A trapezoid ( in North America ) or trapezium ( in Britain and elsewhere ) is a quadrilateral , which is defined as a shape with four sides , which has one set of parallel sides . In North America and in Africa the term trapezium is sometimes defined as a quadrilateral with no parallel sides , though this shape is more usually called an irregular quadrilateral . The term trapezoid has been defined as a quadrilateral without any parallel sides in Britain and elsewhere , but this does not reflect current usage .