Question 17
Four points $O,P,Q,R$ have coordinates $(0,0)$, $(0,30)$, $(x,y)$ and $(20,0)$ respectively, where the point $Q$ lies on the curve $y=50-x^2$ in the first quadrant. Let $\Pi$ be the polygon $OPQR$ with four sides $OP$, $PQ$, $QR$ and $RO$. What is the maximum possible area of $\Pi$ if this area must be an integer?