## Some Parallelo-hexagon Area Ratios

If *G*, *H*, *I*, and *J* are the respective midpoints of the sides *AB*, *BC*, *DE* and *EF* of a *parallelo-hexagon* *ABCDEF* (a hexagon with opposite sides equal and parallel), then area *ABCDEF* = 2 area *GHIJ*.

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If the midpoints of all the sides of a *parallelo-hexagon* *ABCDEF* are connected as shown, then area *ABCDEF* = 4/3 area *GHIJKL* (see below).

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If *G*, *H*, and *I*, are the respective midpoints of the sides *AB*, *CD*, and *EF* of a *parallelo-hexagon* *ABCDEF* are connected as shown, then area *ABCDEF* = 8/3 area *GHI* (see below).

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Some Parallelo-hexagon Area Ratios

Read my papers *Some Hexagon Area Ratios: Problem-solving by related example* and/or *Proof without words: Parallelohexagon-parallelogram Area Ratio*

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Michael de Villiers, updated 27 May 2011.