{"id":39405,"date":"2018-04-04T15:31:20","date_gmt":"2018-04-04T15:31:20","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=39405"},"modified":"2026-03-26T13:05:05","modified_gmt":"2026-03-26T18:05:05","slug":"area-and-perimeter","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/area-and-perimeter\/","title":{"rendered":"How to Find the Area and Perimeter"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_h1AYQFWKOxQ\" 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_h1AYQFWKOxQ\" data-source-videoID=\"h1AYQFWKOxQ\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"How to Find the Area and Perimeter Video\" height=\"720\" width=\"1280\" class=\"size-full\" data-matomo-title = \"How to Find the Area and Perimeter\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_h1AYQFWKOxQ:hover {cursor:pointer;} img#videoThumbnailImage_h1AYQFWKOxQ {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/thumb2.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_h1AYQFWKOxQ\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_h1AYQFWKOxQ\" 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\",\"How to Find the Area and Perimeter\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_h1AYQFWKOxQ\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_h1AYQFWKOxQ\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_h1AYQFWKOxQ\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction YtS_Function() {\n  var x = document.getElementById(\"YtS\");\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=\"YtS_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=\"YtS\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Calculating_Perimeter\" class=\"smooth-scroll\">Calculating Perimeter<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#How_to_Find_Area\" class=\"smooth-scroll\">How to Find Area<\/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_Practice_Problems\" class=\"smooth-scroll\">Area and Perimeter 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>Hey guys! Welcome to this video on finding the area and perimeter of a shape.<\/p>\n<p>The area and perimeter help us to measure two-dimensional shapes.<\/p>\n<p>The area measures the surface of a shape, and perimeter measures the distance around the outside of a shape.<\/p>\n<p>We\u2019ll take a look at how to calculate each, but let\u2019s start with perimeter.<\/p>\n<h2><span id=\"Calculating_Perimeter\" class=\"m-toc-anchor\"><\/span>Calculating Perimeter<\/h2>\n<p>\nTo calculate the perimeter of any polygon, you add up the length of all the sides. For reference, a polygon is any two-dimensional closed shape that\u2019s composed of straight lines.<\/p>\n<h3><span id=\"Perimeter_of_a_Rectangle\" class=\"m-toc-anchor\"><\/span>Perimeter of a Rectangle<\/h3>\n<p>\nLet\u2019s use a rectangular swimming pool as an example.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-1.webp\" alt=\"Blue background with the words &quot;Swimming Pool&quot; written in large white letters.\" width=\"529.72\" height=\"247.18\" class=\"aligncenter size-full wp-image-229399\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-1.webp 1558w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-1-300x140.webp 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-1-1024x478.webp 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-1-768x358.webp 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-1-1536x717.webp 1536w\" sizes=\"(max-width: 1558px) 100vw, 1558px\" \/><br \/>\nWe want to add a safety fence along the outside of the pool. In order to figure out how much material is needed, we first need to figure out the perimeter of the pool. The length of the pool is 15 ft, and the width is 7 ft.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-2.webp\" alt=\"Diagram of a swimming pool labeled &quot;Swimming Pool&quot; in the center, with dimensions shown as 15 feet wide and 7 feet high.\" width=\"2011\" height=\"1067\" class=\"aligncenter size-full wp-image-229402\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-2.webp 2011w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-2-300x159.webp 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-2-1024x543.webp 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-2-768x407.webp 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Swimming-pool-2-1536x815.webp 1536w\" sizes=\"auto, (max-width: 2011px) 100vw, 2011px\" \/><br \/>\nBecause it\u2019s a rectangle, we know that the opposite sides are congruent to each other.<\/p>\n<p>This is all the information we need. Let\u2019s add up all of the sides!<\/p>\n<p>Assuming 15 is equal to \\(a\\), and 7 is equal to \\(b\\), we can use the following formula: \\(\\text{Perimeter} = a + a + b + b\\).<\/p>\n<p>Now let\u2019s plug in our numbers. \\(P=15\\text{ ft}+15\\text{ ft}+7\\text{ ft}+7\\text{ ft}\\). Added together, we get 44 feet.<\/p>\n<p>Alternatively, since we know that there are four sides and that there are two sets of identical sides, we can simplify our formula to \\(P=2a+2b\\). Let\u2019s give it a whirl\u2014I bet we get the same result.