Question

Find the area of the sector. be sure to show all your work.

Answer 1

To calculate the area of the sector you have to use the following formula:

`A_{\text{sector}}=(\theta)/(360º)\cdot\pi r^2`

Where θ represents the measure of the central angle of the sector.

The measure of the central angle is equal to the measure of the intercepted arc, so that θ=80º

So you calculate the area of the sector as follows:

`\begin{gathered} A_{\text{sector}}=(80)/(360)\cdot\pi(4^2) \\ A_{\text{sector}}=(32)/(9)\pi\approx11.17 \end{gathered}`