1. The problem asks to express the perimeter $P$ of a square as a function of its area $A$. 2. Let the side length of the square be $s$. 3. The area of the square is given by $$A = s^2$$. 4. The perimeter of the square is given by $$P = 4s$$. 5. To express $P$ as a function of $A$, solve for $s$ from the area formula: $$s = \sqrt{A}$$. 6. Substitute $s = \sqrt{A}$ into the perimeter formula: $$P = 4\sqrt{A}$$. 7. Therefore, the perimeter as a function of the area is $$P(A) = 4\sqrt{A}$$.