-id1528128\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a sideways U-shape. The top is labeled 6, the left side is labeled 6. An inside horizontal piece is labeled 3. Each of the vertical pieces on the right are labeled 2.\">21.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_203_img.jpg\" alt=\"A geometric shape is shown. It is a sideways U-shape. The top is labeled 6, the left side is labeled 6. An inside horizontal piece is labeled 3. Each of the vertical pieces on the right are labeled 2.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 134px;\"><span id=\"fs-id956782\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a U-shape. The base is labeled 7. The right side is labeled 5. The two horizontal lines at the top and the vertical line on the inside are all labeled 3.\">22.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_204_img.jpg\" alt=\"A geometric shape is shown. It is a U-shape. The base is labeled 7. The right side is labeled 5. The two horizontal lines at the top and the vertical line on the inside are all labeled 3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 224px;\">\n<td style=\"width: 50%; height: 224px;\"><span id=\"fs-id1171497978499\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the bottom left side. The top is labeled 4. The right side is labeled 10. The base is labeled 9. The vertical line from the top of the triangle to the top of the rectangle is labeled 3.\">23.\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_205_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the bottom left side. The top is labeled 4. The right side is labeled 10. The base is labeled 9. The vertical line from the top of the triangle to the top of the rectangle is labeled 3.\" width=\"178\" height=\"222\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 224px;\"><span id=\"fs-id1909808\" data-type=\"media\" data-alt=\"A trapezoid is shown. The bases are labeled 5 and 10, the height is 5.\">24.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_206_img.jpg\" alt=\"A trapezoid is shown. The bases are labeled 5 and 10, the height is 5.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 214px;\">\n<td style=\"width: 50%; height: 214px;\"><span id=\"fs-id1651331\" data-type=\"media\" data-alt=\"Two triangles are shown. They appear to be right triangles. The bases are labeled 3, the heights 4, and the longest sides 5.\">25.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_207_img.jpg\" alt=\"Two triangles are shown. They appear to be right triangles. The bases are labeled 3, the heights 4, and the longest sides 5.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 214px;\"><span id=\"fs-id1171496188721\" data-type=\"media\" data-alt=\"A geometric shape is shown. It appears to be composed of two triangles. The shared base of both triangles is 8, the heights are both labeled 6.\">26.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_208_img.jpg\" alt=\"A geometric shape is shown. It appears to be composed of two triangles. The shared base of both triangles is 8, the heights are both labeled 6.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 193px;\">\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1767054\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is composed of two trapezoids. The base is labeled 10. The height of one trapezoid is 2. The horizontal and vertical sides are all labeled 5.\">27.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_209_img.jpg\" alt=\"A geometric shape is shown. It is composed of two trapezoids. The base is labeled 10. The height of one trapezoid is 2. The horizontal and vertical sides are all labeled 5.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1439058\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a trapezoid attached to a triangle. The base of the triangle is labeled 6, the height is labeled 5. The height of the trapezoid is 6, one base is 3.\">28.\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_210_img.jpg\" alt=\"A geometric shape is shown. It is a trapezoid attached to a triangle. The base of the triangle is labeled 6, the height is labeled 5. The height of the trapezoid is 6, one base is 3.\" width=\"184\" height=\"192\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 286px;\">\n<td style=\"width: 50%; height: 286px;\"><span data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 8, the bottom is 8, the right side is 13, and the width of the smaller rectangle is 2.\">29.\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_211_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 8, the bottom is 8, the right side is 13, and the width of the smaller rectangle is 2.\" width=\"187\" height=\"286\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 286px;\"><span id=\"fs-id1691446\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 12, the right side 7, the base 6. The width of the smaller rectangle is labeled 1.\">30.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_212_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 12, the right side 7, the base 6. The width of the smaller rectangle is labeled 1.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 193px;\">\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\">31.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_213_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%; height: 193px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\">32.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_214_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 165px;\">\n<td style=\"width: 50%; height: 165px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\"><span id=\"fs-id1684566\" data-type=\"media\" data-alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The base of the triangle is labeled 4. The height of the triangle and the diametre of the circle are 8.\">33.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_215_img.jpg\" alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The base of the triangle is labeled 4. The height of the triangle and the diametre of the circle are 8.\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<td style=\"width: 50%; height: 165px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\"><span id=\"fs-id1026279\" data-type=\"media\" data-alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The height of the triangle is labeled 4. The base of the triangle, also the diametre of the semi-circle, is labeled 4.\">34.