Our next Catriona Shearer puzzle.
Spike in the Hive
First, what’s the area of the big hexagons?
There’s a little equilateral triangle in the middle between the hexagons, and its equilateralness means a big hex side is equal to a little hex side plus a triangle side (, from the upper big hex), but also a big hex side is two little hex sides minus a triangle side (, from the lower big hex), and that means and . So the area of a big hex is .
Now, the red triangle area: It’s half base times height, so it’s twice the area of a triangle with the same base and half the height, or twice the area of the same triangle sheared parallel to its base: