jmc

The side of the square of made up of two radii, and the area of the square is $(3+3{)}^2=36$. The unshaded region of the square is composed of four quarter circles, and has the area of one circle, which is $9\pi$. The area of the shaded region is $36-9\pi$ which less than $36-9(3)=9$, closest to $\boxed{7.7}$.