{"id":2911,"date":"2023-05-16T19:38:34","date_gmt":"2023-05-16T19:38:34","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=2911"},"modified":"2025-08-26T03:45:14","modified_gmt":"2025-08-26T03:45:14","slug":"area-and-circumference-learn-it-3","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/area-and-circumference-learn-it-3\/","title":{"raw":"Area and Circumference: Learn It 3","rendered":"Area and Circumference: Learn It 3"},"content":{"raw":"<h2>Find the Area of a Trapezoid<\/h2>\r\n<p>A <strong>trapezoid<\/strong> is four-sided figure, a <em>quadrilateral<\/em>, with two sides that are parallel and two sides that are not. The parallel sides are called the bases. We call the length of the smaller base [latex]b[\/latex], and the length of the bigger base [latex]B[\/latex]. The height, [latex]h[\/latex], of a trapezoid is the distance between the two bases as shown in the image below.<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"291\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223946\/CNX_BMath_Figure_09_04_052.png\" alt=\"A trapezoid, with the top is labeled b and marked as the smaller base. The bottom is labeled B and marked as the larger base. A vertical line forms a right angle with both bases and is marked as h.\" width=\"291\" height=\"129\" \/> Figure 1. This trapezoid has it's bases, b and B, and height, h, labeled[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>The formula for the area of a trapezoid is: [latex]{\\text{Area}}_{\\text{trapezoid}}=\\Large\\frac{1}{2}\\normalsize h\\left(b+B\\right)[\/latex]. Splitting the trapezoid into two triangles may help us understand the formula. The area of the trapezoid is the sum of the areas of the two triangles.<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"179\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223948\/CNX_BMath_Figure_09_04_053.png\" alt=\"A trapezoid, with the top labeled with a small b and the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner.\" width=\"179\" height=\"123\" \/> Figure 2. The trapezoid can be split into two triangles[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>The height of the trapezoid is also the height of each of the two triangles.<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"193\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223949\/CNX_BMath_Figure_09_04_078.png\" alt=\"A trapezoid, with the top labeled with a small b and the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner. The upper right-hand side of the trapezoid forms a blue triangle, with the height of the trapezoid drawn in as a dotted line. The lower left-hand side of the trapezoid forms a red triangle, with the height of the trapezoid drawn in as a dotted line.\" width=\"193\" height=\"122\" \/> Figure 3. The trapezoid's height is equal to the height of both triangles[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>The formula for the area of a trapezoid is:<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"185\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223950\/CNX_BMath_Figure_09_04_056_img.png\" alt=\"The formula for the area of a trapezoid, which is one half h times the quantity of lowercase b plus capital B\" width=\"185\" height=\"40\" \/> Figure 4. The formula of the area of the trapezoid[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>If we distribute, we get:<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"201\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223951\/CNX_BMath_Figure_09_04_079_img.png\" alt=\"The top line says area of trapezoid equals one-half times blue little b times h plus one-half times red big B times h. Below this is area of trapezoid equals A sub blue triangle plus A sub red triangle.\" width=\"201\" height=\"97\" \/> Figure 5. The trapezoid's area formula can be split into the areas of both triangles in the trapezoid[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>properties of trapezoids<\/h3>\r\n<ul id=\"fs-id1429217\">\r\n\t<li>A <strong>trapezoid<\/strong> has four sides.<\/li>\r\n\t<li>Two of its sides are parallel and two sides are not.<\/li>\r\n\t<li>The area, [latex]A[\/latex], of a trapezoid is [latex]\\text{A}=\\Large\\frac{1}{2}\\normalsize h\\left(b+B\\right)[\/latex] .<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox example\">Find the area of a trapezoid whose height is [latex]6[\/latex] inches and whose bases are [latex]14[\/latex] and [latex]11[\/latex] inches. [reveal-answer q=\"247911\"]Show Solution[\/reveal-answer] [hidden-answer a=\"247911\"]\r\n\r\n<table id=\"eip-id1168468452905\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223952\/CNX_BMath_Figure_09_04_080_img-01.png\" alt=\"A trapezoid with one parallel side labeled 11 in and the other labeled 14 in. There is a dotted line between the two parallel sides forming right angles with each of them. It is labeled 6 in.