{"id":836745,"date":"2024-07-16T11:52:17","date_gmt":"2024-07-16T06:22:17","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=836745"},"modified":"2024-07-16T11:52:17","modified_gmt":"2024-07-16T06:22:17","slug":"exam-prep-area-of-isosceles-triangle","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-area-of-isosceles-triangle\/","title":{"rendered":"Area Of Isosceles Triangle with Solved Examples"},"content":{"rendered":"\n<p>An isosceles triangle&#8217;s area is the amount of space it encloses in two dimensions. The general formula for the area of a <a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-maths-shapes\/\"><strong>triangle<\/strong><\/a> is half the product of its base and height. To help you grasp this idea better, we&#8217;ve included a full description of the isosceles triangle area, its formula, and derivation, as well as a few solved sample questions.<\/p>\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-isosceles-triangle\">What is Isosceles Triangle?<\/h2>\n\n\n\n<p>Triangles are three-sided enclosed polygons that can be classified as equilateral, isosceles, or scalene depending on the length of their sides. Isosceles triangles are those with at least two sides of identical length.<\/p>\n\n\n\n<p>An isosceles triangle has specific qualities that differentiate it from other forms of triangles, which are given below:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>There are two equal sides and <a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concept-types-of-angles\/\"><strong>angles<\/strong><\/a>.<\/li>\n\n\n\n<li>An isosceles triangle&#8217;s legs are its two equal sides, and the angle between them is known as the vertex angle or apex angle.<\/li>\n\n\n\n<li>The side opposite the vertex angle is known as the base, and base angles are equal.<\/li>\n\n\n\n<li>The base and apex angles are bisected from the apex angle&#8217;s <a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-perpendicular-axis-theorem\/\"><strong>perpendicular<\/strong><\/a>.<\/li>\n\n\n\n<li>The isosceles triangle is divided into two congruent triangles by the perpendicular drawn from the apex angle, which is also known as the line of symmetry.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-the-area-of-isosceles-triangle\">What is the Area of Isosceles Triangle?<\/h2>\n\n\n\n<p>The area of an isosceles triangle is the total amount of space covered inside its boundaries. If you know the height and base of an isosceles triangle, you can easily compute its area. The area of an isosceles triangle is calculated by multiplying half of its base and height.<\/p>\n\n\n\n<p>Area = (1\/2) \u00d7 (base) \u00d7 (height)<\/p>\n\n\n\n<p>where &#8220;base&#8221; refers to the isosceles triangle&#8217;s base length and &#8220;height&#8221; refers to the perpendicular distance between the base and the opposing vertex.<\/p>\n\n\n\n<p>The area of an isosceles triangle is measured in square units, such as square centimetres, square inches, or square metres, depending on the base and height of the triangle.<\/p>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background\"><strong>Also Read:<\/strong> <a href=\"https:\/\/leverageedu.com\/blog\/arts-with-maths\/\"><strong>Pathways for Arts with Maths Students<\/strong><\/a><\/p>\n\n\n\n<p>Also,<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>The perimeter of the isosceles triangle<\/td><td>P = 2a + b<\/td><\/tr><tr><td>The altitude of the isosceles triangle<\/td><td>h = \u221a(a<sup>2<\/sup> \u2212 b<sup>2<\/sup>\/4)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-list-of-formulas-to-find-isosceles-triangle-area\">List of Formulas to Find Isosceles Triangle Area<\/h2>\n\n\n\n<p>Below is the list of the formulas used to find different Isosceles Triangle Area:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td colspan=\"2\">Formulas to Find Area of Isosceles Triangle<\/td><\/tr><tr><td>Using base and Height<\/td><td>A = \u00bd \u00d7 b \u00d7 hwhere b = base and h = height<\/td><\/tr><tr><td>Using all three sides<\/td><td>A = \u00bd[\u221a(a<sup>2<\/sup> \u2212 b<sup>2<\/sup> \u20444) \u00d7 b]a is the measure of equal sidesb is the base of triangle<\/td><\/tr><tr><td>Using the length of 2 sides and an angle between them<\/td><td>A = \u00bd \u00d7 a \u00d7 b \u00d7 sin(\u03b1)a is the measure of equal sidesb is the base of triangle<\/td><\/tr><tr><td>Using two angles and length between them<\/td><td>A = [a<sup>2<\/sup>\u00d7sin(\u03b2)\u00d7sin(\u03b1)\/ 2\u00d7sin(2\u03c0\u2212\u03b1\u2212\u03b2)]a is the measure of equal sidesb is the base of triangle\u03b1 is the measure of equal angles\u03b2 is the angle opposite to the base<\/td><\/tr><tr><td>Area formula for an isosceles right triangle<\/td><td>A = \u00bd \u00d7 a<sup>2<\/sup>a is the measure of equal sides<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-to-find-the-area-of-an-isosceles-triangle\">How to Find the Area of an Isosceles Triangle?