Express the area A of an equilateral triangle in terms of its perimeter p.
A = sqrt [ p/2 (p/2-a)³ ] 
If the perimeter is \(p\), then the side length is \(\frac{p}{3}\). Draw the altitude to one of the sides. Then, it divides this triangle into two \(30-60-90\) right triangles. Using the properties of such triangles, the altutude is \(\frac{p\sqrt3}{6}\). Thus, the area is \(\frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot \frac{p}{3} \cdot \frac{p\sqrt3 }{6} = \boxed{\frac{p^2 \sqrt3}{36}}\)