\" width=\"243\" height=\"148\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the area of the trapezoid<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let [latex]A=\\text{the area}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4.<strong>Translate.<\/strong> Write the appropriate formula. Substitute.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223953\/CNX_BMath_Figure_09_04_080_img-02.png\" alt=\"The equation A = one half times h times the quantity of little b plus big b. This formula is written again with 6 substituted in for h, 11 substituted in for little b and 14 substituted in for big b.\" width=\"392\" height=\"92\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]A={\\Large\\frac{1}{2}}\\normalsize\\cdot 6(25)[\/latex] [latex]A=3(25)[\/latex] [latex]A=75[\/latex] square inches<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> Is this answer reasonable?<\/td>\r\n<td>\u00a0[latex]\\checkmark[\/latex]\u00a0 see reasoning below<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>&nbsp;<\/p>\r\n<p>If we draw a rectangle around the trapezoid that has the same big base [latex]B[\/latex] and a height [latex]h[\/latex], its area should be greater than that of the trapezoid. If we draw a rectangle inside the trapezoid that has the same little base [latex]b[\/latex] and a height [latex]h[\/latex], its area should be smaller than that of the trapezoid.<\/p>\r\n<center><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223956\/CNX_BMath_Figure_09_04_060.png\" alt=\"A table is shown with 3 columns and 4 rows. The first column has an image of a trapezoid with a rectangle drawn around it in red. The larger base of the trapezoid is labeled 14 and is the same as the base of the rectangle. The height of the trapezoid is labeled 6 and is the same as the height of the rectangle. The smaller base of the trapezoid is labeled 11. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 14 times 6. Below is A sub rectangle equals 84 square inches. The second column has an image of a trapezoid. The larger base is labeled 14, the smaller base is labeled 11, and the height is labeled 6. Below this is A sub trapezoid equals one-half times h times parentheses little b plus big B. Below this is A sub trapezoid equals one-half times 6 times parentheses 11 plus 14. Below this is A sub trapezoid equals 75 square inches. The third column has an image of a trapezoid with a red rectangle drawn inside of it. The height is labeled 6. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 11 times 6. Below is A sub rectangle equals 66 square inches.\" \/><\/center>\r\n<p>&nbsp;<\/p>\r\n\r\nThe area of the larger rectangle is [latex]84[\/latex] square inches and the area of the smaller rectangle is [latex]66[\/latex] square inches. So it makes sense that the area of the trapezoid is between [latex]84[\/latex] and [latex]66[\/latex] square inches Step 7. <strong>Answer<\/strong> the question. The area of the trapezoid is [latex]75[\/latex] square inches. [\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6996[\/ohm2_question]<\/section>\r\n<section class=\"textbox example\">Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of [latex]3.4[\/latex] yards and the bases are [latex]8.2[\/latex] and [latex]5.6[\/latex] yards. How many square yards will be available to plant? [reveal-answer q=\"676574\"]Show Solution[\/reveal-answer] [hidden-answer a=\"676574\"]\r\n\r\n<table id=\"eip-id1168469766721\" class=\"unnumbered unstyled\" style=\"width: 859px;\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 409.183px;\">Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td style=\"width: 424.817px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224005\/CNX_BMath_Figure_09_04_082_img-01.png\" alt=\"A trapezoid with shorter base 5.6 yards and longer base 82 yards and a height of 3.4 yards.\" width=\"418\" height=\"129\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 409.183px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td style=\"width: 424.817px;\">the area of a trapezoid<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 409.183px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td style=\"width: 424.817px;\">Let [latex]A[\/latex] = the area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 409.183px;\">Step 4.<strong>Translate.<\/strong> Write the appropriate formula. Substitute.<\/td>\r\n<td style=\"width: 424.817px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224007\/CNX_BMath_Figure_09_04_082_img-02.png\" alt=\"The equation A = one half times h times the quantity of little b plus big b. The equation is rewritten with 3.4 substituted in for h, 5.6 substituted in for little b and 8.2 substituted in for big b.\" width=\"418\" height=\"101\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 409.183px;\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td style=\"width: 424.817px;\">[latex]A={\\Large\\frac{1}{2}}\\normalsize(3.4)(13.8)[\/latex] [latex]A=23.46[\/latex] square yards.