  A polygon is \textit{small} if it has unit diameter. The maximal area of a
small polygon with a fixed number of sides $n$ is not known when $n$ is even
and $n\geq14$. We determine an improved lower bound for the maximal area of a
small $n$-gon for this case. The improvement affects the $1/n^3$ term of an
asymptotic expansion; prior advances affected less significant terms. This
bound cannot be improved by more than $O(1/n^3)$. For $n=6$, $8$, $10$, and
$12$, the polygon we construct has maximal area.
