{"id":86425,"date":"2021-07-20T14:15:27","date_gmt":"2021-07-20T19:15:27","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=86425"},"modified":"2026-03-26T09:34:08","modified_gmt":"2026-03-26T14:34:08","slug":"area-of-any-triangle","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/area-of-any-triangle\/","title":{"rendered":"Area of Any Triangle"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_nrlNhgk73-M\" 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_nrlNhgk73-M\" data-source-videoID=\"nrlNhgk73-M\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Area of Any Triangle Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Area of Any Triangle\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_nrlNhgk73-M:hover {cursor:pointer;} img#videoThumbnailImage_nrlNhgk73-M {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1733-find-the-area-of-any-triangle-copy-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_nrlNhgk73-M\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_nrlNhgk73-M\" 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 of Any Triangle\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_nrlNhgk73-M\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_nrlNhgk73-M\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_nrlNhgk73-M\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction X8m_Function() {\n  var x = document.getElementById(\"X8m\");\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=\"X8m_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=\"X8m\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Basic_Area_of_a_Triangle_Formula\" class=\"smooth-scroll\">Basic Area of a Triangle Formula<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Area_of_a_Triangle_Given_Lengths_of_All_Three_Sides\" class=\"smooth-scroll\">Area of a Triangle Given Lengths of All Three Sides<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Area_of_an_Isosceles_Triangle\" class=\"smooth-scroll\">Area of an Isosceles Triangle<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Area_of_an_Equilateral_Triangle\" class=\"smooth-scroll\">Area of an Equilateral Triangle<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Review\" class=\"smooth-scroll\">Review<\/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>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on finding the area of any triangle!<\/p>\n<p>In this video, we will cover four different formulas:<\/p>\n<ul>\n<li>Area given base and height<\/li>\n<li>Area given all three side lengths<\/li>\n<li>Area of an isosceles triangle<\/li>\n<li>Area of an equilateral triangle<\/li>\n<\/ul>\n<h2><span id=\"Basic_Area_of_a_Triangle_Formula\" class=\"m-toc-anchor\"><\/span>Basic Area of a Triangle Formula<\/h2>\n<p>\nWe are going to start with the most common formula for area of a triangle.<\/p>\n<p>This is the formula that you will use almost every time and the one that is usually taught in schools: <span style=\"font-style:normal; font-size:90%\">\\(A=\\frac{1}{2}bh\\)<\/span>, where <span style=\"font-style:normal; font-size:90%\">\\(b\\)<\/span> stands for the length of the triangle\u2019s base and <span style=\"font-style:normal; font-size:90%\">\\(h\\)<\/span> stands for the triangle\u2019s height.<\/p>\n<p>This formula is useful for almost every triangle, especially if you are given the base and the height or can easily find them.<\/p>\n<p>Let\u2019s try a couple of examples.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nFind the area of the following triangle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87829\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-1.png\" alt=\"Right triangle with sides of length 7 and 6 inches\" width=\"801\" height=\"760\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-1.png 801w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-1-300x285.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-1-768x729.png 768w\" sizes=\"auto, (max-width: 801px) 100vw, 801px\" \/><\/p>\n<p>In this example, our base is 6 inches and our height is 7 inches. If we plug these values into our formula, we get:<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}bh\\)\\(=\\frac{1}{2}(6\\text{ in})(7\\text{ in})=21\\text{ in}^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nOur area is 21 inches squared.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try another one.<\/p>\n<p>What is the area of this triangle?