1, let the side length of a square be xcm, then the area of the bottom is S=( 10-2x)(8-2x)=48, and the solution is x= 1, and x=8 (excluding), so x= 1. So the side length of a square is 1cm.

2. If the side length of a square is x, the size of lateral area is S=2*( 10-2x)x+2*(8-2x)x=

-8x 2+36x, so the opening direction of the parabola is downward, so there is a maximum value. The symmetry axis is x=9/4. Substituting into the equation gives S=40.5, because 9/4.