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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.

*This problem is taken from the UKMT Mathematical Challenges.*