Given this hexagon $P$, I've got to calculate the Lebesgue measure $\lambda_{2}(P)$ and the Hausdorff measure $\mathscr{H}^1(\partial P)$. My thoughts are: You can leave out the 6 line segments of length 1 that makes the boundary, as they are presentable as graph of a steady function (so their lebesgue measure is zero).My intuition tells me that $\lambda_{2}(P)=6*\frac{\sqrt{3}}{4}= \frac{3\sqrt{3}}{2}$ ( as one triangle has one triangle has the area:$\frac{\sqrt{3}}{4}$) and $\mathscr{H}^1(\partial P)=6$(the lenght of the boundary). I'm not sure if it's right and how to argue the right results. Any help would be greatly aprpreciated.