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.
+128408 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
