  We prove that every unit area convex pentagon is contained in a convex
quadrilateral of area no greater than $3/\sqrt{5}$, and that every unit area
convex hexagon is contained in a convex pentagon of area no greater than $7/6$.
Both results are tight as the case of the regular pentagon (hexagon) shows. We
conjecture that for every $n\ge 6$, every unit area convex $n$ - gon is
contained in a $(n-1)$ - gon of area no greater than
$1+\tan(2\pi/n)\sec(\pi/n)/n$.
