"Be a right triangle ABC with $\angle B=90º$. Two equilateral triangles $ABD$ and $BEC$ are drawn externally in the legs of the triangle $ABC$. Be $G,H$ and $F$ the midpoints of $BE$, $BC$ and $DC$. If the area of $ABC$ is $32$, then the area of $GHF$ is?"
I made the drawing with an arbitrary triangle $6,8,10$ in GeoGebra because i didn't know how to start in this problem, and i got that the area of $ABC$ is $4$ times the area of $GHF$ (the triangle $GHF$ is right too), so the answer will be $8$, but i want to know how to get this mathematically without trigonometry. Any hints?