# Questions: Area of Trapezium

In this post we will discuss area of Trapezium questions. All the questions are solved step by step so that you have in depth understanding of the concept. Trapezium is one of the important part of quantitative aptitude exams like GMAT, CAT, CMAT, SNAP, SSC, IBPS etc., so make sure to invest time in this topic

## Properties of Trapezium

What is Trapezium?
Trapezium is a form of quadrilateral in which two sides are parallel.
If you remember parallelogram you will observe that in the figure all opposing sides are parallel. But in trapezium, there is only two sides which are parallel to each other.

==>The figure shown above is that of a trapezium.
You can easily observe that sides AB and CD are parallel to each other and sides AD & BC are non parallel sides.

==>The parallel sides AB and CD are called Bases.
Here side CD is called Base 1 (B1) and side AB is called Base 2 (B2)

==>The non parallel sides are called legs.

==> I have also shown a perpendicular line called height (h) which is very useful for calculating area of trapezium

==> One important property of trapezium is if you join the midpoint of the non parallel side of the trapezium, its length is equal to half of sum of parallel sides of trapezium

The line EF is made by joining mid point of non parallel sides like AD and BC.
Length of EF = 1/2 (AB + CD)

Types of Trapezium
Mainly three types of trapezoid are there

1. Isosceles Trapezoid : In this trapezium, the non parallel sides are equal

2. Scalene Trapezoid: Here the length of all sides are different

3. Right Trapezium : It has at least two right angle

### Formulas for Trapezium

#### Area of Trapezium Formula

Area of Trapezium is calculated by multiplying sum of parallel sides and height of trapezium and then dividing it by 2

Area of Trapezium = 1/2 * (Sum of Parallel Sides) * Height

Area of Trapezium = 1/2 * (B1 + B2) * h

This is a straightforward formula for calculating area of trapezium so i request you to please remember it for examination purpose

#### Perimeter of Trapezium

Perimeter simply means the sum of all sides of any figure.
For trapezium perimeter calculation, just do the summation of all sides of the given quadrilateral

For the figure above the perimeter of trapezium can be written as ==> b1 + b2 + x + y

#### Angles of Trapezium

There are two points that you have to keep in mind while solving angles of trapezium questions
a. the sum of all angles interior angle of quadrilateral is 360 degree
b. and sum of the angles formed by parallel side and same non parallel side is 180

## Calculate Area of Trapezium

We know that
Area of Trapezium = 1/2 * (sum of parallel sides) * (Perpendicular distance between them)
=> 1/2 * (b1 + b2) * h

In the question it is given that:
b1 = 1.5 meter
b2 = 2.5 meter
h = 6.5 meter

Putting these values in the above formula
Area of Trapezium ==> 1/2 * (1.5 + 2.5) * 6.5

==> 1/2 * 4 * 6.5
==> 6.5 * 2
==> 13 sq. meter

Let ABCD is a trapezium

Given,
AB = 12 meter
DC = 8 meter
Area = 840 sq meter

we know that formula for Area of Trapezium is:
Area of Trapezium => 1/2 * h * (b1 + b2)

==> 840 = 1/2 * h * (12+8)
==> 840 = 1/2 * h * 20
==> h = 84 meter

The depth of the canal is 84 meter

ABCD is the trapezium
Its given in the question that;
BC = 14 cm
AB = CD = 5 cm

we have drawn an perpendicular imaginary line AE and DF which is also the height of the trapezium.
In order to calculate the area of trapezium we have to find value of height (i.e. AE)

we know that BC = 14 cm
The line EF is part of the rectangle ADEF
So EF = 6 cm

The line BC is made of different parts
==>BC = x+6 +x
==>14 = 2x +6
==> 8 = 2x
==> x= 4 cm

Taking triangle ABE which is right angled triangle
Using Pythagoras Theorem

{ AB }^{ 2 }={ BE }^{ 2 }+{ AE }^{ 2 }\\\ \\ 5^{ 2 }={ 4 }^{ 2 }+{ AE }^{ 2 }\\\ \\ { 25 }^{  }={ 16 }^{  }+{ AE }^{ 2 }\\\ \\ 9\quad =\quad { AE }^{ 2 }\\\ \\ 3\quad =\quad AE

Hence the height of the trapezium is 3 cm

Now we know that
==>Area of Trapezium = 1/2 * (Sum of parallel sides) * height

==> Area of Trapezium = 1/2 * (14 +6) * 3 ==> 10*3 ==> 30 sq cm

Hence the required area of trapezium is 30 sq cm