#### Answer

$10602.9$ yd$^{2}$

#### Work Step by Step

The formula for the area of a sector of a circle having radius $r$ and central angle $\theta$ is $A=\frac{1}{2}r^{2}\theta$.
Substituting the values of $r$ and $\theta$ into the formula:
$A=\frac{1}{2}(90)^{2}(\frac{5\pi}{6})$
Solving through a calculator:
$A=\frac{1}{2}(90)^{2}(\frac{5\pi}{6})\approx10602.9$ yd$^{2}$