Let g be GP, vertical BC and horizontal AD be p, connecting EF and eg.

The quadrilateral ABGP has three right angles, so it is a rectangle.

GP=AB=8，AP= 10

According to the folding, EG=BG= 10, BF=EF.

In RT△EPG, EG= 10, GP=8, so EP=6.

AE=AP-EP=4

AF+EF=AF+BF=AB=8

Let AF be x and EF be 8-X.

In RT△AEF, AE +AF？ =EF？

x？ +4? =(8-X)？

x？ + 16=X？ - 16X+64

X=3 .

BE=EF=8-3=5

S trapezoid abge =1/2× (AE+BG )× ab =1/2× (4+10 )× 8 = 56.

s△AEF = 1/2×AE×AF = 1/2×4×3 = 6

s△BGF = 1/2×BF×BG = 1/2×5× 10 = 25

S△EFG=S trapezoid ABGE-S△AEF-S△BGF=56-6-25=25.