Overview

Let $s$ be the length of each side of the square:

1. Relate perimeter $P$ to side length $s$: $P = 4s \implies s = \frac{P}{4}$

2. Relate area $A$ to side length $s$: $A = s^2$

3. Substitute $s = \frac{P}{4}$ to express $A$ as a function of $P$: $A(P) = \left(\frac{P}{4}\right)^2 = \frac{P^2}{16}$