2009 Pascal Problem 22

In the diagram, PQ and RS are diameters of a circle with radius 4. If PQ and RS are perpendicular, what is the area of the shaded region?

\textbf{(A)}\ 16+4\pi\quad \textbf{(B)}\ 8+8\pi\quad \textbf{(C)}\ 8+4\pi\quad \textbf{(D)}\ 16+16\pi\quad \textbf{(E)}\ 16+8\pi

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.