[tex]\begin{gathered} We\text{ have that } \\ \frac{80}{360}=\frac{8}{36}=\frac{2}{9}\text{ } \\ \\ \text{ a section of 80\degree represents 2/9 of the area of the circle, thus the area of the sector is} \\ \\ A_{\text{sector}}=\frac{2}{9}A_{\text{circle}} \\ A_{\text{sector }}=\frac{2}{9}\pi\cdot(4^2) \\ \\ A_{\text{sector}}=\frac{32}{9}\pi \\ \\ \end{gathered}[/tex]
