#### Answer

$\color{blue}{A\approx 10,602.9\space yd^2}$

#### Work Step by Step

RECALL:
The area of a sector $(A)$ intercepted by a central angle $\theta$ on a circle whose radius is $r$ is given by the formula:
$A = \frac{1}{2}r^2\theta$, where $\theta$ is in radian measure.
Substitute the given values of the radius and $\theta$ to obtain:
$A=\frac{1}{2}r^2\theta
\\A=\frac{1}{2}(90.0^2)(\frac{5\pi}{6})
\\A=10602.87521
\\\color{blue}{A\approx 10,602.9\space yd^2}$