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
![36-2\left((\pi\cdot 3^2)/(2)\right) = 36-9\pi](https://img.qammunity.org/2020/formulas/mathematics/middle-school/hd8hpbm97neh32eqh03k3rn4psajm9f1r7.png)
The shaded region is half of this area, so the answer is
![(36-9\pi)/(2) \approx 7.7](https://img.qammunity.org/2020/formulas/mathematics/middle-school/eonxsig3wivhxq3r11qgsp8m1hr3r328ip.png)