Dissection of 2 Regular Hexagons into One

Problem

Dissect $2$ regular hexagons, and use the pieces to make $1$ larger regular hexagon.

Solution

Dissect one of the regular hexagons into $6$ equal triangles as shown on the left.

Arrange these triangles around the outside of the other regular hexagon as shown on the right.

Join the $6$ obtuse angles of those $6$ triangles to make a larger regular hexagon.

The overlapping bits are then cut off and are fitted into the gaps.

$\blacksquare$

Sources

• June 1975: David Wells: On Gems and Generalisations (Games and Puzzles  no. 37)
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Abul Wafa ($\text {940}$ – $\text {998}$): $41$