Question

A rectangle is placed around a semicircle as shown below. The length of the rectangle is 8 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.

PLEASE HELP​

Answer 1

Area of the shaded region = 6.88 cm²

Explanation:

Area of the shaded region = Area of the rectangle - Area of the semicircle

Area of the rectangle = Length × Width

Length of the rectangle = AD = 8 cm

Width of the rectangle = OP = 4 cm [OP, OB and OC are the radii of the circle which are equal in measures]

Area of the rectangle = 8 × 4 = 32 cm²

Area of the semicircle =
`(1)/(2)\pi r^(2)`

=
`(1)/(2)\pi (OP)^(2)`

=
`(1)/(2)\pi (4)^(2)`

= 25.12 cm²

Area of the shaded region = 32 - 25.12

= 6.88 cm²