Answer
$365.3$ m$^{2}$
Work Step by Step
First converting $125^{\circ}$ to radians:
$125^{\circ}=125(\frac{\pi}{180})=\frac{25\pi}{36}$ 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:
$A=\frac{1}{2}(18.3)^{2}(\frac{25\pi}{36})$
Solving through a calculator:
$A=\frac{1}{2}(18.3)^{2}(\frac{25\pi}{36})\approx365.3$ m$^{2}$
