We need write the area of a square as a function of the perimeter.
Let us write the equation of the perimeter.
Let the side of a square be x.
Then the perimeter P = 4x.
==> x = P/4
Now we will write the equation of the area.
==> A = x^2
Now we will substitute with (1).
==> A = (P/4)^2 = p^2 /16
==> A(p) = p^2/ 16.