{"id":4378,"date":"2013-06-29T05:47:18","date_gmt":"2013-06-29T05:47:18","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4378"},"modified":"2026-03-26T12:53:44","modified_gmt":"2026-03-26T17:53:44","slug":"area-and-perimeter-of-a-trapezoid","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/area-and-perimeter-of-a-trapezoid\/","title":{"rendered":"Area and Perimeter of a Trapezoid"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_Xk12Ez2sces\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_Xk12Ez2sces\" data-source-videoID=\"Xk12Ez2sces\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Area and Perimeter of a Trapezoid Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Area and Perimeter of a Trapezoid\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_Xk12Ez2sces:hover {cursor:pointer;} img#videoThumbnailImage_Xk12Ez2sces {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1233-area-and-perimeter-of-a-trapezoid-2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_Xk12Ez2sces\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_Xk12Ez2sces\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Area and Perimeter of a Trapezoid\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Xk12Ez2sces\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Xk12Ez2sces\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_Xk12Ez2sces\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction HkZ_Function() {\n  var x = document.getElementById(\"HkZ\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"HkZ_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"HkZ\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_a_Trapezoid\" class=\"smooth-scroll\">What is a Trapezoid?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#How_to_Find_the_Perimeter_of_a_Trapezoid\" class=\"smooth-scroll\">How to Find the Perimeter of a Trapezoid<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#How_to_Find_the_Area_of_a_Trapezoid\" class=\"smooth-scroll\">How to Find the Area of a Trapezoid<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Area_and_Perimeter_of_a_Trapezoid_Practice_Problems\" class=\"smooth-scroll\">Area and Perimeter of a Trapezoid Practice Problems<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on finding the area and perimeter of a trapezoid!<\/p>\n<h2><span id=\"What_is_a_Trapezoid\" class=\"m-toc-anchor\"><\/span>What is a Trapezoid?<\/h2>\n<p>\nA trapezoid is a four-sided <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/polygons\/\">polygon<\/a>, or \u201cquadrilateral,\u201d that has at least one set of parallel sides. There are two types of sides in a trapezoid: legs and bases. A trapezoid has two legs and two bases.<\/p>\n<p>We can tell which sides are the bases because they are parallel to each other. <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapexoid-brand.png\" alt=\"\" width=\"499.5\" height=\"260.5\" class=\"aligncenter size-full wp-image-86326\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapexoid-brand.png 999w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapexoid-brand-300x156.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapexoid-brand-768x401.png 768w\" sizes=\"(max-width: 999px) 100vw, 999px\" \/><\/p>\n<p>Here, we can see the top and bottom are parallel because of the matching arrows on those sides. <\/p>\n<h2><span id=\"How_to_Find_the_Perimeter_of_a_Trapezoid\" class=\"m-toc-anchor\"><\/span>How to Find the Perimeter of a Trapezoid<\/h2>\n<p>\nWhen we know the lengths of the legs and the lengths of the bases we can find the <strong>perimeter<\/strong> of the trapezoid. The perimeter is the distance around an object. For instance, if we wanted to build a fence around a trapezoid-shaped yard, we\u2019d need to know the perimeter of the yard to know how much fencing to buy. <\/p>\n<h3><span id=\"Trapezoid_Perimeter_Formula\" class=\"m-toc-anchor\"><\/span>Trapezoid Perimeter Formula<\/h3>\n<p>\nFor a trapezoid, the formula for perimeter is \\(P=b_1+b_2+l_1+l_2\\).<\/p>\n<p>We don\u2019t need to remember this formula though, because just like with every other type of polygon, it\u2019s just a fancy way of saying <strong>add all of the sides together<\/strong>!<\/p>\n<p>Let\u2019s go ahead and find the perimeter of this trapezoid:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/solved-trapexoid-brand.png\" alt=\"\" width=\"509\" height=\"256\" class=\"aligncenter size-full wp-image-86329\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/solved-trapexoid-brand.png 1018w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/solved-trapexoid-brand-300x151.