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87835\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-2.png\" alt=\"triangle with height of 4 cm and base of 21 cm\" width=\"905\" height=\"520\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-2.png 905w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-2-300x172.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-2-768x441.png 768w\" sizes=\"auto, (max-width: 905px) 100vw, 905px\" \/><\/p>\n<p>In this example, our base is 21 cm and our height is 4 cm. If we plug these numbers into our formula, we get:<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}bh\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe always write our formula, just so it helps us remember it.<\/p>\n<div class=\"examplesentence\">\\(=\\frac{1}{2}(21\\text{ cm})(4\\text{ cm})=42\\text{ cm}^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe area of our triangle is 42 square centimeters.<\/p>\n<h2><span id=\"Area_of_a_Triangle_Given_Lengths_of_All_Three_Sides\" class=\"m-toc-anchor\"><\/span>Area of a Triangle Given Lengths of All Three Sides<\/h2>\n<p>\nThe second formula we are going to cover is not as well known but is still extremely useful. It is the formula for finding the area of a triangle when you are given the lengths of all three sides. Depending on the triangle, there may be times when you can use the side lengths to find the height of the triangle, but this is not always possible, which is when the following formula comes in handy. <\/p>\n<p><span style=\"font-style:normal; font-size:90%\">\\(A=\\sqrt{s(s-a)(s-b)(s-c)}\\)<\/span>, where <span style=\"font-style:normal; font-size:90%\">\\(s\\)<\/span> is the semi-perimeter of the triangle and <span style=\"font-style:normal; font-size:90%\">\\(a\\)<\/span>, <span style=\"font-style:normal; font-size:90%\">\\(b\\)<\/span>, and <span style=\"font-style:normal; font-size:90%\">\\(c\\)<\/span> are each of the side lengths.<\/p>\n<p>Let\u2019s talk about <strong>semi-perimeter<\/strong> for a minute. Semi-perimeter isn\u2019t something we come across often, so we need to break apart the word to figure out what exactly it means. We know that perimeter is the distance around an object, so it is the lengths of all the sides added together, but what does \u201csemi\u201d mean?<\/p>\n<p>You may think of a semi-circle to help you understand. A semi-circle is half a circle, so in math, \u201csemi\u201d must mean half. Now that we know what each part of the word means separately, let\u2019s put it together. Semi-perimeter must mean half of the perimeter.<\/p>\n<p>Let\u2019s try a couple of examples using this formula.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nWhat is the area of this triangle?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87838\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-3.png\" alt=\"triangle with sides of  7 m, 9 m, and 13 m\" width=\"1002\" height=\"628\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-3.png 1002w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-3-300x188.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-3-768x481.png 768w\" sizes=\"auto, (max-width: 1002px) 100vw, 1002px\" \/><\/p>\n<p>The first thing we want to do is write out our formula. I always recommend doing this because it helps you remember where to plug something in, and writing the formula out repeatedly will help you remember it.<\/p>\n<div class=\"examplesentence\">\\(A=\\sqrt{s(s-a)(s-b)(s-c)}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe know our <span style=\"font-style:normal; font-size:90%\">\\(a\\)<\/span>, <span style=\"font-style:normal; font-size:90%\">\\(b\\)<\/span>, and <span style=\"font-style:normal; font-size:90%\">\\(c\\)<\/span> values, but we don\u2019t know the value of <span style=\"font-style:normal; font-size:90%\">\\(s\\)<\/span>, so before we can plug things into our formula, we need to figure out what <span style=\"font-style:normal; font-size:90%\">\\(s\\)<\/span> is. <span style=\"font-style:normal; font-size:90%\">\\(S\\)<\/span> stands for semi-perimeter, so we want to find the perimeter of our triangle and then divide by 2.<\/p>\n<div class=\"examplesentence\">\\(s=\\frac{7+9+13}{2}=\\frac{29}{2}=14.5\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow that we know that <span style=\"font-style:normal; font-size:90%\">\\(s\\)<\/span> is 14.5, we can plug all our known values into our equation.<\/p>\n<div class=\"examplesentence longmath-container\">\\(A=\\sqrt{14.5(14.5-7)(14.5-9)(14.5-13)}\\)<br \/>\n\\(=\\sqrt{14.5(7.5)(5.5)(1.5)}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhich, when you simplify this out, is approximately equal to 29.95 square meters.