OMK 2010 Problem 4

A semicircle has diameter $XY$ . A square $PQRS$ with side length 12 is inscribed in the semicircle with $P$ and $S$ on the diameter. Square $STUV$ has $T$ on $RS$ , $U$ on the semicircle, and $V$ on $XY$ . What is the area of $STUV$ ?