The properties of a trapezium are that it has four sides, none of which are parallel; the sum of its angles equals 360 degrees; and any three sides are greater than the fourth. A trapezium is a quadrilateral, meaning it has four sides, but it is not a common figure in geometry.
A trapezium is a four-sided shape without any of the sides being parallel or the same length. Because of this unpredictability, according to Math Open Reference, it is not consistently used in geometry alongside other shapes, such as trapezoids and parallelograms.
According to "A Mathematical and Philosophical Dictionary," there are further properties that define a trapezium. For example, if a trapezium is cut diagonally, it will have four proportional triangles. Also, the sum of any two diagonal lines is less than all four lines put together. The area of a trapezium is found by adding two parallel sides together, multiplying this number by one-half and then multiplying this number by the height or distance between those two parallel sides.
To those in the United States, a trapezium is a quadrilateral without any parallel sides and a trapezoid is quadrilateral with one set of parallel sides. To those in England, a trapezium has one set of parallel sides and a trapezoid has none.