Similarly, in the right triangle BFA, BD=AD=FD.

So CD=FD, so the parallelogram CDFG is a diamond.

Let BD=AD=FD=X, then AF = Ag-GF =13-GF =13-DF =13-X.

In the right triangle BFA, BF 2+AF 2 = AB 2, that is, 6 2+(13-x) 2 = (2x) 2.

That is, X=5, perimeter =4*X=20.