Question

Find the area of the shaded region. Round to the nearest hundredth. Use the pi symbol not 3.14, you will get the incorrect answer if you use 3.14.

Answer 1

The shaded region consists of the area of the whole square minus the area of the semicircle

Area of the square= Length x Length = 25ft x 25ft = 625ft^2

`\begin{gathered} \text{Area of the semicircle = }\frac{Area\text{ of circle}}{2} \\ =(\pi r^2)/(2) \\ \text{The diameter of the circle is 25ft} \\ T\text{he radius of the circle = }(25)/(2)ft\text{ = 12.5ft} \\ \text{Area of the semicircle = }\frac{\pi\text{ x 12.5 x 12.5}}{2} \\ =78.125\pi ft^2 \end{gathered}`
`\begin{gathered} \text{Area of the shaded region = (625}^{}-78.125\pi)ft^2 \\ we\text{ will need to convert 645 to }^(\prime)\pi\text{ terms' by dividing it by }\pi \\ 625=(625)/(\pi)\pi\text{ = }198.944\pi \\ \\ \text{The area becomes 198.944}\pi-78.125\pi\text{ = 120.819}\pi ft^2 \\ \approx120.82\pi ft^2\text{ (nearest hundredth)} \end{gathered}`