+130071 Let the side of the square = x
Area of triangle BCE = (1/2) (x) (CE)
3 = (1/2) (x) (CE)
6 / x = CE
So ED = ( x - CE ) = ( x - 6/x)
Area of triangle BAF = (1/2) (x) (AF)
4 = (1/2) (x) (AF)
8/x = AF
So FD = (x - AF) = ( x - 8/x)
And area of FED = (1/2)(FD)(ED)
5 = (1/2) (x - 8/x) (x - 6/x)
10 = (x^2 - 8) (x^2 - 6) / x^2
10x^2 = x^4 - 14x^2 + 48
So
x^4 - 24x^2 + 48 = 0 complete the square
x^4 - 24x^2 + 144 = -48 + 144
(x^2 - 12)^2 = 96
x^2 - 12 = sqrt (96)
x^2 = sqrt (96) + 12 = 4sqrt 6 + 12 = 4 ( sqrt 6 + 3) = area of ABCD ≈ 21.8
