If an equilateral triangle is inscribed in a circle, 2/3 rd the height of the triangle will be the radius of the circle.


Let "a" be the side of the equilateral triangle.

Given sqrt(3)/4 x a^2 = 9 x sqrt(3)

Hence a^2=36

Thus a = 6.

Now height of the equilateral triangle = sqrt(3)/2 x a = sqrt(3)/2 x 6

Hence radius of the circle = 2/3 x sqrt(3)/2 x 6 = 2 x sqrt(3)

Hence area of the circle = 12 pi