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 twodimensional quadrilateral with one pair of sides that are parallel. The parallel sides of a trapezium are called 'bases' while the nonparallel 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.
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Check these interesting articles related to the concept of trapezium shape in geometry.
Trapezium Examples

Example 1: State true or false with reference to the properties of a trapezium:
a.) All squares are trapeziums.
b.) A trapezium is a quadrilateral in which one pair of opposite sides is parallel.
Solution:
a.) True, all squares are trapeziums because in a square the opposite sides are parallel, so it satisfies this property of a trapezium.
b.) True, a trapezium is a quadrilateral in which one pair of opposite sides is parallel.

Example 2: Find the fourth angle of the right trapezium if one of the given angles is 60°.
Solution: As we know, in a right trapezium, there are 2 right angles and the sum of all the interior angles in a trapezium is always 360°.
So, if one of the given angles is 60°, let the missing angle be x°. The fourth angle can be calculated as x° + 90° + 90° + 60° = 360°.
⇒ x° = 360°  (90° + 90° + 60°) = 120°. Therefore, the measure of the fourth angle is 120°. 
Example 3: Find the length of the fourth side of the trapezium, if the rest three sides measure 10 units, 12 units, and 7 units, and the perimeter is 40 units.
Solution: As we know, the trapezium perimeter is given as the sum of all its sides. Let the missing side length be 'a'. Thus, the perimeter is 40 = 10 + 12 + 7 + a.
⇒ a = 40  (10 + 12 + 7) = 11 units. Therefore, the length of the fourth side is 11 units.
FAQs on Trapezium
What is a Trapezium Shape?
A trapezium is a twodimensional quadrilateral that has one pair of parallel sides. The parallel sides of a trapezium are known as 'bases' while the nonparallel sides are called the legs of the trapezium. It looks like a triangle that is cut from the top.
How to find the Area of a Trapezium?
The area of a trapezium can be calculated using the formula, Area of trapezium = 1/2 × Sum of parallel sides × height. This means if we know the length of the parallel sides and the height we can find the area of a trapezium.
Is Trapezium a Quadrilateral?
Yes, trapezium is a quadrilateral. It has four sides, four vertices, and four angles. The sum of all four interior angles of a trapezium is 360 degrees.
Does a Trapezium Have Parallel Sides?
Yes, a trapezium has one pair of parallel sides. These parallel sides are referred to as the bases of the trapezium.
Can a Trapezium have a Right Angle?
Yes, a trapezium can have a right angle. A trapezium with a pair of right angles is known as a right trapezium.
What are the Properties of a Trapezium?
The characteristics of a trapezium are given below:
 A trapezium is a 2D shape and it comes under the category of quadrilaterals.
 There is one pair of parallel sides in a trapezium and these sides are called bases.
 A trapezium has 2 diagonals that always intersect each other.
 The sum of adjacent interior angles of a trapezium is 180°.
 The interior angles in a trapezium always sum up to 360°.
What is the Formula of Area of Trapezium?
The formula which is used to find the area of a trapezium is expressed as, Area of trapezium = 1/2 × Sum of parallel sides × height.
What are the Properties of Isosceles Trapezium?
An isosceles trapezium is one in which the legs, that is, the nonparallel sides are equal to each other.
What is the Difference Between Trapezium and Trapezoid?
A trapezium is also known as a trapezoid. They refer to a foursided polygon having one pair of parallel sides and one pair of nonparallel sides.
What do the Angles in a Trapezium add up to?
There are 4 interior angles in a trapezium which add up to 360° and the adjacent interior angles sum up to 180°.
Is Trapezium a Parallelogram?
No, a trapezium is not a parallelogram because it has only 1 pair of parallel sides. Whereas a parallelogram has 2 pairs of parallel sides.
What does a Trapezium Look Like?
A trapezium looks like a triangle that is cut from the top. Try to draw a triangle and cut it horizontally in between and you can see the shape of a trapezium in the lower figure that is formed.
What are the Trapezium Angle Properties?
Here is a list of the trapezium angle properties:
 There are 4 interior angles in a trapezium which add up to 360°.
 The adjacent interior angles sum up to 180°.
 If a particular trapezium has one pair of right angles, then it is known as a right trapezium.
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