In general, it is virtually impossible.
Regular or semi-regular hexagons can be split into thirds by joining every other vertex to the centre of the hexagon.
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you can split a regular hexagon into 6 triangles
The hexagon can be split into 8 equal trapezoids by creating a smaller hexagon (exactly one half the size) within the hexagon. Draw lines through the center of the hexagon from opposing vertices, and connect the midway points. The space between the two hexagons is filled by six equal trapezoids, and the smaller hexagon bisects to form two more. (see the related link for drawing)
Simple; It's the Hexagon (Hexa=6)
No, a parallelogram is not a hexagon.
There are 9 diagonals in any hexagon!The hexagon does not have to be regular.