<\/p>\n<div class=\"examplesentence\">\\(\\approx 29.95\\text{ m}^{2}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try another one.<\/p>\n<p>Find the area of the following triangle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87841\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-4.png\" alt=\"triangle sides of 12 ft, 24 ft, and 13 ft\" width=\"827\" height=\"596\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-4.png 827w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-4-300x216.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-4-768x553.png 768w\" sizes=\"auto, (max-width: 827px) 100vw, 827px\" \/><\/p>\n<p>The first thing we need to do is write out our equation.<\/p>\n<div class=\"examplesentence\">\\(A=\\sqrt{s(s-a)(s-b)(s-c)}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we need to find our semi-perimeter.<\/p>\n<div class=\"examplesentence\">\\(s=\\frac{12+24+13}{2}=\\frac{49}{2}=24.5\\)<\/div>\n<p>\n&nbsp;<br \/>\nFinally, we plug all our values into the equation.<\/p>\n<div class=\"examplesentence longmath-container\">\\(A=\\sqrt{24.5(24.5-12)(24.5-24)(24.5-13)}\\)\\(=\\sqrt{24.5(12.5)(0.5)(11.5)}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhich, when you simplify it out, is approximately equal to 41.96 square feet.<\/p>\n<h2><span id=\"Area_of_an_Isosceles_Triangle\" class=\"m-toc-anchor\"><\/span>Area of an Isosceles Triangle<\/h2>\n<p>\nThe next formula we are going to look at is a formula for finding the area of an isosceles triangle. The formula is <span style=\"font-style:normal; font-size:90%\">\\(A=\\frac{1}{2}b\\sqrt{a^{2}-\\frac{b^{2}}{4}}\\)<\/span>, where a is the length of one of the two congruent sides and <span style=\"font-style:normal; font-size:90%\">\\(b\\)<\/span> is the length of the unique side.<\/p>\n<p>Let\u2019s try out this formula on a couple of examples.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nWhat is the area of this triangle?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87847\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-5.png\" alt=\"Isosceles triangle with two sides of 7 m and one side 3 m\" width=\"457\" height=\"690\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-5.png 457w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-5-199x300.png 199w\" sizes=\"auto, (max-width: 457px) 100vw, 457px\" \/><\/p>\n<p>First, we\u2019ll write out our formula.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}b\\sqrt{a^{2}-\\frac{b^{2}}{4}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen we want to plug in our known values and solve.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}(3)\\sqrt{(7)^{2}-\\frac{(3)^{2}}{4}}\\)&nbsp;<br \/>\n\\(=\\frac{1}{2}(3)\\sqrt{49-\\frac{9}{4}}\\)&nbsp;<br \/>\n\\(=\\frac{3}{2}\\sqrt{\\frac{196}{4}-\\frac{9}{4}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe 196 over 4 comes from converting our 49 to a fraction. So we did this by multiplying by 4 over 4 so that we have fractions with common denominators and are able to subtract them.<\/p>\n<div class=\"examplesentence\">\\(=\\frac{3}{2}\\sqrt{\\frac{187}{4}}\\)<br \/>\n\\(\\approx 10.26\\text{ m}^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe area of our triangle is approximately 10.26 square meters.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nTry finding the area of this triangle:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87856\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-6.png\" alt=\"Isosceles triangle with two sides of 12 cm and one side of 7 cm\" width=\"782\" height=\"561\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-6.png 782w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-6-300x215.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-6-768x551.png 768w\" sizes=\"auto, (max-width: 782px) 100vw, 782px\" \/><\/p>\n<p>To find the area of our triangle, we are going to first write out our formula and then plug in our values to solve it.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{1}{2}b\\sqrt{a^{2}-\\frac{b^{2}}{4}}\\)&nbsp;<br \/>\n\\(=\\frac{1}{2}(7)\\sqrt{(12)^{2}-\\frac{(7)^{2}}{4}}\\)&nbsp;<br \/>\n\\(=\\frac{7}{2}\\sqrt{144-\\frac{49}{4}}\\)&nbsp;<br \/>\n\\(=\\frac{7}{2}\\sqrt{\\frac{576}{4}-\\frac{49}{4}}\\)&nbsp;<br \/>\n\\(=\\frac{7}{2}\\sqrt{\\frac{527}{4}}\\)&nbsp;<br \/>\n\\(\\approx 40.17\\text{ cm}^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe area of our triangle is approximately 40.17 centimeters squared.