If it's a rectangle, the we have area A = x*y
and perimeter: 2x + 2y = 100
Solve this for x to get x = 50 - y
Use this to replace y in the first equation:
A = (50 - y) * y = 50y - y^2
For the maximum A, take the 1st derivative and set = to 0:
A' = 50 - 2y = 0
y = 25
So, the maximum A for a rectangle comes when it is a square...
With a parallelogram, there is another variable--the angles. I think you will find that the maximum is still 4 equal sides and when the angles are all equal---i.e. when the parallelogram is a SQUARE!!