<\/h2>\n\n\n\n<p>To calculate the area of an isosceles triangle, follow these steps.<\/p>\n\n\n\n<p>Step 1: Determine the length (l) and breadth (b) of the given triangle.<\/p>\n\n\n\n<p>Step 2: Multiply the values from step 1 and divide by 2.<\/p>\n\n\n\n<p>Step 3: The value produced is the needed area, measured in m<sup>2<\/sup>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-derivation-for-isosceles-triangle-area-using-heron-s-formula\">Derivation for Isosceles Triangle Area Using Heron\u2019s Formula<\/h2>\n\n\n\n<p>The area of an isosceles triangle can be calculated using Heron&#8217;s formula, as explained below.<\/p>\n\n\n\n<p>According to Heron\u2019s formula,<\/p>\n\n\n\n<p><strong>Area = \u221a[s(s\u2212a)(s\u2212b)(s\u2212c)]<\/strong><\/p>\n\n\n\n<p>Where, s = \u00bd(a + b + c)<\/p>\n\n\n\n<p>Now, for an isosceles triangle,<\/p>\n\n\n\n<p>s = \u00bd(a + a + b)<\/p>\n\n\n\n<p>= s = \u00bd(2a + b)<\/p>\n\n\n\n<p>Or, s = a + (b\/2)<\/p>\n\n\n\n<p>Now,<\/p>\n\n\n\n<p>Area = \u221a[s(s\u2212a)(s\u2212b)(s\u2212c)]<\/p>\n\n\n\n<p>Or, Area = \u221a[s (s\u2212a)<sup>2<\/sup> (s\u2212b)]<\/p>\n\n\n\n<p>= Area = (s\u2212a) \u00d7 \u221a[s (s\u2212b)]<\/p>\n\n\n\n<p>Substituting the value of \u201cs\u201d<\/p>\n\n\n\n<p>= Area = (a + b\/2 \u2212 a) \u00d7 \u221a[(a + b\/2) \u00d7 ((a + b\/2) \u2212 b)]<\/p>\n\n\n\n<p>= Area = b\/2 \u00d7 \u221a[(a + b\/2) \u00d7 (a \u2212 b\/2)]<\/p>\n\n\n\n<p><strong>Or, area of isosceles triangle = b\/2 \u00d7 \u221a(a<\/strong><strong><sup>2<\/sup><\/strong><strong> \u2212 b<\/strong><strong><sup>2<\/sup><\/strong><strong>\/4)<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Area of Isosceles Right Triangle Formula<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">The formula for Isosceles Right Triangle Area = \u00bd \u00d7 a<sup>2<\/sup><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Deriviation:<\/strong><\/p>\n\n\n\n<p>An isosceles right triangle&#8217;s perimeter is equal to the sum of its sides.<\/p>\n\n\n\n<p>Assume the two sides are equal. Using Pythagoras&#8217; theorem, the uneven side is calculated to be a\u221a2.<\/p>\n\n\n\n<p>Therefore, the perimeter of an isosceles right triangle is a+a+a\u221a2.<\/p>\n\n\n\n<p>= 2a+a\u221a2<\/p>\n\n\n\n<p>= a(2+\u221a2)<\/p>\n\n\n\n<p>= a(2+\u221a2)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-area-of-isosceles-triangle-using-trigonometry\">Area of Isosceles Triangle Using Trigonometry<\/h2>\n\n\n\n<p>Using Length of 2 Sides and the angle between them,<\/p>\n\n\n\n<p>A = \u00bd \u00d7 b \u00d7 c \u00d7 sin(\u03b1)<\/p>\n\n\n\n<p>Using 2 Angles and Length between them<\/p>\n\n\n\n<p>A = [c<sup>2<\/sup>\u00d7sin(\u03b2)\u00d7sin(\u03b1)\/ 2\u00d7sin(2\u03c0\u2212\u03b1\u2212\u03b2)]<\/p>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/blog\/maths-books-for-competitive-exams\/\"><strong>Maths Books for Competitive Exams<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-solved-example\">Solved Example<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find the area of an isosceles triangle with a base length of 10 cm and a height of 17 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution,<\/p>\n\n\n\n<p>Base of the triangle (b) = 10 cm<\/p>\n\n\n\n<p>Height of the triangle (h) = 17 cm<\/p>\n\n\n\n<p>Area of Isosceles Triangle = (1\/2) \u00d7 b \u00d7 h<\/p>\n\n\n\n<p>= (1\/2) \u00d7 10 \u00d7 17<\/p>\n\n\n\n<p>= 5 \u00d7 17<\/p>\n\n\n\n<p>= 85 cm<sup>2<\/sup><\/p>\n\n\n\n<p>The area of the given isosceles triangle is 85 cm<sup>2<\/sup>.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Find the length of the base of an isosceles triangle with an area of 243 cm<sup>2<\/sup> and an altitude of 9 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution,<\/p>\n\n\n\n<p>Area of the triangle, A = 243 cm<sup>2<\/sup><\/p>\n\n\n\n<p>Height of the triangle (h) = 9 cm<\/p>\n\n\n\n<p>The base of the triangle = b =?<\/p>\n\n\n\n<p>Area of Isosceles Triangle = (1\/2) \u00d7 b \u00d7 h<\/p>\n\n\n\n<p>243 = (1\/2) \u00d7 b \u00d7 9<\/p>\n\n\n\n<p>243 = (b \u00d7 9)\/2<\/p>\n\n\n\n<p>b = (243 \u00d7 2)\/9<\/p>\n\n\n\n<p>b = 54 cm<\/p>\n\n\n\n<p>The altitude of the given isosceles triangle is 54 cm.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>Find the lengths of the equal sides of an isosceles triangle with a base of 24 cm and an area of 60 cm<sup>2<\/sup>.