# 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 $$ABCD$$.

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