Half of a hexagon is a trapezoid.
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trapeziod
a trapezoid
One half. Two trapezoids placed long base-to-long base create a hexagon.
a square ----------- Assuming it's a regular hexagon, it can be one of two shapes depending on whether you cut it in half on a side or on a vertex. On a side, it is an irregular pentagon. On a vertex, it is a trapezoid (quadrilateral).
If you bisect a regular hexagon (cut in half from one vertex to the opposite vertex) the shape you get is a trapezoid. If you bisect the hexagon from the midpoint of one side to the midpoint of the opposite side, then the shape you would is a pentagon, similar looking to home plate in baseball.