Consider $P_i$ which is a regular $i$-gon in $\mathbb{R}^2$ and whose diameter is $1$.
Define a compact set $X$ to be a union of convex hulls of copies of $P_i,\ i\geq 3$, which is in some rectangle $[0,100]^2\subset \mathbb{R}^2$.
i) Prove that there is $D$ s.t.
${\rm length}\ \partial X <D$
where $D$ is independent of $X$
ii) Then prove that $X$ has $\epsilon =\epsilon (X)>0$ s.t. any $0<r<\epsilon$ implies that $r$-tubular neighborhood $U_r(X)$ has
$$ {\rm area}\ U_r(X) \leq {\rm area}\ X + Cr$$
Here $C$ is independent of $X$.