# Solution to the Divided Hexagon II Puzzle +-- {.image} [[DividedHexagonII.png:pic]] > What fraction of this regular hexagon is shaded? =-- ## Solution by [[Equilateral Triangles]] and [[Hexagons]] +-- {.image} [[DividedHexagonIILabelled.png:pic]] =-- 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.