Andrea inscribes a circle inside a regular hexagon, circumscribes a circle around it, and calculates the area between them (region $A$). Bethany does the same with a regular nonagon (9 sides). Both polygons have side length $3$. Which of the following is true of the areas $A,B$?

1. For a regular $n$-gon with side $s$: $R^2-r^2=\frac{s^2}4\left(\frac1{\sin^2(\pi/n)}-\frac1{\tan^2(\pi/n)}\right)=\frac{s^2}4$, independent of $n$.
2. So the area between circles is always $\pi s^2/4$, regardless of the number of sides.
3. Since both polygons have side $3$: $\boxed{A=B}$.