  Consider the problem of fnding the smallest area convex $k$-gon containing
$n\in\mathbb{N}$ congruent disks without an overlap. By using Wegner inequality
in sphere packing theory we give a lower bound for the area of such polygons.
For several cases where this bound is tight we construct corresponding optimal
polygons. We also discuss its solution for some cases where this bound is not
tight, e.g. $n = 2$ and $k$ is odd, and $n = 3$; $k = 4$. On the way to prove
our results we prove a result on geometric invariants between two polygons
whose sides are pairwise parallel, and give a new characterisation for the
trisectrix of Maclaurin.
