What is the area of a square as a function of its perimeter?

The area A of a square can be expressed as a function of its perimeter P. Let’s explore how.

A square’s perimeter is given by the formula:

P = 4s

where s represents the length of one side of the square. To find the area, we use the formula:

A = s²

Now, we can solve the perimeter equation for s:
s = P / 4

Next, we substitute this expression for s into the area formula:

A = (P / 4)²

Now simplifying this gives us:
A = P² / 16

Therefore, the area of a square as a function of its perimeter can be expressed as:

A(P) = P² / 16

This shows that the area of a square is directly proportional to the square of its perimeter divided by 16.