Question

A rectangle is placed around a semicircle as shown below. The length of the rectangle is 12 cm. Find the area of the shaded region.

Use the value 3.14 for at, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

15.48 ft^2

Explanation:

According to the image we have the following information:

the length of the rectangle = diameter of the semicircle, therefore it is 12 feet

, the radius of the semicircle (half the diameter) = width of the rectangle = 12/2 ft = 6 ft

We also know that the area of the shaded region would be equal to the area of the rectangle minus the area of the semicircle.

Therefore, we replace:

Area of the rectangle = width * length

Ar = 6 ft * 12 ft = 72 ft ^ 2

Area of the semicircle = [1/2] * π * (r ^ 2)

As = [1/2] * 3.14 * (6 feet) ^ 2 = 56.52 ft ^ 2

We replace in the area of the shaded region

shaded region area = 72 ft ^ 2 - 56.52 ft ^ 2 =

Shaded region area = 15.48 ft ^ 2