Answer:
Approximately [tex]215[/tex] square units.
Step-by-step explanation:
The area of this figure is equal to:
[tex]\begin{aligned}& \text{Area of figure} \\ =\; & \text{Area of square} \\ &+ \text{Area of circle} \\ &- \text{Area of overlap}\end{aligned}[/tex].
The area of the square is [tex]8^{2} = 64[/tex] square units.
The area of the circle of radius [tex]r = 8[/tex] is [tex]\pi\, r^{2} = 8^{2}\, \pi = 64\, \pi[/tex] square units.
Refer to the diagram attached. In this figure, the overlap between the square and the circle is a sector of radius [tex]r= 8[/tex]. The angle of this sector is [tex]90^{\circ}[/tex]- same as the measure of the interior angle of the square.
The area of this sector would then be:
[tex]\begin{aligned} & \pi\, r^{2} \times \frac{90^{\circ}}{360^{\circ}} = 16\, \pi \end{aligned}[/tex].
Therefore, the area of the figure would be:
[tex]\begin{aligned}& \text{Area of figure} \\ =\; & \text{Area of square} \\ &+ \text{Area of circle} \\ &- \text{Area of overlap} \\ =\; & 64 + 64\, \pi - 16\, \pi \\ \approx\; & 215 \end{aligned}[/tex].
