{"id":3054,"date":"2021-07-17T14:55:41","date_gmt":"2021-07-17T14:55:41","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3054"},"modified":"2021-12-18T22:24:47","modified_gmt":"2021-12-18T16:54:47","slug":"what-is-the-formula-for-triangle-area","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-formula-for-triangle-area\/","title":{"rendered":"Formula for Triangle Area"},"content":{"rendered":"

Earlier we find Area of Triangle<\/strong> by using the formula –<\/p>\n

\n

Area of Triangle = \\(\\sqrt{s(s-a)(s-b)(s-c)}\\)<\/p>\n

where s = \\(a+b+c\\over 2\\)<\/p>\n

and a, b, c are the sides of the triangle.<\/p>\n<\/blockquote>\n

we have used this heron’s formula to find the area of a triangle when the lengths of its sides are given.<\/p>\n

Here, we will learn what is the formula for triangle area in terms of coordinates of its vertices.<\/p>\n

Formula for Triangle Area<\/h2>\n

The area of triangle, the coordinates of whose vertices are A(\\(x_1,y_1\\)), B(\\(x_2,y_2\\)) and C(\\(x_3,y_3\\)) is given by –<\/p>\n

\n

Area of Triangle ABC = \\(1\\over 2\\) |[\\(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\\)]|<\/p>\n<\/blockquote>\n\n\n

Example : <\/span>Find the area of a triangle whose vertices are A(3, 2), B(11, 8) and C(8, 12).<\/p>\n

Solution : <\/span>Let A = (\\(x_1, y_1\\)) = (3, 2), B = (\\(x_2, y_2\\)) = (11, 8) and C = (\\(x_3, y_3\\)) = (8, 12) be the given points. Then,

\nArea of Triangle ABC = \\(1\\over 2\\) |[\\(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\\)]|

\n\\(\\implies\\) A = |[\\(3(8-12)+11(12-2)+8(2-8)\\)]|

\n\\(\\implies\\) A = |(-12+110-48)| = 25 sq. units<\/p>\n\n\n

Remarks :<\/strong><\/p>\n

\n

(i) If the area of triangle joining three points is zero, then the points are collinear.<\/p>\n

(ii) If altitude of any equilateral triangle is P, then its area = \\(P^2\\over {\\sqrt{3}}\\). If ‘a’ be the side of equilateral triangle, then its area = (\\(a^2\\sqrt{3}\\over 4\\))<\/p>\n<\/blockquote>\n\n\n

Example : <\/span>Prove that the area of triangle whose vertices are (t, t-2), (t+2, t+2) and (t+3, t) is independent of t.<\/p>\n

Solution : <\/span>Let A = (\\(x_1, y_1\\)) = (t, t-2), B = (\\(x_2, y_2\\)) = (t+2, t+2) and C = (\\(x_3, y_3\\)) = (t+3, t) be the vertices of given triangle. Then,

\nArea of Triangle ABC = \\(1\\over 2\\) |[\\(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\\)]|

\n\\(\\implies\\) A = |[\\(t(t+2-t)+(t+2)(t-t+2)+(t+3)(t-2-t-2)\\)]|

\n\\(\\implies\\) A = |(2t+2t+4-4t-12)| = |-4| = 4 sq. units

\nClearly, area of triangle ABC is independent of t.<\/p>\n\n\n\n

\n
Next – How to Separate Pair of Straight Lines<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – How to Find the Distance Between Two Parallel Lines<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Earlier we find Area of Triangle by using the formula – Area of Triangle = \\(\\sqrt{s(s-a)(s-b)(s-c)}\\) where s = \\(a+b+c\\over 2\\) and a, b, c are the sides of the triangle. we have used this heron’s formula to find the area of a triangle when the lengths of its sides are given. Here, we will …<\/p>\n

Formula for Triangle Area<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[32],"tags":[658,659,660],"yoast_head":"\nFormula for Triangle Area - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn what is the formula for triangle area , and how to find area of triangle using the formula with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-is-the-formula-for-triangle-area\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Triangle Area - 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