A geometry problem by Yellow Tomato

Geometry Level pending

Given \( \overline{AB} = 7 \) in \( \sqsubset\!\sqsupset{ ABCD} \) with \( \overline{AB} \parallel \overline{CD} \). With extension of the rectangle from midpoint E on \( \overline{AB} \) to point G and \( \overline{EG} = 12 \) and \( \overline{EG} \bot \overline{AB} \) another midpoint placed on \( \overline{EG} \), point F. And extension of \( \overline{BC} \) to point H where \( \overline{BH} = 17 \) Another point I, the midpoint of \( \overline{CD}\). Where \( \overline{FI}=20 \) Find the ratio of the area of \( \triangle{HFI} : \sqsubset\!\sqsupset{ABCD} \) to the nearest hundred thousand.

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