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 834px;\" colspan=\"2\">Step 6. <strong>Check:<\/strong> Is this answer reasonable? Yes. The area of the trapezoid is less than the area of a rectangle with a base of [latex]8.2[\/latex] yd and height [latex]3.4[\/latex] yd, but more than the area of a rectangle with base [latex]5.6[\/latex] yd and height [latex]3.4[\/latex] yd.<center><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224012\/CNX_BMath_Figure_09_04_066.png\" alt=\"A table with two rows. the first row is split into three columns. The first column is the formula Area of a rectangle (shown in red) equals base times height. On the next line under this it has numbers plugged into the formula; the base, 8.2 in parentheses times the height 3.4 in parentheses. Under this is it has the result 27.88 yards squared. The second column is the formula Area of a trapezoid with numbers already plugged in; one half times 3.4 yards times the quantity of 5.6 plus 8.2. Under this is has the result 23.46 yards squared. The third column is the formula Area of a rectangle (shown in blue) equals base times height. On the next line under it has number plugged into the formula; the base, 5.6 in parentheses times the height 3.4 in parentheses. Under this it has the result 19.04 yards squared. The second row shows that the Area of the red rectangle is greater than the Area of a trapezoid is greater than the Area of the blue rectangle. Beneath this, it shows the areas 27.88 for the red rectangle, 23.46 for the trapezoid, and 19.04 for the blue rectangle.\" \/><\/center><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 409.183px;\">Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td style=\"width: 424.817px;\">Vinny has [latex]23.46[\/latex] square yards in which he can plant.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6998[\/ohm2_question]<\/section>","rendered":"<h2>Find the Area of a Trapezoid<\/h2>\n<p>A <strong>trapezoid<\/strong> is four-sided figure, a <em>quadrilateral<\/em>, with two sides that are parallel and two sides that are not. The parallel sides are called the bases. We call the length of the smaller base [latex]b[\/latex], and the length of the bigger base [latex]B[\/latex]. The height, [latex]h[\/latex], of a trapezoid is the distance between the two bases as shown in the image below.<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 291px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223946\/CNX_BMath_Figure_09_04_052.png\" alt=\"A trapezoid, with the top is labeled b and marked as the smaller base. The bottom is labeled B and marked as the larger base. A vertical line forms a right angle with both bases and is marked as h.\" width=\"291\" height=\"129\" \/><figcaption class=\"wp-caption-text\">Figure 1. This trapezoid has it&#8217;s bases, b and B, and height, h, labeled<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The formula for the area of a trapezoid is: [latex]{\\text{Area}}_{\\text{trapezoid}}=\\Large\\frac{1}{2}\\normalsize h\\left(b+B\\right)[\/latex]. Splitting the trapezoid into two triangles may help us understand the formula. The area of the trapezoid is the sum of the areas of the two triangles.<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 179px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223948\/CNX_BMath_Figure_09_04_053.png\" alt=\"A trapezoid, with the top labeled with a small b and the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner.\" width=\"179\" height=\"123\" \/><figcaption class=\"wp-caption-text\">Figure 2. The trapezoid can be split into two triangles<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The height of the trapezoid is also the height of each of the two triangles.<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 193px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223949\/CNX_BMath_Figure_09_04_078.png\" alt=\"A trapezoid, with the top labeled with a small b and the bottom with a big B. A diagonal is drawn in from the upper left corner to the bottom right corner. The upper right-hand side of the trapezoid forms a blue triangle, with the height of the trapezoid drawn in as a dotted line. The lower left-hand side of the trapezoid forms a red triangle, with the height of the trapezoid drawn in as a dotted line.