Question

A rectangle is placed around a semicircle as shown below. The width of the rectangle is 9ft. Find the area of the shaded region. Use the value 3.14 for (pie), and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

The diagram below will help us answer the question

From the diagram above, Area of the shaded region is

`Area\text{ of shaded region = Area of rectangle - Area of semi-circle }`

From the diagram, the rectangle has a width of 9 ft, which is also the radius of the semi-circle. So the length of the rectangle is also equal to the diameter of the semi-circle, which is

`\begin{gathered} 2*9=18ft \\ So\text{ length of rectangle = 18 ft} \\ width\text{ = 9 ft } \\ Area\text{ of rectangle = length }*\text{ width } \\ =18*9 \\ =162\text{ ft}^2 \end{gathered}`

Area of a semi-circle is given as

`\begin{gathered} Area\text{ of semi-circle = }(1)/(2)*\pi r^2 \\ =(1)/(2)*3.14*9^2 \\ =(1)/(2)*3.14*81 \\ =127.17 \end{gathered}`

Area of shaded region becomes

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

Hence the answer is 34.83 square-feet