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/solved-trapexoid-brand-768x386.png 768w\" sizes=\"auto, (max-width: 509px) 100vw, 509px\" \/><\/p>\n<div class=\"examplesentence\">\\(10+21+12+16=59 m\\)<\/div>\n<p>\n&nbsp;<br \/>\nThat\u2019s all there is to it! Let\u2019s move on to <strong>area<\/strong>. <\/p>\n<h2><span id=\"How_to_Find_the_Area_of_a_Trapezoid\" class=\"m-toc-anchor\"><\/span>How to Find the Area of a Trapezoid<\/h2>\n<p>\nHere\u2019s a trapezoid on some graph paper:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph.png\" alt=\"\" width=\"537\" height=\"287\" class=\"aligncenter size-full wp-image-86332\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph.png 1074w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-300x160.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-1024x547.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-768x410.png 768w\" sizes=\"auto, (max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Remember that area is a measure of how many square units will fit inside a shape. How many squares are inside our trapezoid?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-filled.png\" alt=\"\" width=\"537\" height=\"288.5\" class=\"aligncenter size-full wp-image-86335\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-filled.png 1074w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-filled-300x161.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-filled-1024x550.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapzeoid-on-graph-filled-768x413.png 768w\" sizes=\"(max-width: 1074px) 100vw, 1074px\" \/><\/p>\n<p>There are 24 full squares plus eight half squares, which means the area of the trapezoid is 28 square units. But what if we don\u2019t have graph paper or a conveniently sized trapezoid? That\u2019s why we need a formula! <\/p>\n<h3><span id=\"Trapezoid_Area_Formula\" class=\"m-toc-anchor\"><\/span>Trapezoid Area Formula<\/h3>\n<p>\nThe formula for finding the <strong>area<\/strong> of a trapezoid is \\(A=h(\\frac{b_1+b_2}{2})\\).<\/p>\n<p>Note that dividing the sum of the bases by two is the average of those lengths. Because our sample problem is on a graph, we can see that the top base, which we\u2019ll call base 1, is three units long. Our bottom base, base 2, is 11 units longs. The height of the trapezoid, which is the distance between the bases, is four units: <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/graph-filled-chair.png\" alt=\"\" width=\"544.5\" height=\"292.5\" class=\"aligncenter size-full wp-image-86344\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/graph-filled-chair.png 1089w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/graph-filled-chair-300x161.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/graph-filled-chair-1024x550.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/graph-filled-chair-768x413.png 768w\" sizes=\"(max-width: 1089px) 100vw, 1089px\" \/><\/p>\n<p>For area, we don\u2019t need the measurements of the two legs, just the two bases and the height, which can also be called the <strong>altitude<\/strong>. Since we have all three we can plug them into our formula:<\/p>\n<div class=\"examplesentence\">\\(A=h(\\frac{b_1+b_2}{2})=4(\\frac{3+11}{2})\\)\\(=4(\\frac{14}{2})=4(7)\\)\\(=28\\) units\\(^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nThat&#8217;s the same answer we got when we counted! <\/p>\n<p>Let\u2019s try another one:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapexoid-part-2.png\" alt=\"\" width=\"314.5\" height=\"284\" class=\"aligncenter size-full wp-image-86362\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapexoid-part-2.png 629w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/07\/trapexoid-part-2-300x271.png 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><\/p>\n<p>Okay, it looks a bit different than the trapezoid we just did. But we can tell it\u2019s a trapezoid because it has one set of <strong>parallel sides<\/strong>. We can use the formula, so now we just need to figure out which numbers go where. The parallel sides are the bases so we can set base one as 6 centimeters and base two as 3 centimeters. There\u2019s no dashed or colored line inside the trapezoid connecting the bases that would clearly