SOLUTION: A circle is inscribed in an equilateral triangle, the radius of the circle is 6 cm. Find the area of the triangle.

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Question 319824: A circle is inscribed in an equilateral triangle, the radius of the circle is 6 cm. Find the area of the triangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The apothem of the triangle is equal to the radius of the inscribed circle and related to the side, s, by,
ap=%28sqrt%283%29%2As%29%2F6=6
s=36%2Fsqrt%283%29
The area of the triangle is
A=%28sqrt%283%29%2F4%29%2As%5E2
A=%28sqrt%283%29%2F4%29%2A%2836%2Fsqrt%283%29%29%5E2
A=108sqrt%283%29cm^2