Answer
$\color{blue}{A \approx 8,060 \space yd^2}$
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.
Convert the angle measure to radians by multiplying $\dfrac{\pi}{180^o}$ to the given angle to obtain:
$40.0^o
\\=40\cdot\dfrac{\pi}{180^o}
\\=\dfrac{2\pi}{9}$
Substitute the given values of the the central angle and radius to obtain:
$A=\frac{1}{2}r^2\theta
\\A=\frac{1}{2}(152^2)(\frac{2\pi}{9})
\\A=8,064.817408
\\\color{blue}{A \approx 8,060 \space yd^2}$