be the height, but the bottom side is connecting the bases and is perpendicular to them, as we can tell by the right angle symbol. So 4 centimeters is the height, even though it\u2019s sideways! Let\u2019s plug it all in: <\/p>\n<div class=\"examplesentence\">\\(A=h(\\frac{b_1+b_2}{2})=4(\\frac{6+3}{2})\\)\\(=4(\\frac{9}{2})=4(4.5)\\)\\(=18\\) cm\\(^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis formula also works to find the area of <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/area-and-perimeter-of-a-parallelogram\/\">parallelograms<\/a> too. That\u2019s because all parallelograms are trapezoids since they have at least one set of parallel sides. In fact, all parallelograms have two sets.<\/p>\n<p>That\u2019s about all there is to finding the perimeter and area of trapezoids.<\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.mathopenref.com\/trapezoidarea.html\"target=\"_blank\">\u201cArea of a Trapezoid. Definition, Formula and Calculator &#8211; Math Open Reference.\u201d n.d. <\/a><\/li>\n<li><a href=\"https:\/\/www.mathopenref.com\/trapezoid.html\"target=\"_blank\">\u201cTrapezoid &#8211; Math Word Definition &#8211; Math Open Reference.\u201d n.d.<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the area of a trapezoid?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Each of the two parallel sides of a trapezoid is a <em>base<\/em>. The distance between the bases (measured perpendicular to each) is the <em>height<\/em>.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-1.svg\" alt=\"A trapezoid with parallel sides labeled &quot;a&quot; (top) and &quot;b&quot; (bottom), and height &quot;h&quot; shown with a dashed line and right angle markers.\" width=\"347.9\" height=\"170.1\" class=\"aligncenter size-full wp-image-286729\"  role=\"img\" \/><\/p>\n<p>To find the area of a trapezoid, we multiply the average length of the two bases by the height. In symbols, if the lengths of the bases are \\(a\\) and \\(b\\) and the height is \\(h\\) (see diagram), then the area, \\(A\\), of the trapezoid is \\(A=\\frac{(a+b)}{2}h\\), which we can also write as \\(A=\\frac{1}{2}(a+b)h\\).<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the area of the trapezoid below?<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-2.svg\" alt=\"A trapezoid with parallel sides of 5 cm and 9 cm, a height of 3 cm, and right angles shown at the left.\" width=\"347.9\" height=\"170.1\" class=\"aligncenter size-full wp-image-286732\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">Start by plugging in the applicable numbers into the formula:<\/p>\n<p style=\"text-align: center; line-height: 55px; margin-bottom: 0em\">\\(A=\\dfrac{5+9}{2}\\cdot 3=\\dfrac{14}{2}\\cdot 3\\)\\(\\:=7\\cdot 3=21\\text{ cm}^2\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Why does the area formula for a trapezoid work?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The area formula for a trapezoid works because it comes from the formula for the area of a parallelogram. The trapezoid below (with solid sides) has bases of length \\(a\\) and \\(b\\) and height \\(h\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-3.svg\" alt=\"A parallelogram with base b and height h is shown; an identical shape is shaded and combined to form a rectangle with width a + b and height h.\" width=\"345.8\" height=\"165.2\" class=\"aligncenter size-full wp-image-286735\"  role=\"img\" \/><\/p>\n<p>Suppose we make a copy of it, rotate it halfway around, and place it adjoining the original trapezoid so that legs (non-parallel sides) of the same length coincide (the shaded trapezoid with dashed sides). Together, these figures form a parallelogram with a base of length \\(a+b\\) and height \\(h\\).<\/p>\n<p>By the standard formula, the area of this parallelogram is: <\/p>\n<p style=\"text-align: center\">\\(a=b\\times h=(a+b)h\\)<\/p>\n<p> The area of the original trapezoid is half of this, or \\(\\frac{(a+b)}{2}h\\).<\/p>\n<p>This same procedure works for every trapezoid.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What units do you use for the area of a trapezoid?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>We measure the area of a trapezoid, like all areas, in square units (square feet, square inches, square meters, etc.), which are sometimes written as &#8220;ft<sup>2<\/sup>,&#8221; &#8220;in<sup>2<\/sup>,&#8221; m<sup>2<\/sup>,&#8221; etc.