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).

Please install Java (version 1.4 or later) to use JavaSketchpad applets.

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).

Please install Java (version 1.4 or later) to use JavaSketchpad applets.

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.