Question

A triangle is placed in a semicircle with a radius of 9ft, as shown below. Find the area of the shaded region.

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

Answer 1

The height is given as 9 ft. this is also the radius of the circle.

The base of the triangle would be 2 times the radius = 18 feet.

The area of the triangle is 1/2 x 9 x 18 = 81 square feet.

The area of the semi circle is : 1/2 x PI x r^2 = 1/2 x 3.14 x 9^2 = 127.17

The area of the shaded region is the area of the triangle minus the area of the semi circle:

127.17 - 81 = 46.17 square feet.