The volume of the box is:
Since the bas is a square, let one side be x and the height be h, such that:
This equals A^3;
Now, the Surface area is given by:
You have two equations now. Substitute h in the second equation and differentiate with respect to x and solve for 0, to get the value of x in those conditions (Don't forget that A^3 is a constant).
Then, substitute the value of x to get the value of h.