The diagram shows a polygon ABCDEFG, in which $FG =6$ and $GA=AB=BC=CD=DE=EF$.
Also $BDFG$ is a square.
The area of the whole polygon is exactly twice the area of $BDFG$.
Find the length of the perimeter of the polygon.
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.