# 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

# 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. 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

Few examples of 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

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?

AnsTrapezoid 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.