Question

In the given figure abc is an equilateral triangle inscribed in a circle of radius 20 cm. Find the area of shaded region

Answer 1

All vertices of equilateral triangle on the circle. It means triangle is circumscribed. Radius of circle is 4 cm.

Let ,Radius = R and side of equilateral triangle is A. Height of triangle = H.

R = 2H / 3.

H^2 = A^2 — (A/2)^2

H^2= 3 A^2 / 4.

H = √3 A / 2.

3R/2 = √3 A / 2.

A = √3 R.

A = 4√3.

Area of Circle = π R^2 = 3.14 x 4^2 = 50.24

area of circle = √3 A^2 / 4 = 12 √3 = 20.4

Remaining area =50.24 - 20.4 = 29.84 sq. cm