Question 8
Let $ABC$ be an equilateral triangle whose area is 36 cm$^2$, and $EFD$ be an isosceles triangle with $EF=FD$. The point $F$ is the centre of triangle $ABC$, and the points $B$ and $C$ are the midpoints of $EF$ and $FD$, respectively, as shown in the diagram below. If $BG\perp EF$ and $CH\perp DF$, what is the area, in cm$^2$, of the shaded region?
