Question 101
Points $E, F, G, H$ are chosen on segments $AB, BC, CD, DA$, respectively, of square $ABCD$. Given that segment $EG$ has length $7$, segment $FH$ has length $8$, and that $EG$ and $FH$ intersect inside $ABCD$ at an acute angle of $30^{\circ}$, then compute the area of square $ABCD$.