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_216_img.jpg\" alt=\"A geometric shape is shown. A triangle is attached to a semi-circle. The height of the triangle is labeled 4. The base of the triangle, also the diametre of the semi-circle, is labeled 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\"><span id=\"fs-id1110047\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\">35.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_217_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\"><span id=\"fs-id1171487155290\" data-type=\"media\" data-alt=\"A geometric shape is shown. A trapezoid is shown with a semi-circle attached to the top. The diametre of the circle, which is also the top of the trapezoid, is labeled 8. The height of the trapezoid is 6. The bottom of the trapezoid is 13.\">36.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_218_img.jpg\" alt=\"A geometric shape is shown. A trapezoid is shown with a semi-circle attached to the top. The diametre of the circle, which is also the top of the trapezoid, is labeled 8. The height of the trapezoid is 6. The bottom of the trapezoid is 13.\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1496731\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.\"><span id=\"fs-id1968285\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the top on the left side and a circle attached to the top right corner. The diametre of the circle is labeled 5. The height of the triangle is labeled 5, the base is labeled 4. The height of the rectangle is labeled 6, the base 11.\">37.\u00a0<img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_219_img.jpg\" alt=\"A geometric shape is shown. It is a rectangle with a triangle attached to the top on the left side and a circle attached to the top right corner. The diametre of the circle is labeled 5. The height of the triangle is labeled 5, the base is labeled 4. The height of the rectangle is labeled 6, the base 11.\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/td>\n<td style=\"width: 50%; height: 14px;\"><span id=\"fs-id1171505974568\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.\"><span id=\"fs-id1783446\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a trapezoid with a triangle attached to the top, and a circle attached to the triangle. The diametre of the circle is 4. The height of the triangle is 5, the base of the triangle, which is also the top of the trapezoid, is 6. The bottom of the trapezoid is 9. The height of the trapezoid is 7.\">38.\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_220_img.jpg\" alt=\"A geometric shape is shown. It is a trapezoid with a triangle attached to the top, and a circle attached to the triangle. The diametre of the circle is 4. The height of the triangle is 5, the base of the triangle, which is also the top of the trapezoid, is 6. The bottom of the trapezoid is 9. The height of the trapezoid is 7.\" width=\"182\" height=\"326\" data-media-type=\"image\/jpeg\" \/>\u00a0<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1349800\">In the following exercises, solve.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id2021160\">39. A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee64a27674df00e4facb33048c55d282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\" \/> feet long, and the triangles are isosceles right triangles. Find the area of the park.<\/p>\n<p><span id=\"fs-id1593422\" data-type=\"media\" data-alt=\"A square is shown with four triangles coming off each side.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_221_img.jpg\" alt=\"A square is shown with four triangles coming off each side.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%;\">40. A gift box will be made from a rectangular piece of cardboard measuring <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 by <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;\" \/> inches, with squares cut out of the corners of the sides, as shown. The sides of the squares are <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. Find the area of the cardboard after the corners are cut out.<\/p>\n<p><span id=\"fs-id1723514\" data-type=\"media\" data-alt=\"A rectangle is shown. Each corner has a gray shaded square. There are dotted lines drawn across the side of each square attached to the next square.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_222_img.jpg\" alt=\"A rectangle is shown. Each corner has a gray shaded square. There are dotted lines drawn across the side of each square attached to the next square.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1578705\">41. Perry needs to put in a new lawn. His lot is a rectangle with a length 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;\" \/> feet and a width of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c4b0a8a79b7bd0e6e72a5fca0be9982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> feet. The house is rectangular and measures <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;\" \/> feet by <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. His driveway is rectangular and measures <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 by <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;\" \/> feet, as shown. Find the area of Perry\u2019s lawn.<\/p>\n<p><span id=\"fs-id1364316\" data-type=\"media\" data-alt=\"A rectangular lot is shown. In it is a home shaped like a rectangle attached to a rectangular driveway.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_223_img.jpg\" alt=\"A rectangular lot is shown. In it is a home shaped like a rectangle attached to a rectangular driveway.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1747055\">42. Denise is planning to put a deck in her back yard. The deck will be a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef1de01de6c1dafc34e5a8de4d0b9dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: -1px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f15216525a104cb2751502ca5c9e89d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"34\" style=\"vertical-align: -1px;\" \/> rectangle with a semicircle of diametre <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, as shown below. Find the area of the deck.<\/p>\n<p><span id=\"fs-id1909803\" data-type=\"media\" data-alt=\"A picture of a deck is shown. It is shaped like a rectangle with a semi-circle attached to the top on the left side.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_224_img.jpg\" alt=\"A picture of a deck is shown. It is shaped like a rectangle with a semi-circle attached to the top on the left side.