In the figure, $ABCD$ is a square and $EFD$ is a right angle triangle. In the figure $DE=EC$ $\angle EFD=30^{\circ}$; $FH=\dfrac{FE}{3}$ ; $FG=\dfrac{FD}{2}$ , The area of the $FGH$ sector is $6$, what is the area of the $ABCD$ square?