Question

A rectangle is placed around a semicircle as shown below. The width of the rectangle is 9 yd. Find the area of the shaded region.Use the value 3.14 r*pi and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

Given:

The width of the rectangle is 9 yd.

Required:

To find the area of the shaded region.

Step-by-step explanation:

From the given figure,

Width of the rectangle is 9 yd.

Therefore, the radius of the semicircle is 9yd.

And the length of the rectangle is diameter of the semicircle.

`\begin{gathered} =2*9 \\ =18yd \end{gathered}`

Now, the area of the rectangle is,

`\begin{gathered} A=L* W \\ =9*18 \\ =162yd^2 \end{gathered}`

Now the area of the semicircle is,

`\begin{gathered} A=(\pi r^2)/(2) \\ =(3.14*9^2)/(2) \\ =(254.34)/(2) \\ =127.17yd^2 \end{gathered}`

Now the area of the shaded region = Area of the rectangle - Area of the semicircle.

`\begin{gathered} =162-127.17 \\ =34.83\text{ yd}^2 \end{gathered}`

Final Answer:

The area of the shaded region is 34.83 yd square.