Question

The diameter was of four half circles are sides of a square with a side length of 7 cm.

Find the exact area of the shaded region in terms of pi. (Please show work)

Answer 1

shaded area = 24.5π -49

Explanation:

The area of a segment of a circle is given by the formula ...

A = 1/2r²(θ -sin(θ))

Here, the radius of the circle is (7 cm)/2 = 3.5 cm, and the angle of interest is π/2 radians.

There are 8 segments of this size in the shaded area, so we have ...

shaded area = 8(1/2)(3.5 cm)²(π/2 -sin(π/2))

shaded area = 24.5π -49