<\/p>\n<p>Usually, we use the square of the unit used to measure the bases and height of the trapezoid. For instance, if we measure the bases and height in centimeters, we usually give the area in square centimeters.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the perimeter of a trapezoid?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The perimeter of a figure is the distance around it. We find the perimeter of a trapezoid by adding up the lengths of its four sides.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the perimeter of a trapezoid using the Pythagorean theorem?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>If we do not know the lengths of all four sides of a trapezoid, sometimes we have enough other information to find the lengths of the missing sides using the Pythagorean theorem. <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the perimeter of the trapezoid below?<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-4.svg\" alt=\"A trapezoid with top base 2 cm, height 4 cm, bottom base 9 cm, and side segments labeled 3 cm and 4 cm; non-parallel sides labeled c and d.\" width=\"306.99\" height=\"272.97\" class=\"aligncenter size-full wp-image-286738\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">In this trapezoid, the bases are 2&nbsp;cm and 9&nbsp;cm, the height is 4&nbsp;cm, and the longer base sticks out past the shorter base by 3&nbsp;cm on the left and 4&nbsp;cm on the right. This makes sides \\(c\\) and \\(d\\) hypotenuses of right triangles with sides whose lengths we know.<\/p>\n<p>By the Pythagorean theorem: <\/p>\n<p style=\"text-align: center; line-height: 45px\">\\(c^2=3^2+4^2=9+16=25\\)<br \/>\\(c=\\sqrt{25}=5\\text{ cm}\\)<\/p>\n<p>Similarly: <\/p>\n<p style=\"text-align: center; line-height: 45px\">\\(d^2=4^2+4^2=16+16=32\\)<br \/>\\(d=\\sqrt{32}=\\sqrt{16\\cdot2}\\)\\(\\:=\\sqrt{16}\\cdot \\sqrt{2}\\)\\(\\:=4\\sqrt{2}\\approx 5.7\\text{ cm}\\)<\/p>\n<p> Now we can find the perimeter, \\(P\\), of the trapezoid by adding up the four sides: <\/p>\n<p style=\"text-align: center; line-height: 45px; margin-bottom: 0em\">\\(P=9+5+2+4\\sqrt{2}\\)\\(\\:=16+4\\sqrt{2}\u224816+5.7\\)\\(\\:=21.7\\text{ cm}\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you find the area of a trapezoid without the height?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>If we do not know the height of a trapezoid, sometimes we have enough other information to find the height using the Pythagorean theorem. <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the area of the trapezoid below?<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-5.svg\" alt=\"A trapezoid with top base 2 cm, bottom base 9 cm, left side 5 cm, left segment 3 cm, and height h marked with a dashed line and a right angle.\" width=\"306.99\" height=\"272.97\" class=\"aligncenter size-full wp-image-286723\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\"> In this trapezoid, the bases are 2 cm and 9 cm, the longer base sticks out 3 cm past the shorter base on the left, and the left leg (the non-parallel side) is 5&nbsp;cm. This makes the dashed line a side of a right triangle whose hypotenuse and other side we know.<\/p>\n<p>By the Pythagorean theorem: <\/p>\n<p style=\"text-align: center; line-height: 45px\">\\(h^2+3^2=5^2\\)<br \/>\\(h^2+9=25\\)<\/p>\n<p> Therefore: <\/p>\n<p style=\"text-align: center; line-height: 45px\">\\(h^2=16\\)<br \/>\\(h=\\sqrt{16}=4\\text{ cm}\\)<\/p>\n<p>This means that the height of the trapezoid is 4&nbsp;cm.<\/p>\n<p>Now we can apply the standard formula to find the area of this trapezoid: <\/p>\n<p style=\"text-align: center; line-height: 55px; margin-bottom: 0.2em\">\\(A=\\dfrac{(a+b)}{2}h=\\dfrac{(2+9)}{2}\\times4\\)\\(\\:=\\dfrac{11}{2}\\times4=\\dfrac{11}{1}\\times 2=22\\text{ cm}^2\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Area_and_Perimeter_of_a_Trapezoid_Practice_Problems\" class=\"m-toc-anchor\"><\/span>Area and Perimeter of a Trapezoid Practice Problems<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the perimeter of this trapezoid?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-6.svg\" alt=\"A trapezoid with top base 23 inches, bottom base 27 inches, and both non-parallel sides measuring 12 inches each.\" width=\"351.65\" height=\"162.5\" class=\"aligncenter size-full wp-image-286756\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-1-1\">74 in<\/div><div class=\"PQ\"  id=\"PQ-1-2\">86 in<\/div><div class=\"PQ\"  id=\"PQ-1-3\">142 in<\/div><div class=\"PQ\"  id=\"PQ-1-4\">300 in<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the perimeter of a trapezoid, add all four side lengths together.