What is the least possible area of Malika’s garden?

What is the greatest possible area?

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.