# Hexagon and Concentric Circles +-- {.image} [[HexagonandConcentricCircles.png:pic]] > The regular hexagon has a side length of $3$, and the rings are equally spaced. What's the total shaded area? =-- ## Solution by [[Interior Angle]] of a [[Regular Hexagon]] and [[Area of a Circle]] The [[interior angle]] of a [[regular hexagon]] is $120^\circ$, which is one third of a full turn. The part of the outer ring is $\frac{2}{3} (\pi 3^2 - \pi 2^2)$, that of the middle ring is $\frac{1}{3} (\pi 2^2 - \pi 1^2)$, and of the inner ring is $\frac{2}{3} (\pi 1^2)$. Putting that together gives: $$ \frac{2}{3} (\pi 3^2 - \pi 2^2) + \frac{1}{3} (\pi 2^2 - \pi 1^2) + \frac{2}{3} (\pi 1^2) = 5 \pi. $$