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171505622498\">43. <strong data-effect=\"bold\">Area of a Tabletop<\/strong> Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f422fa9f1e6c9dea6765cf78ebf1335_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"25\" style=\"vertical-align: -1px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be24569cd12199a5c7d5f5e3d538836a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> rectangle with a semicircle at each end, as shown. a) Find the area of the table with one leaf up. b) Find the area of the table with both leaves up.<\/p>\n<p><span id=\"fs-id2057237\" data-type=\"media\" data-alt=\"An image of a table is shown. There is a rectangular portion attached to a semi-circular portion. There is another semi-circular leaf folded down on the other side of the rectangle.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_225_img.jpg\" alt=\"An image of a table is shown. There is a rectangular portion attached to a semi-circular portion. There is another semi-circular leaf folded down on the other side of the rectangle.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%;\">44.<strong data-effect=\"bold\"> Painting<\/strong> Leora wants to paint the nursery in her house. The nursery is an <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c58d70e94d276722b1adfef96025253e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-877317090d4f81e14ac6fb6820d4ae27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"34\" style=\"vertical-align: -1px;\" \/> rectangle, and the ceiling 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;\" \/> feet tall. There is a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be24569cd12199a5c7d5f5e3d538836a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc15ab6d577515af85ffa8cb6cf608b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#46;&#53;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> door on one wall, a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be24569cd12199a5c7d5f5e3d538836a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc15ab6d577515af85ffa8cb6cf608b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#46;&#53;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> closet door on another wall, and one <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a655c4a21337431999ca27fae54b4c74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-43f73bb900fb0616653619bb417538ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#46;&#53;&#45;&#102;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -1px;\" \/> window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?<\/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%;\">45. Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.<\/p>\n<p><span id=\"fs-id1759532\" data-type=\"media\" data-alt=\"A geometric shape is shown. It is a vertical rectangle attached to a horizontal rectangle. The width of the vertical rectangle is 3, the left side is labeled 6, the bottom is labeled 9, and the width of the horizontal rectangle is labeled 3. The top of the horizontal rectangle is labeled 6, and the distance from the top of that rectangle to the top of the other rectangle is labeled 3.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_05_226_img.jpg\" alt=\"A geometric shape is shown. It is a vertical rectangle attached to a horizontal rectangle. The width of the vertical rectangle is 3, the left side is labeled 6, the bottom is labeled 9, and the width of the horizontal rectangle is labeled 3. The top of the horizontal rectangle is labeled 6, and the distance from the top of that rectangle to the top of the other rectangle is labeled 3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%;\">46. A circle has a diametre 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;\" \/> feet. Find the area of the circle a) using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-980f77b67737a79200c69c26bf9f365c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> b) using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da5064f8df8d52c5cf0c9150d7a271ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#50;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>. c) Which calculation to do prefer? Why?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 style=\"text-align: left;\">Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 91.3242%; height: 226px;\">\n<tbody>\n<tr style=\"height: 103px;\">\n<td style=\"width: 36.9863%;\">1.<\/p>\n<p>a) 43.96 in.<\/p>\n<p>b) 153.86 sq. in.<\/td>\n<td style=\"width: 27.245%;\">3.<\/p>\n<p>a) 53.38 ft<\/p>\n<p>b) 226.865 sq. ft<\/td>\n<td style=\"width: 27.0167%;\">5. 62.8 ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">7. 37.68 in.<\/td>\n<td style=\"width: 27.245%;\">9. 6.908 ft<\/td>\n<td style=\"width: 27.0167%;\">11. 52 in.<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">13. 5.5 m<\/td>\n<td style=\"width: 27.245%;\">15. 24 ft<\/td>\n<td style=\"width: 27.0167%;\">17. 6.5 mi<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">19. 16 sq. units<\/td>\n<td style=\"width: 27.245%;\">21. 30 sq. units<\/td>\n<td style=\"width: 27.0167%;\">23. 57.5 sq. units<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">25. 12 sq. units<\/td>\n<td style=\"width: 27.245%;\">27. 67.5 sq. units<\/td>\n<td style=\"width: 27.0167%;\">29. 89 sq. units<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 36.9863%;\">31. 44.81 sq. units<\/td>\n<td style=\"width: 27.245%;\">33. 41.12 sq. units<\/td>\n<td style=\"width: 27.0167%;\">35. 35.13 sq. units<\/td>\n<\/tr>\n<tr style=\"height: 10px;\">\n<td style=\"width: 36.9863%;\">37. 95.625 sq. units<\/td>\n<td style=\"width: 27.245%;\">39. 187,500 sq. ft<\/td>\n<td style=\"width: 27.0167%;\">41. 9400 sq. ft<\/td>\n<\/tr>\n<tr style=\"height: 33px;\">\n<td style=\"width: 36.9863%;\">43. a) 6.5325 sq. ft\u00a0 b) 10.065 sq. ft<\/td>\n<td style=\"width: 27.245%;\">45.\u00a0Answers will vary.<\/td>\n<td style=\"width: 27.0167%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cSolve Geometry Applications: Circles and Irregular Figures\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":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-613","chapter","type-chapter","status-publish","hentry"],"part":398,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/613","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\/613\/revisions"}],"predecessor-version":[{"id":614,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/613\/revisions\/614"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/398"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/613\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=613"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=613"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=613"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}