There are three types of trapezoid. There is the right trapezoid, which has two right angles, isosceles trapezoid, which has two of its non-parallel sides equal in length and the scalene trapezoid, which does not have equal sides or angles.

The trapezoid, or trapezium, is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs or the lateral sides. If the sides are not parallel, it can be said that there are two pairs of bases.

The term trapezium has been in use in English since 1570. The first recorded use of the Greek word translated trapezoid was by Marinus Proclus in his commentary on the first book of Euclid's Elements. The use of the term trapezoid is what is current in the United States and Canada. In all other languages that use a word derived from the Greek for this figure, the form closest to trapezium is used.

In architecture, the trapezoid is used to refer to symmetrical doors, windows and buildings built wider at the base, tapering towards the top, in Egyptian style. If these have straight sides and sharp angular corners, their shapes are usually isosceles trapezoids. This was the standard style for the doors and windows of the Incas.