AIME Problem 4

Geometry Level 4

In the diagram below, ABCDABCD is a square. Point EE is the midpoint of AD\overline{AD}. Points FF and GG lie on CE\overline{CE}, and HH and JJ lie on AB\overline{AB} and BC\overline{BC}, respectively, so that FGHJFGHJ is a square. Points KK and LL lie on GH\overline{GH}, and MM and NN lie on AD\overline{AD} and AB\overline{AB}, respectively, so that KLMNKLMN is a square. The area of KLMNKLMN is 99. Find the area of FGHJFGHJ.

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