<\/p>\n<h2><span id=\"Area_of_an_Equilateral_Triangle\" class=\"m-toc-anchor\"><\/span>Area of an Equilateral Triangle<\/h2>\n<p>\nThe last formula we are going to look at is the formula for an equilateral triangle. This formula is <span style=\"font-style:normal; font-size:90%\">\\(A=\\frac{\\sqrt{3}}{4}a^{2}\\)<\/span>, where <span style=\"font-style:normal; font-size:90%\">\\(a\\)<\/span> is the length of one of the sides.<\/p>\n<p>Let\u2019s look at a couple of examples.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nWhat is the area of an equilateral triangle with a side length of 2 ft?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87859\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-7.png\" alt=\"Equilateral triangles with sides of length 2 ft\" width=\"710\" height=\"606\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-7.png 710w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-7-300x256.png 300w\" sizes=\"auto, (max-width: 710px) 100vw, 710px\" \/><\/p>\n<p>First, we\u2019re going to write out our formula.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{\\sqrt{3}}{4}a^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we are going to plug in our value for <span style=\"font-style:normal; font-size:90%\">\\(a\\)<\/span>.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{\\sqrt{3}}{4}(2)^{2}=\\frac{\\sqrt{3}}{4}(4)=\\sqrt{3}\\text{ ft}^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo the area of our triangle is the square root of 3 feet squared.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try one more example involving an equilateral triangle.<\/p>\n<p>What is this triangle\u2019s area?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87862\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-8.png\" alt=\"equilateral triangles with sides of 9 in\" width=\"598\" height=\"574\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-8.png 598w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-8-300x288.png 300w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>We find the area by writing out our formula and then substituting in our <span style=\"font-style:normal; font-size:90%\">\\(a\\)<\/span> value.<\/p>\n<div class=\"examplesentence\">\\(A=\\frac{\\sqrt{3}}{4}a^{2}\\)<br \/>\n\\(=\\frac{\\sqrt{3}}{4}(9)^{2}\\)&nbsp;<br \/>\n\\(=\\frac{\\sqrt{3}}{4}(81)\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhich, when you simplify it, is approximately 35.07 square inches.<\/p>\n<div class=\"examplesentence\">\\(\\approx 35.07\\text{ in}^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe area of our triangle is approximately 35.07 inches squared.<\/p>\n<hr>\n<h2><span id=\"Review\" class=\"m-toc-anchor\"><\/span>Review<\/h2>\n<p>\nWe covered a lot of formulas in this video, but I hope they were helpful. Each of these formulas is useful, but the two most common ones are the first two we covered. If you don\u2019t already have those two memorized, I would recommend doing that because they will come up frequently in your math classes.<\/p>\n<p>Before we go, let\u2019s look at a review question.<\/p>\n<p>If you are given the triangle shown below, which area formula should you use?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-87865\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-9.png\" alt=\"Triangle with sides of 7 cm, 12 cm, and 19 cm\" width=\"591\" height=\"287\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-9.png 591w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Area-of-Any-Triangle-9-300x146.png 300w\" sizes=\"auto, (max-width: 591px) 100vw, 591px\" \/><\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li style=\"margin-bottom: 1em;\">\\(A=\\frac{1}{2}bh\\)<\/li>\n<li style=\"margin-bottom: 1em;\">\\(A=\\sqrt{s(s-a)(s-b)(s-c)}\\)<\/li>\n<li style=\"margin-bottom: 1em;\">\\(A=\\frac{1}{2}b\\sqrt{a^{2}-\\frac{b^{2}}{4}}\\)<\/li>\n<li>\\(A=\\frac{\\sqrt{3}}{4}a^{2}\\)<\/li>\n<\/ol>\n<div style=\"text-align: center; margin-bottom: 20px;\"><button class=\"buttontranscript\" onClick=\"toggle('Answer1')\">Show Answer<\/button><\/div>\n<div id=\"Answer1\" style=\"display:none; box-shadow: 1.5px 1.5px 5px grey; background-color:#E0E0E0; padding: 30px; padding-bottom: 15px; width: 60%; margin: auto; text-align: center;\">\n<strong>The correct answer is B!<\/strong><\/p>\n<p style=\"text-align: left;\">We are given all three side lengths, so this is the most direct formula to plug our values into.<\/p>\n<\/div>\n<p>\n&nbsp;<br \/>\nI hope this video was helpful. 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