The picture shows 4 circles which each have a radius of 1.5 inches. Find the area of the shaded region in square inches.

Question

I understand how to get the area of the circle , but the shaded region is what I cannot find. The circles are all touching and the shaded region includes the space in between the 4 circles and one of the circles.

Answer 1

Assuming that the shaded region is the four pointed "star" made by the four circles, connect the centers of the four circles. this makes a square with sides of 3 inches. The area of this square is 9 in². Now subtract the four sectors. They add up to one circle - area of π(1.5)², or 2.25π.

 

The area of the shaded region is 9 - 2.25π in², or approximately 2 in².