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

`= 1/2*BC*AD`

`= 1/2*10.276*8.9`

`= 45.73`

* So the area of the triangle is 45.73square inch*` `

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