Answer
$18.29 \ cm^2$
Work Step by Step
Our aim is to compute the area of a circle.
Let $A$ be the area of a circle.
$A=\pi r^2$
Plug the given data in the above equation to obtain:
$A=3.14 (8)^2=200.96 \ cm^2$
In order to get the arc length $l$, we need to multiply the area of a circle by $\dfrac{90^{\circ}}{360^{\circ}}$.
So, we have: $A=\dfrac{90^{\circ}}{360^{\circ}} \times 200.96 =50.24 \ cm^2$
The area of a triangle is equal to: $A=\dfrac{1}{2}(8)(8) \sin 90^{\circ}=32 \ cm^2$
Thus, the area of a shaded region is:$A=50.24 -32=18.29 \ cm^2$