Notes
dissected hexagon solution

Dissected Hexagon

Solution by Properties of a Regular Hexagon and Area of a Triangle

Drawing the line segment $E D$ in the above diagram shows that the unshaded region comprises six congruent triangles. Each has base one half of the side length of the hexagon and height one half of its height. The regular hexagon itself comprises six congruent equilateral triangles, each with base one side length of the hexagon and height one half of its height. Therefore, each of the thinner triangles has area half of that of one of the equilateral triangles, and so the unshaded area comprises half the hexagon.