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cutting a square into an octagon

Source: LIMIT 2019 CAS1 P2

April 28, 2021
geometry

Problem Statement

From a square with sides of length 2m2m, corners are cut away so as to form a regular octagon. What is the area of the octagon in m2m^2? <spanclass=′latex−bold′>(A)</span> 23<span class='latex-bold'>(A)</span>~2\sqrt3 <spanclass=′latex−bold′>(B)</span> 43<span class='latex-bold'>(B)</span>~\frac4{\sqrt3} <spanclass=′latex−bold′>(C)</span> 4(2−1)<span class='latex-bold'>(C)</span>~4\left(\sqrt2-1\right) <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
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