Two Triangles in a Decagon

Puzzle August 11, 2020

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What fraction of this regular decagon is shaded?

SOLUTION

Let $S$ be the area of the regular decagon.

Connect points $C$ and $F$ . Since $AB$ , $DE$ , and is parallel to $CF$ from symmetry, we get that $S(ABC) = S(ABO) = S(DEO) = S(DEF) = S/10$ .

Therefore, $80\%$ of the total area is shaded.

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