<\/p>\n<div class=\"examplesentence\">\\(P=2(15) +2(7)=44\\text{ ft}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<div class=\"notice\" style=\"padding-bottom: 0px;\"> If you need help with perimeters of a rectangle, click here: <\/p>\n<div class=\"buttonlinks\"> <a href=\"https:\/\/www.mometrix.com\/academy\/calculating-the-perimeter-of-rectangles\/\">Perimeter of Rectangles<\/a> <\/div>\n<\/p>\n<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Perimeter_of_a_Square\" class=\"m-toc-anchor\"><\/span>Perimeter of a Square<\/h3>\n<p>\nWe can apply this same sort of principle to finding the perimeter of a square.<\/p>\n<p>A square has four equal sides, so we can say that the perimeter of a square is \\(4 \\times a\\).<\/p>\n<p>This principle also applies with an equilateral triangle. Because all three sides are the same, \\(P=3 \\times a\\). An isosceles triangle has two sides that are the same, so the perimeter is \\(2a+b\\). I think you get the point.<\/p>\n<p>Now, the only shape whose perimeter may seem a little less obvious to find is our friend the circle. You may have heard of the term <strong>circumference<\/strong>. Circumference is the measurement of the distance around a circle, which is similar to the perimeter of a polygon.<\/p>\n<p>Because there are no straight sides on a circle, the circumference can be calculated by multiplying the diameter of the circle times pi (\\(C=\\pi d\\)) or by multiplying the radius times 2 times pi (\\(C=2\\pi r\\)).<\/p>\n<p>Okay, we\u2019ve covered perimeter, now let\u2019s move on to area.<\/p>\n<h2><span id=\"How_to_Find_Area\" class=\"m-toc-anchor\"><\/span>How to Find Area<\/h2>\n<p>\nWhen we were looking at the perimeter of different shapes, we were able to simplify the formulas. This gave us different formulas for different shapes, but each one followed the same principles.<\/p>\n<p>Similarly, when finding the area of an object, the formula will be different for different shapes, but they all serve the same purpose: calculating the amount of space a shape occupies.<\/p>\n<p>So, let\u2019s take a look at different shapes and their area formulas.<\/p>\n<h3><span id=\"Area_Formulas\" class=\"m-toc-anchor\"><\/span>Area Formulas<\/h3>\n<p>\nA square, a rectangle, and a parallelogram all share a formula, which is \\(A=bh\\), commonly referred to as &#8220;length times width.&#8221;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Suqare-rectangle-parallelogram-area.webp\" alt=\"Diagrams of a square, rectangle, and parallelogram with bases labeled &quot;b&quot; and heights &quot;h.&quot; Each shape&#039;s area formula is given as A = bh.\" width=\"1972\" height=\"669\" class=\"aligncenter size-full wp-image-229405\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Suqare-rectangle-parallelogram-area.webp 1972w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Suqare-rectangle-parallelogram-area-300x102.webp 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Suqare-rectangle-parallelogram-area-1024x347.webp 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Suqare-rectangle-parallelogram-area-768x261.webp 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Suqare-rectangle-parallelogram-area-1536x521.webp 1536w\" sizes=\"auto, (max-width: 1972px) 100vw, 1972px\" \/><br \/>\nThe area of a triangle is \\(A=\\frac{1}{2}bh\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Triangle-area.webp\" alt=\"Diagram of a triangle with base (b) and height (h) labeled. The area formula is shown as A = 1\/2 bh.\" width=\"260.8\" height=\"267.6\" class=\"aligncenter size-full wp-image-229408\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Triangle-area.webp 652w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Triangle-area-292x300.webp 292w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><br \/>\nThe area for a trapezoid is \\(A=\\frac{1}{2}(b_1+b_2)h\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Trapezoid-area.webp\" alt=\"Diagram of a trapezoid showing bases (b_1) and (b_2) with height (h). Formula for area: (A = frac{1}{2} (b_1 + b_2) h).\" width=\"260.8\" height=\"267.6\" class=\"aligncenter size-full wp-image-229411\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Trapezoid-area.webp 652w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Trapezoid-area-292x300.webp 292w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><br \/>\nThe area of a circle is \\(A=\\pi r^2\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Circle-area.webp\" alt=\"Diagram of a circle with radius labeled &quot;r&quot; and area formula shown as A = \u03c0r\u00b2.\" width=\"260.8\" height=\"267.6\" class=\"aligncenter size-full wp-image-229414\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Circle-area.webp 652w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Circle-area-292x300.webp 292w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><br \/>\nNow let\u2019s look at some examples of how to solve for the area of a triangle and the area of a trapezoid.<\/p>\n<h3><span id=\"Area_of_a_Triangle_Example\" class=\"m-toc-anchor\"><\/span>Area of a Triangle Example<\/h3>\n<p>\nGiven that a triangle has a base of 6 centimeters and a height of 4 centimeters, calculate the area by substituting the values into the triangle area formula (\\(A=\\frac{1}{2}bh\\)). It\u2019s important to know that the height of a triangle will always make a right angle with the base.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Triangle-example.webp\" alt=\"Blue triangle with a base of 6 cm and a height of 4 cm, marked with a dashed line and a right angle.