smc

A side length of the triangle is $\frac{p}{3}$. An altitude of the triangle, by 30-60-90 triangles, is $\frac{p\sqrt{3}}{6}$. Because all classical triangle centers coincide on an equilateral triangle, by centroid properties a circumradius is $\frac{p\sqrt{3}}{9}$. Finally, the area of the circumcircle is $\frac{\pi p^2}{27}\to \boxed{\frac{\pi p^2}{27}}$.