#### Answer

$1885.0$ mi$^{2}$

#### Work Step by Step

First converting $135^{\circ}$ to radians:
$135^{\circ}=135(\frac{\pi}{180})=\frac{3\pi}{4}$ radians
The formula for the area of a sector of a circle having radius $r$ and central angle $\theta$ is $A=\frac{1}{2}r^{2}\theta$.
Substituting the values of $r$ and $\theta$ into the formula:
$A=\frac{1}{2}(40.0)^{2}(\frac{3\pi}{4})$
Solving through a calculator:
$A=\frac{1}{2}(40.0)^{2}(\frac{3\pi}{4})\approx1885.0$ mi$^{2}$