# Trapezium and their properties

3 min readAccording to Euclidean geometry, trapezium is a quadrilateral which has one pair of opposite sides equal. The origin of the word trapezium was from the Greek word Trapeza meaning table. With the help of examples let us understand in details about **trapezium** and their features.

**The definition of trapezium**

In simple terms a trapezium is a two dimension quadrilateral. It seems it is developed from four straight lines which is having a pair of parallel opposite sides. The opposite sides are referred to as the base and the non- parallel sides would be the legs of a trapezium. The plane shape is closed which possess four sides along with four corners.

An example would throw more light on things. Let us consider a trapezium XYZW. WZ and XY is the base, with YZ and XW replicating the legs of a trapezium. The shapes of a trapezium is depicted among objects all around us.

**Trapezium and its types**

As mentioned below there are three different types of trapezium

- Right trapezium
- Scalene trapezium
- Isosceles trapezium

Based on the measurement of angles or length of the arms classification of trapezium occurs.

Considering a trapezium ABCD it becomes easy to define the various trapezium types

- In an isosceles trapezium the legs are of equal length as AD= BC
- In a scalene trapezium neither of the sides or the angles would be equal
- Right trapezium indicates that the angles would be in a pair

**The properties of a trapezium**

Each quadrilateral would be having their own set of properties that would make it identifiable and different from the rest. Such properties would be giving more geographical institutions about the space. Some of the properties of a trapezium are listed below

- It is in the form of a 2D shape
- The base of the trapezium is parallel to each other
- Coming to the diagonals of a trapezium they would intersect each other
- The adjacent angles of a trapezium shoot up to 180 degree
- The sum of all the interior angles of a trapezium is 360 degrees

**The area and perimeter of a trapezium**

Let us example things with a trapezium possessing length of parallel sides, where b is the unit and the altitude is H. The area of a trapezium is arrived when you calculate an average of the bases and then you multiply the result to the altitude. An example of a trapezium is AB+DC/2 * AM (a+b)/2* h where CD and AB indicate the base and the altitude is AM. By this formula the **area of trapezium** is calculated

Coming to the perimeter of a trapezium it would be the sum of all the sides. Hence the perimeter of a trapezium ABCD= AB+ BC+ CD+ AD

**Do you consider trapezium to be a quadrilateral?**

The trapezium is a quadrilateral. There are four verticals, four sides and four angles. The sum of all the angles of a trapezium is 360 degrees.

**Does the trapezium have right angles**?

Yes the trapezium would be having a right angle. Any trapezium with a pair of right angles is known by the name of right trapezium.

**Does the trapezium have parallel sides?**

The trapezium is known to have a pair of parallel sides that are termed as the bases.

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