Circles & Lines · Medium problem

Rectangle $ABCD$ has $AB = 14$ and $BC = 10$, with its vertices labeled in order around it. Point $P$ lies on side $\overline{AB}$ with $AP = 5$, point $Q$ lies on side $\overline{BC}$ with $BQ = 4$, and point $R$ lies on side $\overline{CD}$ with $DR = 9$. What is the area of triangle $PQR$?