The area of a circular sector is given by:
[tex]A=\frac{\pi r^2\alpha}{360}[/tex]where r is the radius of the sector and alpha is the subtended angle.
In this case we have r= 15 in and alpha=210°. Plugging this values we have:
[tex]\begin{gathered} A=\frac{\pi(15)^2(210)}{360} \\ =412.33 \end{gathered}[/tex]Therefore the area is 412.33 squared inches.
