Question

A circle is placed in a square with a side length of , as shown below. 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

The diameter of the circle is the same as the lenght of a side of the square, hence the diameter is 4 ft

The radius of the circle becomes

`radius=(diameter)/(2)=(4)/(2)=2\text{ ft}`

so the radius of the circle is 2 ft.

The area of the shade region is calculated as

`area\text{ of shaded region = area of square - area of circle}`

area of square becomes

`\begin{gathered} area\text{ of square = length}* length \\ =4*4 \\ =16\text{ ft}^2 \end{gathered}`

area of the circle becomes

`\begin{gathered} area\text{ of circle = }\pi r^2 \\ =3.14*2^2 \\ =3.14*4 \\ =12.56\text{ ft}^2 \end{gathered}`

So, the shaded area becomes

`\begin{gathered} area\text{ of shaded region = area of square - area of circle} \\ =16-12.56 \\ =3.44\text{ ft}^2 \end{gathered}`
`3.44\text{ ft}^2`