Answer
$\color{blue}{A\approx 1,885.0 \space mi^2}$
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 to radians to obtain:
$135^o
\\=135^o\cdot \dfrac{\pi}{180^o}
\\=\dfrac{3\pi}{4}$
Substitute the given values of the radius and $\theta$ to obtain:
$A=\frac{1}{2}r^2\theta
\\A=\frac{1}{2}(40.0^2)(\frac{3\pi}{4})
\\A=1884.955592
\\\color{blue}{A\approx 1,885.0 \space mi^2}$
