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We prove that every unit area convex pentagon is contained in a convexquadrilateral of area no greater than $3/\sqrt{5}$, and that every unit areaconvex 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. Weconjecture that for every $n\ge 6$, every unit area convex $n$ - gon iscontained in a $(n-1)$ - gon of area no greater than$1+\tan(2\pi/n)\sec(\pi/n)/n$.

On the smallest area $n-1$-gon containing a convex $n$-gon