let $a(n)$ be the minimum area of convex lattice $n$-gons. (here lattice is the usual lattice of integer points in $r^2$.) g. e. andrews proved in 1963 that $a(n)>cn^3$ for a suitable positive $c$. we show here that $\lim a(n)/n^3$ exists. our computations suggest that the value of the limit is very close to $0.0185067\ldots$. it turns out further that the convex lattice $n$-gon $p_n$ with area $a(n)$ has elongated shape: after a suitable lattice preserving affine transformation $p_n$ is very close to the ellipsoid whose halfaxis have length $0.00357n^2$ and $1.656n$. this is joint work with norihide tokushige.