How Many Trapezoids Can You Draw?

All the popular mathematics blogs seem to challenge readers to come up with answers; I might as well try the same, so I can be disheartened by the responses. In a pair of earlier essays I talked about the problem of drawing differently-shaped trapezoids so as to not overlook figures that might be trapezoids just because the intuition focuses on one shape over others.

So how many different shapes of trapezoids are there to draw? Let me lay out some ground rules.

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