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MathNet 2016-part-07 — 182 problems (EN–VI) Question 71

Math Olympiad Vault · MathNet 2016-part-07 — 182 problems (EN–VI)

Question 71

Dodecagon $Q W A R T Z S P H I N X$ has all side lengths equal to $2$, is not self-intersecting (in particular, the twelve vertices are all distinct), and moreover each interior angle is either $90^{\circ}$ or $270^{\circ}$. What are all possible values of the area of $\triangle S I X$?