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Given a convex $(n+1)$-gon $A$, I want to find the convex $n$-gon $B$ of smallest area that contains $A$. Specifically, I want a bound on the area of $B$. I can work out specific examples, but have no idea on how to tackle the general case (I am hoping that someone can point me towards some research, if it exists). this code golf post explains the same problem (except I only care about convex polygons).

This stack exchange post gives an answer in the case of a square.

Intuitively, in the case where there is a very small side length (relatively), it seems like the adjacent sides can be "extended" outside of $A$ until they intersect (assuming the adjacent angles are obtuse).

Edit: let's assume that $diam(A) < N$ for some constant $N$.

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