f,4 mathz,,find the length of AE.

Assumed it is the green area that is twice the red area.
Let AE = x.
So ED = EF = GC = (1-x).
AE = BG = FG = x.
Area of red zone = (EF + AB) x AE/2 = ( 1 -x + 1)x/2 = (2-x)x/2.
Area of green zone = (FG + DC) x GC/2 = (x + 1)(1-x)/2.
So the equation is
x(2-x) = (x +1)(1-x)/2
2x(2 - x) = (x +1)(1 -x)
4x - 2x^2 = x - x^2 + 1 - x
x^2 - 4x + 1 = 0
x = [4 +/- sqrt(16 - 4)]/2 = (4 +/- sqrt12)/2 = 2 +/- sqrt3
x = 2 - sqrt 3 = 0.27cm. ( 2 + sqrt 3 is rej. because side of square is only 1 cm).