<\/li>\n<\/ol>\n\n\n\n<p>Solution,<\/p>\n\n\n\n<p>We know:<\/p>\n\n\n\n<p>The base of the isosceles triangle = 24 cm<\/p>\n\n\n\n<p>Area of the isosceles triangle = 60 cm<sup>2<\/sup><\/p>\n\n\n\n<p>Area of isosceles triangle = b\/2 \u00d7 \u221a(a<sup>2<\/sup> \u2212 b<sup>2<\/sup>\/4)<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<p>60 = (24\/2)\u221a(a<sup>2<\/sup> \u2212 24<sup>2<\/sup>\/4)<\/p>\n\n\n\n<p>60 = 12\u221a(a<sup>2<\/sup> \u2212 144)<\/p>\n\n\n\n<p>5 = \u221a(a<sup>2<\/sup>\u2212144)<\/p>\n\n\n\n<p>Squaring both sides, we get,<\/p>\n\n\n\n<p>25 = a<sup>2<\/sup>\u2212144<\/p>\n\n\n\n<p>a<sup>2<\/sup> = 169<\/p>\n\n\n\n<p>= a = 13 cm<\/p>\n\n\n\n<p>The length of the equal sides of the given isosceles triangle is 13 cm.<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-link-color wp-elements-c9a46442faf11e423b1770b9dd8055f1\"><strong>Related Posts<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Order of Operations and PEMDAS Rule<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/blog\/how-to-calculate-percentage-of-marks\/\"><strong>How to Calculate Percentage of Marks?<\/strong><\/a><br><\/td><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/blog\/bsc-maths-syllabus\/\"><strong>BSc Maths Syllabus<\/strong><\/a><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>Word Problems on Arithmetic Operations<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>20 Most Famous Indian Mathematicians<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>Geometry Questions for GMAT Quant Section<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-faqs\">FAQs<\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1721107086167\"><strong class=\"schema-faq-question\">What is the formula for the area of an isosceles triangle?<\/strong> <p class=\"schema-faq-answer\">To compute the area of an isosceles triangle, use the following formula:<br\/>A = \u00bd \u00d7 b \u00d7 h<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1721107108699\"><strong class=\"schema-faq-question\">What is the formula for the perimeter of an isosceles triangle?<\/strong> <p class=\"schema-faq-answer\">The perimeter of an isosceles triangle can be calculated using the following formula:<br\/>P = 2a + b<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1721107138588\"><strong class=\"schema-faq-question\">What is the area of an isosceles triangle?<\/strong> <p class=\"schema-faq-answer\">The area of a figure is defined as the space enclosed by its bounds. As a result, the area of an isosceles triangle is defined as the space occupied by the triangle itself.<\/p> <\/div> <\/div>\n\n\n\n<p>This was all about the \u201c<strong><em>Area Of Isosceles Triangle<\/em><\/strong>\u201d.&nbsp; For more such informative blogs, check out our <a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/study-material\/maths\/\"><strong>Maths Section<\/strong><\/a>, or you can learn more about us by visiting our <a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/study-material\/\"><strong>Study Material Section<\/strong><\/a> page.<\/p>\n","protected":false},"excerpt":{"rendered":"An isosceles triangle&#8217;s area is the amount of space it encloses in two dimensions. The general formula for&hellip;\n","protected":false},"author":124,"featured_media":836767,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[369,476,396],"tags":[],"class_list":{"0":"post-836745","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-indian-exams","8":"category-maths","9":"category-study-material"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Area Of Isosceles Triangle with Solved Examples - Leverage Edu Discover<\/title>\n<meta name=\"description\" content=\"To help you grasp this idea better, we&#039;ve included a full description of the isosceles triangle area, its formula, and derivation.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-area-of-isosceles-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Area Of Isosceles Triangle with Solved Examples\" \/>\n<meta property=\"og:description\" content=\"To help you grasp this idea better, we&#039;ve included a full description of the isosceles triangle area, its formula, and derivation.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-area-of-isosceles-triangle\/\" \/>\n<meta property=\"og:site_name\" content=\"Leverage Edu Discover\" \/>\n<meta property=\"article:published_time\" content=\"2024-07-16T06:22:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/9\/2024\/07\/15073902\/Area-Of-Isosceles-Triangle.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"640\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"argima\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"argima\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Area Of Isosceles Triangle with Solved Examples - 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