{"id":11416,"date":"2022-07-08T22:53:51","date_gmt":"2022-07-08T17:23:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11416"},"modified":"2022-07-08T22:53:55","modified_gmt":"2022-07-08T17:23:55","slug":"prove-that-the-area-of-an-equilateral-triangle-described-on-one-side-of-square-is-equal-to-half-the-area-of-the-equilateral-described-on-one-of-the-diagonals","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-the-area-of-an-equilateral-triangle-described-on-one-side-of-square-is-equal-to-half-the-area-of-the-equilateral-described-on-one-of-the-diagonals\/","title":{"rendered":"Prove that the area of an equilateral triangle described on one side of square is equal to half the area of the equilateral described on one of the diagonals."},"content":{"rendered":"

Solution :<\/h2>\n

Given<\/strong> : A square ABCD, equilateral triangles BCE and ACF have been drawn on side BC and the diagonal AC respectively.\"triangles\"<\/p>\n

To Prove<\/strong> : \\(area(\\triangle BCE)\\) = \\(1\\over 2\\)\\(area(\\triangle DEF)\\)<\/p>\n

Proof<\/strong> : Since all equilateral triangles are similar.<\/p>\n

\\(\\implies\\)\u00a0 \\(\\triangle\\) BCE ~ \\(\\triangle\\) ACF<\/p>\n

\\(area(\\triangle BCE)\\over area(\\triangle ACF)\\) = \\({BC}^2\\over {AC}^2\\)<\/p>\n

Since, Diagonal = \\(\\sqrt{2}\\) side, So, AC = \\(\\sqrt{2}\\) BC<\/p>\n

\\(\\implies\\) \\(area(\\triangle BCE)\\over area(\\triangle ACF)\\) = \\({BC}^2\\over {\\sqrt{2} BC}^2\\)<\/p>\n

\\(\\implies\\)\u00a0 \\(area(\\triangle BCE)\\over area(\\triangle ACF)\\) = \\(1\\over 2\\)<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given : A square ABCD, equilateral triangles BCE and ACF have been drawn on side BC and the diagonal AC respectively. To Prove : \\(area(\\triangle BCE)\\) = \\(1\\over 2\\)\\(area(\\triangle DEF)\\) Proof : Since all equilateral triangles are similar. \\(\\implies\\)\u00a0 \\(\\triangle\\) BCE ~ \\(\\triangle\\) ACF \\(area(\\triangle BCE)\\over area(\\triangle ACF)\\) = \\({BC}^2\\over {AC}^2\\) Since, Diagonal …<\/p>\n

Prove that the area of an equilateral triangle described on one side of square is equal to half the area of the equilateral described on one of the diagonals.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,912],"tags":[],"yoast_head":"\nProve that the area of an equilateral triangle described on one side of square is equal to half the area of the equilateral described on one of the diagonals. - Mathemerize<\/title>\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\/prove-that-the-area-of-an-equilateral-triangle-described-on-one-side-of-square-is-equal-to-half-the-area-of-the-equilateral-described-on-one-of-the-diagonals\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that the area of an equilateral triangle described on one side of square is equal to half the area of the equilateral described on one of the diagonals. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given : A square ABCD, equilateral triangles BCE and ACF have been drawn on side BC and the diagonal AC respectively. 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