Answer
$\frac{9\pi}{5}\approx5.65$ m$^{2}$
Work Step by Step
If $\theta$ (in radians) is a central angle in a circle with radius $r$, then the area of the sector formed by angle $\theta$ can be calculated as $A=\frac{1}{2}r^{2}\theta$.
We are given that $\theta=\frac{2\pi}{5}$ and $r=3$ m.
Therefore, $A=\frac{1}{2}(3^{2})(\frac{2\pi}{5})=\frac{1}{2}(9)(\frac{2\pi}{5})=\frac{1\times9\times2\pi}{2\times5}=\frac{18\pi}{10}=\frac{9\pi}{5}\approx5.65$ m$^{2}$.
