check the picture below.
so the circle has a radius of 4, and the square has all sides of 8, we can simply get the area of the square, and the area of the circle, and subtract the area of the circle, what's leftover, is just the shaded area.
[tex] \bf \stackrel{\textit{area of the square}}{(8\cdot 8)}~~-~~\stackrel{\textit{area of the circle}}{\stackrel{\pi r^2}{\pi 4^2}}\implies 64-16pi\qquad \approx \qquad 13.7345175 [/tex]
