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There are two common definitions of the trapezium.  The American definition is a Quadrilateral with no
Parallel sides.  The British definition for a trapezium is a Quadrilateral with two sides 
Parallel.  Such a trapezium is equivalent to a Trapezoid and therefore has Area
See also Diamond, Lozenge, Parallelogram, Quadrilateral, Rhomboid, Rhombus, Skew Quadrilateral, Trapezoid