\" width=\"302.1\" height=\"282.3\" class=\"aligncenter size-full wp-image-229417\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Triangle-example.webp 1007w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Triangle-example-300x280.webp 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Triangle-example-768x718.webp 768w\" sizes=\"(max-width: 1007px) 100vw, 1007px\" \/> <\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}(6 \\times 4)\\)<\/div>\n<p>\n&nbsp;<br \/>\nStart by multiplying 6 times 4 to get a product of 24.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}(24)\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, multiply 1\/2 times 24 (the same as dividing by 2), which gives us a solution of 12 cm<sup>2<\/sup>.<\/p>\n<div class=\"examplesentence\">\\(A=12\\text{ cm}^2\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Area_of_a_Trapezoid_Example\" class=\"m-toc-anchor\"><\/span>Area of a Trapezoid Example<\/h3>\n<p>\nNow, let&#8217;s say you have a trapezoid with a height equal to 7 inches, base 1 equal to 8 inches, and base 2 equal to 6 inches.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Trapezoid-example.webp\" alt=\"A blue trapezoid with a height of 7 inches, top side 6 inches, and bottom side 8 inches.\" width=\"298.8\" height=\"327.96\" class=\"aligncenter size-full wp-image-229420\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Trapezoid-example.webp 830w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Trapezoid-example-273x300.webp 273w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Trapezoid-example-768x843.webp 768w\" sizes=\"(max-width: 830px) 100vw, 830px\" \/><\/p>\n<p>Given this, we can substitute our numbers into the formula for the area of a trapezoid:<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}(8 + 6)7\\)<\/div>\n<p>\n&nbsp;<br \/>\nStart by finding the sum of 8 and 6.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}(14)7\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, multiply 14 by 7 to get a product of 98.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}(98)\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, you can multiply 98 by 1\/2 or divide 98 by 2 to get a solution of 42 in<sup>2<\/sup>.<\/p>\n<div class=\"examplesentence\">\\(A=42\\text{ in}^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nThat&#8217;s it for this review. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\">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 area?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Each shape has a unique area formula. Here are some of the most common: <\/p>\n<ul>\n<li style=\"margin-bottom: 10px\"><strong style=\"font-weight: 600\">Circle:<\/strong> \\(A=\\pi r^2\\)<\/li>\n<li style=\"margin-bottom: 10px\"><strong style=\"font-weight: 600\">Square:<\/strong> \\(A=s^2\\)<\/li>\n<li style=\"margin-bottom: 10px\"><strong style=\"font-weight: 600\">Rectangle:<\/strong> \\(A=lw\\)<\/li>\n<li style=\"margin-bottom: 10px\"><strong style=\"font-weight: 600\">Triangle:<\/strong> \\(A=\\frac{1}{2}bh\\)<\/li>\n<li style=\"margin-bottom: 10px\"><strong style=\"font-weight: 600\">Parallelogram:<\/strong> \\(A=bh\\)<\/li>\n<li style=\"margin-bottom: 10px\"><strong style=\"font-weight: 600\">Trapezoid:<\/strong> \\(A=\\frac{1}{2} (b_1+b_2)h\\)<\/li>\n<\/ul>\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?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find perimeter by adding together the lengths of each side of the figure.<\/p>\n<div class=\"lightbulb-example-2\" style=\"min-width: 75%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the perimeter of this figure?<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimeter-Example-1.svg\" alt=\"A rectangular L-shaped figure with labeled side lengths: 4 in, 7 in, 3 in, 13 in, 7 in, and 20 in.\" width=\"366.6\" height=\"155.35\" class=\"aligncenter size-full wp-image-286771\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(P = 4 + 7 + 3 + 13 + 7 + 20 = 54 \\mathrm{\\:in}\\)<\/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 triangle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The most common way to find the area of a triangle is by multiplying its base times its height and dividing by 2: <\/p>\n<p style=\"text-align: center\">\\(A=\\dfrac{1}{2}bh\\)<\/p>\n<div class=\"lightbulb-example-2\" style=\"min-width: 75%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the area of this triangle?<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimeter-Example-2.svg\" alt=\"A right triangle with a base of 12 cm, a height of 6 cm, and a right angle at the bottom left corner.\" width=\"267.8\" height=\"155.35\" class=\"aligncenter size-full wp-image-286774\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(A=\\dfrac{1}{2} bh=\\dfrac{1}{2} (12)(6)=36 \\mathrm{\\: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;\">How do you find the perimeter of a rectangle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the perimeter of a rectangle by multiplying its length by 2 and its width by 2 and adding the values, or by adding its length and width and then multiplying by 2: <\/p>\n<p style=\"text-align: center\">\\(P = 2l + 2w\\)<\/p>\n<div class=\"lightbulb-example-2\" style=\"min-width: 75%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the perimeter of this rectangle?