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.
+130511 Dividing the shaded area in half from the bottom left vertex of the figure to the point of intersection we have this area :
Area of a quarter circle with a radius of 12 - area of a right triangle with legs of 12 =
pi (12)^2 / 4 = (1/2) (12)^2 = (12)^2 ( pi/4 - 1/2)
And by symmetry the total shaded area =
2 (12^2) ( pi/4 - 1/2) = 288 ( pi/4 - 1/2) units^2 ≈ 82.19 units^2
