# Find the area of square \(ABCD\)

**Geometry**Level 4

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 \(ABCD\).