Question 13
On square $ABCD,$ points $E,$ $F,$ $G,$ and $H$ lie on sides $\overline{AB},$ $\overline{BC},$ $\overline{CD},$ and $\overline{DA},$ respectively, so that $\overline{EG} \perp \overline{FH}$ and $EG = FH = 34.$ Segments $\overline{EG}$ and $\overline{FH}$ intersect at a point $P,$ and the areas of the quadrilaterals $AEPH,$ $BFPE,$ $CGPF,$ and $DHPG$ are in the ratio $269 : 275 : 405 : 411.$ Find the area of square $ABCD.$
