Answer
$1060.29 \text{ ft}^{2}$
Work Step by Step
We have:
radius $r=30\text{ ft}$
central angle: $\theta=135^{\circ}=135\times\frac{\pi}{180}\text{ rad}=\frac{3\pi}{4}\text{ rad}$
The area of a sector is given by the formula $A= \frac{1}{2}r^{2}\theta$.
Use this formula to obtain:
$A=\frac{1}{2}\times(30\text{ ft})^{2}\times\frac{3\pi}{4}$
$A=\frac{675\pi}{2}\text{ ft}^{2}\approx 1060.29 \text{ ft}^2$.
Thus, the area of the lawn that receives water is approximately $1060.29 \text{ square feet}$.
