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.
+37146 See image below
1/4 of the circle minus the triangle is 1/2 of the shaded area
1/4 of the circle 1/4 pi (12^2) = 36pi
area of triangle 1/2 * 12 * 12 = 72
36 pi - 72 * 2 = 72pi - 144 = ____________ units2
+2407 I really need to figure out how to make diagrams.... sorry if this is confusing.
Notice that 1/2 of the grey space is 1/4 of a circle - the right triangle.
So the total area of the grey space is 2(6^2*pi/4 - 6*6/2).
2(6^2*pi/4 - 6*6/2) = 18pi - 18
=^._.^=
+37146 See image below
1/4 of the circle minus the triangle is 1/2 of the shaded area
1/4 of the circle 1/4 pi (12^2) = 36pi
area of triangle 1/2 * 12 * 12 = 72
36 pi - 72 * 2 = 72pi - 144 = ____________ units2
