Answer
$\approx 1131$ i$n^{2}$
Work Step by Step
The area $A$ of a sector with central angle of $\theta$ radians is
$ A=\displaystyle \frac{1}{2}r^{2}\theta$.
The area swept is the difference of the larger ($r_{2}=$34 in)
and smaller ($r_{1}$=14 in) sectors.
$ A=\displaystyle \frac{1}{2}(r_{2}^{2}-r_{1}^{2})\cdot\theta$
To convert into radians, multiply the angle by $\pi/180^{o}$.
$\displaystyle \theta=135^{o}\cdot\frac{\pi}{180^{o}}$ rad$=\displaystyle \frac{3\pi}{4}$ rad
$A=\displaystyle \frac{1}{2}(r_{2}^{2}-r_{1}^{2})\cdot\frac{3\pi}{4}=\frac{1}{2}(34^{2}-14^{2})\cdot\frac{3\pi}{4}$
$\approx$1130.97335529 square inches
$\approx 1131$ i$n^{2}$
