Question

What is the difference between the greatest and least possible areas of the rectangle

Answer 1

You haven't given any information at all to describe the rectangle ... perimeter, dimensions, etc. That's kind of important.

Using all of the information you provided, I can only tell you this:

-- The greatest possible area = (1/4 of the rectangle's perimeter)² .

-- The least possible area = the smallest positive number you can think of.

-- Their difference is

(1/4 of the perimeter)² - (the smallest positive number you can think of) .