See the attached figure radius of the circle = r = 6 the length of one side of the equilateral triangle = L the height if the triangle = h
The shaded area is the required area. ∴The area = (1/3) (area of circle - area of triangle )
area of circle = π r² = π * 6² = 36 π
An equilateral triangle is inscribed in a circle of radius r ∴ The length of one side of the triangle = √3 * r = 6√3 and the height of the triangle = (√3 /2) * 6√3 = 9
∴ Area of the triangle = 0.5 * 9 * 6√3 = 27√3
The required area = (1/3) (area of circle - area of triangle ) = (1/3) * ( 36π - 27√3 ) = 12π - 9√3
