Question

A rectangle is placed around a semicircle as shown below. The width of the rectangle is 8 yd. Find the area of the shaded regiorUse the value 3.14 for 1, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

It is given that,

`\begin{gathered} Radius\text{ of semicircle = width of rectangle = 8 yd} \\ Diameter\text{ of semicircle = length of rectangle = 16 yd} \\ \pi\text{ = 3.14} \end{gathered}`

The area of the semicircle is calculated as,

`\begin{gathered} Area\text{ = }\pi* r^2 \\ Area\text{ = 3.14 }*\text{ 8 }*\text{ 8/2} \\ Area\text{ = 100.48 yd}^2 \end{gathered}`

The area of the rectangle is calculated as,

`\begin{gathered} Area\text{ = Length }*\text{ Breadth} \\ Area\text{ = 16 yd }*\text{ 8 yd} \\ Area\text{ = 128 yd}^2 \end{gathered}`

The area of the shaded region is calculated as,

`\begin{gathered} Area\text{ of shaded region = Area of rectangle - Area of semicircle} \\ Area\text{ of shaded region = 128 yd}^2\text{ - 100.48 yd}^2 \\ Area\text{ of shaded region = 27.52 yd} \end{gathered}`