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Hexagonal Puzzle

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Task.

Dissect a regular hexagon into nine pentagons that are congruent to each other. Make the hexagon into a nine-piece puzzle cut out of poster board or card stock. The pieces can be arranged in many interesting shapes.

A solution.

A regular hexagon can be dissected into 36 right triangles, as shown in Figure 1. Four such triangles can form a pentagon (the shaded area in Figure 1).

The whole hexagon can be dissected into 9 such pentagons as shown in Figure 2.

Notice that three central pentagons also form a smaller regular hexagon.

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