The area of a square is:
A=s^2, solve this for s
s=√A
The "diagonal" is the hypotenuse of a right triangle with legs of length s.
By the Pythagorean Theorem:
d=√(s^2+s^2)
d=√(2s^2), and since we found that s=√A earlier:
d=√(2A), and since we are told that A=128m^2
d=√256
d=16m