<\/p>\n<p style=\"text-align:center;\">\\(P=23+12+27+12=74\\text{ in}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the area of this trapezoid?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-7.svg\" alt=\"A trapezoid with bases of 12 cm and 15 cm, a height of 6 cm, and a non-parallel side labeled 7 cm.\" width=\"351.65\" height=\"162.5\" class=\"aligncenter size-full wp-image-286759\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">96 cm<sup>2<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">81 cm<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-3\">57 cm<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-4\">41 cm<sup>2<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for area of a trapezoid is: <\/p>\n<p style=\"text-align:center;\">\\(A=\\frac{1}{2}(b_1+b_2)h\\)<\/p>\n<p>The length base 1 is 12 cm. The length of base 2 is 15 cm. The length of the height is 6 cm.<\/p>\n<p style=\"text-align:center;\">\\(A=\\frac{1}{2}(12+15)(6)\\)\\(=\\frac{1}{2}(27)(6)=81\\text{ cm}^2\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the perimeter of this trapezoid?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-8.svg\" alt=\"A trapezoid with top base 11 in, bottom base 13 in, non-parallel sides 6 in each, and height marked as 4 in with a dashed line.\" width=\"334.1\" height=\"162.5\" class=\"aligncenter size-full wp-image-286762\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">34 in<\/div><div class=\"PQ\"  id=\"PQ-3-2\">48 in<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">36 in<\/div><div class=\"PQ\"  id=\"PQ-3-4\">42 in<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Find the perimeter of the trapezoid by adding the lengths of all four sides together.<\/p>\n<p style=\"text-align:center;\">\\(P=11+6+13+6=36\\text{ in}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the area of this trapezoid?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-9.svg\" alt=\"A quadrilateral with side lengths labeled: top 4 ft, left 3 ft, bottom 6 ft, and right 5 ft.\" width=\"251.55\" height=\"162.5\" class=\"aligncenter size-full wp-image-286765\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">17 ft<sup>2<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\">15 ft<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-4-3\">18 ft<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-4-4\">23 ft<sup>2<\/sup><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula for area of a trapezoid is:<\/p>\n<p style=\"text-align:center;\">\\(A=\\frac{1}{2}(b_1+b_2)h\\)<\/p>\n<p>The length of base 1 is 4 ft. The length of base 2 is 6 ft. The length of the height is 3 ft.<\/p>\n<p style=\"text-align:center;\">\\(A=\\frac{1}{2}(4+6)(3)=\\frac{1}{2}(10)(3)\\)\\(=15\\text{ ft}^2\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the perimeter of this trapezoid?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimieter-of-a-Trapezoid-Example-10.svg\" alt=\"A labeled trapezoid with sides measuring 12 cm, 15 cm, 8 cm, and 20 cm.\" width=\"330.2\" height=\"162.5\" class=\"aligncenter size-full wp-image-286753\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">153 cm<\/div><div class=\"PQ\"  id=\"PQ-5-2\">140 cm<\/div><div class=\"PQ\"  id=\"PQ-5-3\">47 cm<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-4\">55 cm<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the perimeter of a trapezoid, add the lengths of all four sides together.<\/p>\n<p style=\"text-align:center;\">\\(P=15+8+20+12=55\\text{ cm}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":100330,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4378","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-area-and-perimeter-videos","7":"page_category-finding-areas-in-geometry","8":"page_category-math-advertising-group","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4378","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=4378"}],"version-history":[{"count":8,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4378\/revisions"}],"predecessor-version":[{"id":286726,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4378\/revisions\/286726"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100330"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}