2012 Cayley Problem 23

In the diagram, points P, Q and R lie on a circle with centre O and radius 12, and point S lies on OR. If \angle POR = 135^\circ, the area of trapezoid OPQS is closest to

\textbf{(A)}\ 216\quad \textbf{(B)}\ 144\quad \textbf{(C)}\ 108\quad \textbf{(D)}\ 112.5\quad \textbf{(E)}\ 114.6

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 Cayley contests here.