Angle AOB has a measure of 2π 3 radians. The shaded region (a sector of the circle) has an area of 12π 2 cm . Find the exact area of triangle AOB.

Question

Angle AOB has a measure of 2π 3 radians. The shaded region (a sector of the circle) has an area of 12π 2 cm . Find the exact area of triangle AOB.

using trignometry

Answer 1

If the shaded area is the sector AOB, the area of the sector is

(2/3)π * πr²/2π = 12π² => r² =36π

The area of the triangle AOB = (1/2)*36π*sin(2π/3)

I will leave the arithmetic to you!