Problem Solving

An equilateral triangle that has an area of 9 3^1/2 is inscribed in a circle. What is the
area of the circle?
A . 6pi B. 9pi C. 12 pi D. 9pi 3^1/2 E. 18pi 3^1/2

radhika1306 wrote:An equilateral triangle that has an area of 9 3^1/2 is inscribed in a circle. What is the
area of the circle?
A . 6pi B. 9pi C. 12 pi D. 9pi 3^1/2 E. 18pi 3^1/2

For this question first find the measure of the side -

Area = 1/2 b*h

For an equilateral triangle h = b * root 3 by 2

so 1/2 * b * b * 3^1/2 * 1/2 = 9 3^1/2

so b^2 = 9*4

so b =6

radius of circle with the equilateral triangle inscribed in it is side/ 3^1/2

so area of circle = pie r^2 =12 pi

Ans is C