<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimeter-Example-3.svg\" alt=\"A rectangle with a length of 12 inches and a width of 4 inches is shown.\" width=\"275.6\" height=\"110.5\" class=\"aligncenter size-full wp-image-286777\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(P = 2(12) + 2(4) = 24 + 8 = 32 \\mathrm{\\:in}\\)<\/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 circle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the area of a circle by multiplying pi (\\(\\pi\\)) times the radius squared: <\/p>\n<p style=\"text-align: center\">\\(A=\\pi r^2\\)<\/p>\n<div class=\"lightbulb-example-2\" style=\"min-width: 75%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: What is the area of this circle?<\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimeter-Example-4.svg\" alt=\"A circle with a radius labeled 7 inches, extending from the center to the edge.\" width=\"186.15\" height=\"185.3\" class=\"aligncenter size-full wp-image-286768\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; margin-bottom: 0em\">\\(A=\\pi (7)^2=49\\pi \\mathrm{\\:in}^2 \\approx 156.86 \\mathrm{\\:in}^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;\">How do you find the perimeter of a triangle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Find the perimeter of a triangle by adding the lengths of all three sides together.<\/p>\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_Practice_Problems\" class=\"m-toc-anchor\"><\/span>Area and Perimeter 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 area of this rectangle?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimeter-Example-5.svg\" alt=\"A rectangle with a length of 19 cm and a width of 7 cm is shown, with measurements labeled on the top and right sides.\" width=\"339.2\" height=\"147.2\" class=\"aligncenter size-full wp-image-286795\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">52 cm<sup>2<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">133 cm<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-3\">47 cm<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-1-4\">154 cm<sup>2<\/sup><\/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 area of a rectangle, multiply its length by its width.<\/p>\n<p style=\"text-align:center;\">\\(A=lw\\)<\/p>\n<p>The length is 19 cm and the width is 7 cm.<\/p>\n<p style=\"text-align:center;\">\\(A=19\\times7=133\\mathrm{\\:cm}^2\\)<\/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 a square with a side length of 4 in?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">28 in<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-2\">24 in<sup>2<\/sup><\/div><div class=\"PQ\"  id=\"PQ-2-3\">12 in<sup>2<\/sup><\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">16 in<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>To find the area of a square, square the length of its side.<\/p>\n<p style=\"text-align:center; line-height: 45px\">\\(A=s^2\\)<br \/>\n\\(A=(4)^2=16\\text{ in}^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 rectangle?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimeter-Example-6.svg\" alt=\"A rectangle with a length of 22 cm and a width of 8 cm is shown, with dimensions labeled on the top and right sides.\" width=\"339.2\" height=\"147.2\" class=\"aligncenter size-full wp-image-286798\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">192 cm<\/div><div class=\"PQ\"  id=\"PQ-3-2\">176 cm<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">60 cm<\/div><div class=\"PQ\"  id=\"PQ-3-4\">30 cm<\/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>The formula for perimeter of a rectangle is:<\/p>\n<p style=\"text-align:center;\">\\(P=2(l+w)\\)<\/p>\n<p>The length is 22 cm and the width is 8 cm.<\/p>\n<p style=\"text-align:center;\">\\(P=2(22+8)=2(30)=60\\text{ cm}\\)<\/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 perimeter of this pentagon?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Area-and-Perimeter-Example-7.svg\" alt=\"A pentagon-shaped figure with a 6 ft base, two sides of 7 ft each, and two upper sides of 9 ft each forming a pointed top.\" width=\"200.8\" height=\"286.4\" class=\"aligncenter size-full wp-image-286801\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">38 ft<\/div><div class=\"PQ\"  id=\"PQ-4-2\">26 ft<\/div><div class=\"PQ\"  id=\"PQ-4-3\">42 ft<\/div><div class=\"PQ\"  id=\"PQ-4-4\">59 ft<\/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>Find the perimeter of a figure by adding the lengths of all the sides together.<\/p>\n<p style=\"text-align:center;\">\\(P=9+9+7+6+7=38\\text{ ft}\\)<\/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 formula for finding the perimeter of a rectangle?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(P=4s\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(P=2a+b+c\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(P=a+b+c\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-4\">\\(P=2l+2w\\)<\/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>Find the perimeter of a rectangle by adding double the length plus double the width, or add the length and width together and then double that number.<\/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 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