Answer
$A=8064.8$ yd$^{2}\approx8060$ yd$^{2}$
Work Step by Step
Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$.
Step 2: First, we have to convert the angle from degrees to radians:
$40^{\circ}=40(\frac{\pi}{180})=\frac{2\pi}{9}$ radians
Step 3: Substituting the values provided by the question into the formula, $A=\frac{1}{2}(152)^{2}(\frac{2\pi}{9})$
Step 4: $A=\frac{23104\pi}{9}$
Step 5: Therefore, $A=8064.8$ yd$^{2}\approx8060$ yd$^{2}$
