The area of the square is 36 squared inches, because it is a square with a side of 6 inches.
The two semicircles have a radius of 3 inches. If we subtract their areas from the area of the square, we have
[tex]36-2\left(\dfrac{\pi\cdot 3^2}{2}\right) = 36-9\pi[/tex]
The shaded region is half of this area, so the answer is
[tex]\dfrac{36-9\pi}{2} \approx 7.7[/tex]
