Notes
divided hexagon ii solution

Solution to the Divided Hexagon II Puzzle

Solution by Equilateral Triangles and Hexagons

By considering the decomposition into equilateral triangles and half equilateral triangles, the containing rectangle is equivalent in area to $8$ equilateral triangles and the hexagon to $6$. The unshaded strip in the centre is one third of the rectangle, so is $\frac{8}{3}$rds of an equilateral triangle. The shaded region is therefore $6 - \frac{8}{3} = \frac{10}{3}$rds of an equilateral triangle and so is $\frac{10}{18} = \frac{5}{9}$ths of the hexagon.