Find the area of square ABCDABCD

Geometry Level 4

On square ABCDABCD, points E,F,GE,F,G, and HH lie on sides AB,BC,CD,\overline{AB},\overline{BC},\overline{CD}, and DA,\overline{DA}, respectively, so that EGFH\overline{EG} \perp \overline{FH} and EG=FH=34EG=FH = 34. Segments EG\overline{EG} and FH\overline{FH} intersect at a point PP, and the areas of the quadrilaterals AEPH,BFPE,CGPF,AEPH, BFPE, CGPF, and DHPGDHPG are in the ratio 269:275:405:411.269:275:405:411. Find the area of square ABCDABCD.

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