\" width=\"193\" height=\"122\" \/><figcaption class=\"wp-caption-text\">Figure 3. The trapezoid&#8217;s height is equal to the height of both triangles<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The formula for the area of a trapezoid is:<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 185px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223950\/CNX_BMath_Figure_09_04_056_img.png\" alt=\"The formula for the area of a trapezoid, which is one half h times the quantity of lowercase b plus capital B\" width=\"185\" height=\"40\" \/><figcaption class=\"wp-caption-text\">Figure 4. The formula of the area of the trapezoid<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>If we distribute, we get:<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 201px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223951\/CNX_BMath_Figure_09_04_079_img.png\" alt=\"The top line says area of trapezoid equals one-half times blue little b times h plus one-half times red big B times h. Below this is area of trapezoid equals A sub blue triangle plus A sub red triangle.\" width=\"201\" height=\"97\" \/><figcaption class=\"wp-caption-text\">Figure 5. The trapezoid&#8217;s area formula can be split into the areas of both triangles in the trapezoid<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>properties of trapezoids<\/h3>\n<ul id=\"fs-id1429217\">\n<li>A <strong>trapezoid<\/strong> has four sides.<\/li>\n<li>Two of its sides are parallel and two sides are not.<\/li>\n<li>The area, [latex]A[\/latex], of a trapezoid is [latex]\\text{A}=\\Large\\frac{1}{2}\\normalsize h\\left(b+B\\right)[\/latex] .<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Find the area of a trapezoid whose height is [latex]6[\/latex] inches and whose bases are [latex]14[\/latex] and [latex]11[\/latex] inches. <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q247911\">Show Solution<\/button> <\/p>\n<div id=\"q247911\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-id1168468452905\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223952\/CNX_BMath_Figure_09_04_080_img-01.png\" alt=\"A trapezoid with one parallel side labeled 11 in and the other labeled 14 in. There is a dotted line between the two parallel sides forming right angles with each of them. It is labeled 6 in.\" width=\"243\" height=\"148\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the area of the trapezoid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let [latex]A=\\text{the area}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong>Translate.<\/strong> Write the appropriate formula. Substitute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223953\/CNX_BMath_Figure_09_04_080_img-02.png\" alt=\"The equation A = one half times h times the quantity of little b plus big b. This formula is written again with 6 substituted in for h, 11 substituted in for little b and 14 substituted in for big b.\" width=\"392\" height=\"92\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]A={\\Large\\frac{1}{2}}\\normalsize\\cdot 6(25)[\/latex] [latex]A=3(25)[\/latex] [latex]A=75[\/latex] square inches<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> Is this answer reasonable?<\/td>\n<td>\u00a0[latex]\\checkmark[\/latex]\u00a0 see reasoning below<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>If we draw a rectangle around the trapezoid that has the same big base [latex]B[\/latex] and a height [latex]h[\/latex], its area should be greater than that of the trapezoid. If we draw a rectangle inside the trapezoid that has the same little base [latex]b[\/latex] and a height [latex]h[\/latex], its area should be smaller than that of the trapezoid.<\/p>\n<div style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223956\/CNX_BMath_Figure_09_04_060.png\" alt=\"A table is shown with 3 columns and 4 rows. The first column has an image of a trapezoid with a rectangle drawn around it in red. The larger base of the trapezoid is labeled 14 and is the same as the base of the rectangle. The height of the trapezoid is labeled 6 and is the same as the height of the rectangle. The smaller base of the trapezoid is labeled 11. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 14 times 6. Below is A sub rectangle equals 84 square inches. The second column has an image of a trapezoid. The larger base is labeled 14, the smaller base is labeled 11, and the height is labeled 6. Below this is A sub trapezoid equals one-half times h times parentheses little b plus big B. Below this is A sub trapezoid equals one-half times 6 times parentheses 11 plus 14. Below this is A sub trapezoid equals 75 square inches. The third column has an image of a trapezoid with a red rectangle drawn inside of it. The height is labeled 6. Below this is A sub rectangle equals b times h. Below is A sub rectangle equals 11 times 6. Below is A sub rectangle equals 66 square inches.