Dissection of 2 Regular Hexagons into One

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

Solution

 * 2-Regular-Hexagons-into-1.png

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.