Two sectors of a circle of radius $12$ overlap as shown, with $P$ and $R$ as the centers of the respective circles. Determine the area of the shaded region.

Guest Jun 29, 2018

#1**+1 **

We can find half of the area of the shaded region as follows

Area of a sector of 1/6 of a circle with a radius of 12 - Area of a triangle with sides of 12 and an included angle of 60° =

(1/2) 12^2 ( pi/3) - (1/2) 12^2 sin (60) =

(1/2) 12^2 ( pi /3 - √3/2)

So...the shaded area is twice this =

12^2 ( pi /3 - √3/2) units^2 ≈ 26.1 units^2

CPhill
Jun 29, 2018