Answer
$19085.2$ km$^{2}$
Work Step by Step
First converting $270^{\circ}$ to radians:
$270^{\circ}=270(\frac{\pi}{180})=\frac{3\pi}{2}$ 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:
$A=\frac{1}{2}(90.0)^{2}(\frac{3\pi}{2})$
Solving through a calculator:
$A=\frac{1}{2}(90.0)^{2}(\frac{3\pi}{2})\approx19085.2$ km$^{2}$
