Write the area A of a square as a function of its perimeter P ...?

The answer is A = P²/16

The perimeter P of a square is sum of its sides s: P = s + s + s + s = 4s

The area A of a square with side s is: A = s * s = s²

Step 1: Solve s from the formula for the perimeter.

Step 2: substitute s from the formula for the perimeter into the formula for the area.

Step 1:

P = 4s

s = P/4

Step 2:

A = s²

s = P/4

A = (P/4) ²

A = P²/4²

A = P²/16