Answer
$6.28\text{ m}^2.$
Work Step by Step
Here, $r$ denotes the radius of the sector of the circle.
The Area of sector can be computed by the formula:
$A=\frac{\theta}{360^\circ}\cdot \pi \cdot r^2$,where $\theta$ is is the central angle measure in degrees.
Hence $A=\frac{45^\circ}{360^\circ}\cdot \pi \cdot (4\text{ m})^2=2\pi\approx6.28\text{ m}^2.$
