Notes
four hexagons solution

Solution to the Four Hexagons Puzzle

Four Hexagons

Four regular hexagons. What’s the pink area?

Solution by Transformations

Four hexagons labelled

In the above diagram, rhombus ABCDA B C D transforms to AEFBA E F B through a rotation of 60 60^\circ clockwise. This same transformation takes the point GG to point HH. So GCG C is transformed to HFH F and hence these have the same length. The length of GHG H is twice the length of a side of the smallest hexagon, so the area of the pink hexagon is four times the area of the smallest, hence is 4848.