The center of the base is the point where the diagonals intersect.
First, let's find the length of the diagonal.
Draw in one diagonal; this will give us a right triangle whose hypotenuse is the diagonal,
and whose sides are the sides of the box.
We can use the Pythagorean Theorem: c2 = a2 + b2 ---> c2 = 162 + 162
c2 = 256 + 256 = 512 ---> c = sqrt(512) = 16
To find he distance from the center of the base to a corner of the opposite base:
draw a right triangle from the center of the base to a corner of the base then up the side.
From the center of the base to a corner of the base is one-half of a diagonal = 8.
Up the side is 4.
We can again use the Pythagoren theorem with one side = 8, the other side = 4, and we
need to find the hypotenuse: c2 = a2 + b2 ---> c2 = 82 + 42 = 64 + 16 = 80
---> c = sqrt(80)