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** **** **** Trapezium -Definition, Properties, Types and Area **

# Trapezium

**Definition**:-A **trapezium **is a type of quadrilateral (2D shape) in which two opposite sides are parallel and two opposite sides are not parallel .Parallel sides are referred as the bases and non-parallel sides are known as the legs of the **Trapezium**.

__Trapezium -Definition, Properties, Types and Area__

A convex Quadrilateral with at least single pair of parallel sides is known as **Trapezium** in English outside North America . And Trapezium is also known as a **Trapezoid **in American and Canada English.

# Properties of Trapezoid:-

Basic **properties of Trapezoid** are stated below.

- One pair of opposite side is parallel.
- Consecutive angles are supplementary. i.e. <A+<D=180° .
- The line that joins the mid point of two non parallel sides is always parallel to the base of the
**trapezium**(mid-segment=(AB+CD) /2). - Sum of the internal angles is 360°.

# Types of Trapezium/Trapezoid

**Trapezoid**is of

**Three types**mainly

#### 1**.Right Trapezoid **: –It is a type of Trapezoid having two right angles.

Trapezium -Definition, Properties, Types and Area |

#### 2**.Isosceles Trapezium :- **It is a type of Trapezoid in which base angles are equal and therefore non- parallel sides left and right are also equal.

Trapezium -Definition, Properties, Types and Area |

#### 3.**Scalene Trapezoid**:–It is a** type of Trapezoid** which has neither equal angles nor equal sides.

# Area Of Trapezoid

**Area of Trapezoid**= 1/2(sum of parallel sides)*distance between them.

How to find the **Area of Trapezium(samlamb chaturbhuj).**

Below figure ABCD is a **Trapezium **in which AC diagonal creates two triangles in it.

If we able to find the area of two triangles ,then we also able to find the area of **Trapezium ** by adding two areas of triangles.

△ACD and △ABC are two triangles.

Area of triangle △ACD= 1/2*h*CD .

Area of triangle △ABC = 1/2*h*AB .

**Area of Trapezoid** ABCD = Area of triangle △ACD + Area of triangle △ABC

= 1/2*h*CD + 1/2*h*AB

=1/2*h(CD+AB).

=1/2*h*(AB+CD) —-is the **Area of Trapezoid** ABCD

Trapezium -Definition, Properties, Types and Area |

Example: Find the **Area of Trapezoid** whose parallel sides are 120 m. and 75m. respectively.

And distance between two parallel lines is 58m.

Ans-** ****Area of Trapezoid** = 1/2(sum of parallel sides)*distance between them.

= 1/2*(120+75)*58.

=1/2*195*58

=5655 sq. meter.

Example:-How many sides of a Trapezium(Trapezium ke kitne side hote hai) ?

Answer:- There are four sides of a Trapezium as it is a type of Quadrilateral. A **trapezium **is a type of quadrilateral (2D shape) in which two opposite sides are parallel and two opposite sides are not parallel .

# Perimeter Of Trapezoid

**Perimeter of a Trapezoid** = sum of all four sides.

Example : Find the **Perimeter ****of Trapezoid** whose parallel sides are 120 m. and 75m. respectively and non-parallel sides are 105 meters and 72 meters.

Ans-As we know the **Perimeter ****of Trapezoid** is the sum of all four sides.

**Perimeter of a Trapezoid** = 120+75+105+72= 372 meters.

**Real Life Examples of Trapezoid shaped objects**

**Real life Trapezoid shaped objects**are listed below

- Table top
- Pop corn Tub
- Handbags
- Doors and Windows
- Flower base

Trapezium -Definition, Properties, Types and Area |

Frequently Asked Questions:

1.What is a **Trapezium Shape**?

**Ans**– A trapezium is a type of quadrilateral (2D shape) in which two opposite sides are parallel and two opposite sides are not parallel .

2.How many types of trapezium are there?

**Ans**–**Trapezoid** is of Three types mainly

**right Trapezoid****isosceles Trapezoid****scalene Trapezoid**

3.Does a trapezium have equal sides?

**Ans**– yes. **Isosceles Trapezium ** is a type of Trapezoid in which base angles are equal and therefore non- parallel sides left and right are also equal.

4.Can a trapezoid have two right angles?

**Ans-yes. ****Right Trapezoid ** is a type of Trapezoid having two right angles.

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