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Find the area of an equilateral triangle with an apothem 8.9 inches long.
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By the apothegm it divides the base length equally in a equilateral triangle.
If the triangle is ABC and apothegm is AD then;
`BD = CD`
`AD = 8.9`
`AB = 2BD = 2CD`
By Pythagorean law for triangle ABD;
`AD^2+BD^2 = AB^2`
`8.9^2+BD^2 = (2BD)^2`
`8.9^2 = 4BD^2-BD^2`
`8.9^2 = 3BD^2`
`sqrt(8.9^2/3) = BD`
`5.138 = BD`
So `BC = 2*BD = 10.276 in`
Area of triangle
So the area of the triangle is 45.73square inch` `
Posted by jeew-m on April 9, 2013 at 12:34 AM (Answer #2)
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