\" \/><\/div>\n<p>&nbsp;<\/p>\n<p>The area of the larger rectangle is [latex]84[\/latex] square inches and the area of the smaller rectangle is [latex]66[\/latex] square inches. So it makes sense that the area of the trapezoid is between [latex]84[\/latex] and [latex]66[\/latex] square inches Step 7. <strong>Answer<\/strong> the question. The area of the trapezoid is [latex]75[\/latex] square inches. <\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6996\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6996&theme=lumen&iframe_resize_id=ohm6996&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox example\">Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of [latex]3.4[\/latex] yards and the bases are [latex]8.2[\/latex] and [latex]5.6[\/latex] yards. How many square yards will be available to plant? <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q676574\">Show Solution<\/button> <\/p>\n<div id=\"q676574\" class=\"hidden-answer\" style=\"display: none\">\n<table id=\"eip-id1168469766721\" class=\"unnumbered unstyled\" style=\"width: 859px;\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td style=\"width: 409.183px;\">Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td style=\"width: 424.817px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224005\/CNX_BMath_Figure_09_04_082_img-01.png\" alt=\"A trapezoid with shorter base 5.6 yards and longer base 82 yards and a height of 3.4 yards.\" width=\"418\" height=\"129\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 409.183px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 424.817px;\">the area of a trapezoid<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 409.183px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td style=\"width: 424.817px;\">Let [latex]A[\/latex] = the area<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 409.183px;\">Step 4.<strong>Translate.<\/strong> Write the appropriate formula. Substitute.<\/td>\n<td style=\"width: 424.817px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224007\/CNX_BMath_Figure_09_04_082_img-02.png\" alt=\"The equation A = one half times h times the quantity of little b plus big b. The equation is rewritten with 3.4 substituted in for h, 5.6 substituted in for little b and 8.2 substituted in for big b.\" width=\"418\" height=\"101\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 409.183px;\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td style=\"width: 424.817px;\">[latex]A={\\Large\\frac{1}{2}}\\normalsize(3.4)(13.8)[\/latex] [latex]A=23.46[\/latex] square yards.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 834px;\" colspan=\"2\">Step 6. <strong>Check:<\/strong> Is this answer reasonable? Yes. The area of the trapezoid is less than the area of a rectangle with a base of [latex]8.2[\/latex] yd and height [latex]3.4[\/latex] yd, but more than the area of a rectangle with base [latex]5.6[\/latex] yd and height [latex]3.4[\/latex] yd.<\/p>\n<div style=\"text-align: center;\"><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224012\/CNX_BMath_Figure_09_04_066.png\" alt=\"A table with two rows. the first row is split into three columns. The first column is the formula Area of a rectangle (shown in red) equals base times height. On the next line under this it has numbers plugged into the formula; the base, 8.2 in parentheses times the height 3.4 in parentheses. Under this is it has the result 27.88 yards squared. The second column is the formula Area of a trapezoid with numbers already plugged in; one half times 3.4 yards times the quantity of 5.6 plus 8.2. Under this is has the result 23.46 yards squared. The third column is the formula Area of a rectangle (shown in blue) equals base times height. On the next line under it has number plugged into the formula; the base, 5.6 in parentheses times the height 3.4 in parentheses. Under this it has the result 19.04 yards squared. The second row shows that the Area of the red rectangle is greater than the Area of a trapezoid is greater than the Area of the blue rectangle. Beneath this, it shows the areas 27.88 for the red rectangle, 23.46 for the trapezoid, and 19.04 for the blue rectangle.\" \/><\/div>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 409.183px;\">Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td style=\"width: 424.817px;\">Vinny has [latex]23.46[\/latex] square yards in which he can plant.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6998\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6998&theme=lumen&iframe_resize_id=ohm6998&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":20,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":71,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/2911"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":26,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/2911\/revisions"}],"predecessor-version":[{"id":15652,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/2911\/revisions\/15652"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/71"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/2911\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=2911"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=2911"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=2911"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=2911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}