2005 Fermat Problem 22

In the diagram, a semi-circle has diameter XY. Rectangle PQRS is inscribed in the semi-circle with PQ = 12 and QR = 28. Square STUV has T on RS, U on the semi-circle and V on XY. The area of STUV is closest to

\textbf{(A)}\ 12\quad \textbf{(B)}\ 13\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 14\quad \textbf{(E)}\ 15

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 Fermat contests here.