area with inscribed figures

Question

A rectangle is placed around a semicircle as shown below. The length of the rectangle is 12cm. Find the area of the shaded region. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

Since you didn't post the figure, I'm going to make a few guesses about it. First, I assume that the semicircle is inscribed within the rectangle. If so, the radius of the circle is 12/2 = 6 cm and the height (width) of the rectangle is also 6 cm.

Second, I assume that the "shaded region" is the area of the rectangle outside of the semicircle. If so, then:

Area of Shaded region = Area of rectangle - Area of semicircle

Look up the formulae for these two areas. The rectangle has a length of 12 cm and width of 6 cm. The semicircle has a radius of 6 cm. The area of a semicircle is half the area of a full circle.