Školjka

%V0 Let $P$ be a polygon that is convex and symmetric to some point $O$. Prove that for some parallelogram $R$ satisfying $P\subset R$ we have $$\frac{|R|}{|P|}\leq \sqrt 2$$ where $|R|$ and $|P|$ denote the area of the sets $R$ and $P$, respectively. Proposed by Witold Szczechla, Poland