AMC 8 1994 Problem 19

Around the outside of a $4$ by $4$ square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters. Another square, $ABCD$, has its sides parallel to the corresponding sides of the original square, and each side of $ABCD$ is tangent to one of the semicircles. The area of the square $ABCD$ is

$\text{(A)}\ 16 \text{(B)}\ 32 \text{(C)}\ 36 \text{(D)}\ 48 \text{(E)}\ 64$