A geometry problem by Yellow Tomato

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.