  A small polygon is a polygon of unit diameter. The maximal area of a small
polygon with $n=2m$ vertices is not known when $m \ge 7$. In this paper, we
construct, for each $n=2m$ and $m\ge 3$, a small $n$-gon whose area is the
maximal value of a one-variable function. We show that, for all even $n\ge 6$,
the area obtained improves by $O(1/n^5)$ that of the best prior small $n$-gon
constructed by Mossinghoff. In particular, for $n=6$, the small $6$-gon
constructed has maximal area.
