The greatest possible area with a fixed length of fencing (perimeter) is a circle.
Circumference = 2 pi x radius = 24 m
Radius = (24 m) / (2 pi) = 12 m / pi
Area of a circle = pi x radius squared = (pi) x (12 m / pi)^2 = 144 / pi = 45.837 square meters.
=====================================
The rectangle with the greatest possible area for a fixed perimeter is the square.
Each side of the square = 24 / 4 = 6 meters
Area of a square = (side) squared = 36 square meters
=====================================
There is no 'least possible' area. The longer and skinnier you make it,
the less area it will have.
Here are some examples. Each one has 24 m of fencing:
5 m x 7 m = 35 square meters
4 x 8 = 32 square meters
3 x 9 = 27 square meters
2 x 10 = 20 square meters
1 x 11 = 11 square meters
0.5 x 11.5 = 5.75 square meters
0.1 x 11.9 = 1.19 square meters
1 centimeter x 11.99 meters = 0.1199 square meters
1 millimeter by 11.999 meters = 0.011999 square meters
The longer and skinnier the garden is, the less area it has.
