# 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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