∵ quadrilateral ABCD is a square,
∴AD=AB=BC=CD,∠D=∠B=∠BCD=90,
Fold △ADE in half along AE to △AFE,
∴AD=AF,DE=EF,∠D=∠AFE=90,
∴AB=AF,∠B=∠AFG=90,
In Rt△ABG and Rt△AFG,
∫AB = AFAG = AG,
∴△ABG≌△AFG(HL),
∴BG=FG,
CD = 3DE,CD=6,
∴DE=EF=2,CE=4,
Let BG=FG=x, then CG=6-x, GE=x+2,
In Rt△GCE, ∫GE2 = CG2+CE2,
∴(x+2)2=(6-x)2+42,
The solution is x=3,
∴BG=3,
BG = GF = 3,
∴CG=3,EC=6-2=4,
∴GE=32+42=5,
∵ 12CM? GE= 12GC? European community,
∴CM×5× 12=3×4× 12,
∴CM=2.4,
∴S△FGC= 12GF×CM= 185.
So the answer is 185.