jmc

Note that since the area is $\pi r^2=324\pi$, where $r$ is the radius, we must have $r=\sqrt{324}=18$. Thus the distance from the center of the hexagon to a vertex is $18$, and we can break up the hexagon into $6$ equilateral triangles, each of which has side length $18$. The area of an equilateral triangle of side length $s$ is $\frac{s^2\sqrt{3}}{4}$, so the area of each equilateral triangle is $81\sqrt{3}$, making the total $6(81\sqrt{3})=\boxed{486\sqrt{3}}$.