I have been asked this question from a junior and could not solve the question in a simple way. I am asking help on this platform.
For a triangle $ABC$, Points $D, E$ on $AB$, where $AD:DE:EB=2:2:1$. Point $H$ on $AC$, where $AH:HC=5:3$. Point $G$ on $BC$, where $BG:GC=1:1$. Point $F$ is the intersection between $DG$ and $EH$.
Given area $ADFH$ = 100 $cm^2$, find area $BEFG$.
The difficulty is I don't see any line parallel, so I can't find any similar triangle.
What I have derived from triangle area formula is area $AEH$: area $ABC$ = $1:2$ and area $BDG$: area $ABC$ = $3:10$. But to get area $DEF$'s ratio, I spend quite a long time finding the ratio $EF:FH$.
This should not be such a hard question, so I want to know if there is an easier way of finding the answer.