Find the area of an equilateral triangle inscribed in a circle with a circumference of 18 Pi cm.
The radius of the circle can be found as
18pi = 2pi * r
18pi / (2pi) = r = 9
We can divide the equilateral triangle into three congruent triangles.....the area of of of these triangles is given by
(1/2) r^2 *sqrt (3) / 2 = (1/2) 9^2 * sqrt (3) / 2 = 81 sqrt (3) / 4 cm^2
So....the area of the equilateral triangle = 3 (81)sqrt (3) / 4 cm^2 = (243)sqrt (3) / 4 cm^2