Question

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

Answer 1

Step 1

Write the given data:

Radius r of the semi-circle = 4 yd

Width of the rectanhle = 4 yd

Length of the rectangle = 2 x 4 = 8 yd

Step 2

Write the formula for the area of the shaded region:

`\begin{gathered} Area\text{ of the shaded region} \\ =\text{ Area of a rectangle - Area of the semi-circl} \\ =\text{ W }*\text{ L - }(\pi r^2)/(2) \\ =\text{ 4}*\text{ 8 - }(3.14*4^2)/(2) \\ =\text{ 32 - 25.12} \\ =\text{ 6.88 yd}^2 \end{gathered}`

Final answer

6.88