To calculate the area of the sector you have to use the following formula:
[tex]A_{\text{sector}}=\frac{\theta}{360º}\cdot\pi r^2[/tex]
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:
[tex]\begin{gathered} A_{\text{sector}}=\frac{80}{360}\cdot\pi(4^2) \\ A_{\text{sector}}=\frac{32}{9}\pi\approx11.17 \end{gathered}[/tex]
