Trapezium - Properties, Formula, Definition, Examples - Cuemath

Trapezium

A trapezium is a quadrilateral in which one pair of opposite sides is parallel. Let us learn more about the trapezium definition, the properties of a trapezium, the different types of trapeziums, the angles of a trapezium and the diagonals of a trapezium, along with some trapezium examples.

1.	What is a Trapezium in Maths?
2.	Types of Trapezium
3.	Properties of Trapezium
4.	Trapezium Formulas
5.	FAQs on Trapezium

What is a Trapezium in Maths?

A trapezium is a two-dimensional quadrilateral with one pair of sides that are parallel. The parallel sides of a trapezium are called 'bases' while the non-parallel sides are known as the 'legs' of the trapezium.

Trapezium Definition

A trapezium is a closed plane shape having four sides in which one pair of opposite sides are parallel. Observe the trapezium figure given below which shows a trapezium WZYX in which WZ is parallel to XY and these are the bases while WX and ZY are the legs of the trapezium.

Types of Trapeziums

There are mainly three different types of trapeziums which are given below:

• Isosceles Trapezium
• Scalene Trapezium
• Right Trapezium

Trapeziums are classified on the basis of the length of legs or the measurement of their angles. The definition of each type of trapezium along with its shape is given below.

Properties of Trapezium

Every quadrilateral has its own properties which make it identifiable and different from the rest. These properties give more insights into the geometrical construction of a shape. The basic properties of a trapezium are listed below:

• A trapezium is a 2D shape.
• The bases of a trapezium are parallel to each other.
• The diagonals of a trapezium always intersect each other.
• The adjacent interior angles sum up to 180°.
• The sum of all the interior angles in a trapezium is always 360°.

Angles of a Trapezium

There are 4 interior angles in a trapezium which add up to 360° and the adjacent interior angles sum up to 180°.

Diagonals of a Trapezium

Since a trapezium is a quadrilateral it has 2 diagonals and they both intersect each other.

Trapezium Formulas

The formulas of a trapezium are mainly related to the area of a trapezium and the perimeter of a trapezium. Let us take the example of a trapezium diagram in which the parallel sides are named as 'a' and 'b' respectively and the height (altitude) is named as 'h'. Observe the trapezium ABCD given below to understand the trapezium formulas given after that.

• The formula that is used to find the area of a trapezium is expressed as follows. Area of trapezium = 1/2 × Sum of parallel sides × height. In this figure, it can be written as, Area of trapezium = 1/2 × (a + b) × h, where 'a' and 'b' are the parallel sides and 'h' is the height of the trapezium.
• The perimeter of a trapezium can be calculated by adding the length of all the 4 sides. This means the formula that is used to find the perimeter of a trapezium is expressed as follows. Perimeter of trapezium = Sum of all 4 sides. In this figure, it can be written as, Perimeter of trapezium ABCD = AB + BC + CD + DA.

☛ Related Articles

Check these interesting articles related to the concept of trapezium shape in geometry.

• Quadrilaterals
• Trapezoid
• Area of Trapezoid
• Trapezoid Formula
• Trapezium Area Calculator
• Isosceles Trapezoid