The formula to calculate the area of a sector is given to be:
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]where
[tex]\begin{gathered} \theta=\text{ angle of the sector} \\ r=\text{ radius of the sector} \end{gathered}[/tex]From the image provided in the question, we have:
[tex]\begin{gathered} \theta=150\degree \\ r=17\text{ yd} \end{gathered}[/tex]Therefore, the area of the sector is given to be:
[tex]\begin{gathered} A=\frac{150}{360}\times3.14\times17^2 \\ A=378.1 \end{gathered}[/tex]The area of the sector is 378.1 square yards.