Obviously △ abg △ ADF (SAS) gets ∠GAB=∠FAD, so ∠ GAE = ∠ BAE+∠ FAD = 90-∠ EAF = 45 = ∠ EAF.

So we get △ age △ AFE (SAS), GE=BE+DF=EF.

Let BE=x and DF=7-x, because EF=7.

The side length of a square is 8, so CE=8-x, CF = 8-(7-x) =1+x.

Then in △CEF, from Pythagorean theorem, there are (8-x) 2+(1+x) 2 = 7 2, and for simplification, there is also x 2-7x+8 = 0.

s△efc=ec*fc/2=(8-x)( 1+x)/2=(-x^2+7x+8)/2=(8+8)/2=8