US usage, definition 1: A quadrilateral which has a pair of opposite
sides which are parallel. The parallel sides are called the bases,
and the other two sides are called the legs.
US usage, definition 2: A quadrilateral which has one parallel pair of opposite sides and one non-parallel pair of opposite sides. The parallel sides are called the bases, and the other two sides are called the legs.
UK usage: The same as the US word trapezium. The UK word trapezium means the same as the US word trapezoid, and vice-versa.
Commentary: Under US definition 1, a parallelogram is a type of trapezoid. Under US definition 2, a parallelogram is not a type of trapezoid. Regardless of which definition you prefer, the trapezoid area formula can be used to find the area of a parallelogram.
rectangle, square, height
of a trapezoid, trapezoid rule, polygon