Answer
$6.28\text{ m}^{2}$
Work Step by Step
We have:
radius $r=4\text{ m}$
central angle $\theta=45^{\circ}=\frac{\pi}{4}\,rad$
The area of a sector is given by the formula $A=\frac{1}{2}r^{2}\theta$ where $\theta$ is in radians and $r$ i the radius.
Using the formula above gives:
$A=\frac{1}{2}\times (4\text{ m})^{2}\times \frac{\pi}{4}=2\pi\,m^{2}\approx6.28\,m^{2}$
Thus, the area of the sector rounded to two decimal places is $6.28\text{ m}^{2}$.
