If the perimeter is fixed and you want to use it to enclose the greatest
possible area, then you form the perimeter that you have into a circle.
If it must be a rectangle, then the greatest possible area you can enclose
with the perimeter that you have is to form it into a square.
Since the perimeter that you have is 18 inches, form it into a square
with sides that are 4.5 inches long.
The area of the square is (4.5)² = 20.25 square inches.
There is no such thing as the 'least possible' area of the rectangle.
The longer and skinnier you make it, the less area it will have, even
if you keep the same perimeter. No matter how small you make the
area, it can always be made even smaller, by making the rectangle
even longer and skinnier. You can make the area as small as you
want it. You just can't make it zero.
Example:
Width = 0.0001 inch
Length = 8.9999 inches
Perimeter = 18 inches
Area = 0.00089999 square inch.
So, the difference between the greatest and least possible area
of the rectangle with the perimeter of 18 inches is
(20.25) - (the smallest positive number you can think of) square inches.
