[[!redirects subdivided hexagon ii solutions]] # Solution to the [[Subdivided Hexagon II]] Puzzle +-- {.image} [[SubdividedHexagonII.jpeg:pic]] > What fraction of this regular hexagon is shaded? =-- ## Solution by Subdivision of a [[Regular Hexagon]] into [[Equilateral Triangles]] +-- {.image} [[SubdividedHexagonIIAnnotated.jpeg:pic]] =-- Consider the hexagon as divided above. The main diagonals divide the [[regular hexagon]] into six [[equilateral triangles]]. The other lines then divide those triangles into four smaller equilateral triangles, resulting in $24$ triangles in total. Twelve of these are shaded, so $\frac{12}{24} = \frac{1}{2}$ of the hexagon is shaded.