We start with this square. Let the square have dimensions s ft × s ft



We partition it this way, the squares to cut out are 1 ft each, and
there are two from each side so the middle piece is s-2



Then we cut away the squares and have this:



When we fold up the flaps we will have a rectangular solid

whose length = L = s-2, whose width = W = s-2, and whose height = H = 1

V = LWH

and we are given that the volume of the box is 4 cubic feet, so

4 = (s-2)(s-2)(1)
4 = (s-2)(s-2)
4 = s²-2s-2s+4
4 = s²-4s+4
0 = s²-4s
0 = s(s-4)

s = 0  s-4 = 0
       s = 4

We ignore the zero solution.  So the sheet to cut 
should be 4 ft × 4 ft.

Edwin