Question

What is the area of the shaded region if the radius of the circle is 6 in.

Answer 1

Then, the area of 1/4 of the circle is:

`\begin{gathered} A=\text{ }(\theta)/(360)\text{ x }\pi r^2 \\ A=\text{ }(90)/(360)\text{ x }\pi r^2 \\ A\text{ = }(1)/(4)\pi\text{ 6}^2 \\ A=\text{ 9}\pi \\ \\ \end{gathered}`

The area of the triangle is:

`\begin{gathered} A=\text{ }\frac{b\text{ x h }}{2} \\ A\text{ = }\frac{6\text{ x 6}}{2} \\ A=\text{ 18in}^2 \end{gathered}`

The area of the shaded region is the area of 1/4 of the circle minus the area of the triangle:

`\begin{gathered} A\text{ = 9}\pi\text{ - 18 in}^2 \\ A=\text{ 28.27in}^2\text{ - 18in}^2 \\ A=\text{ 10.27in}^2 \end{gathered}`