AHSME 1973 Problem 4

Two congruent 30-60-90 are placed so that they overlap partly and their hypotenuses coincide. If the hypotenuse of each triangle is 12, the area common to both triangles is $\textbf{(A)}\ 6\sqrt3 \textbf{(B)}\ 8\sqrt3 \textbf{(C)}\ 9\sqrt3 \textbf{(D)}\ 12\sqrt3 \textbf{(E)}\ 24$