Notes
subdivided hexagon ii solution

Solution to the Subdivided Hexagon II Puzzle

Solution by Subdivision of a Regular Hexagon into Equilateral Triangles

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.