Theory - Area of Trapezium is Equal to half the Product of its Altitude & sum of its parallel Sides Class 9 Notes | EduRev

Mathematics (Maths) Class 9

Created by: Indu Gupta

Class 9 : Theory - Area of Trapezium is Equal to half the Product of its Altitude & sum of its parallel Sides Class 9 Notes | EduRev

The document Theory - Area of Trapezium is Equal to half the Product of its Altitude & sum of its parallel Sides Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.
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Objective:

To show that the area of a trapezium is equal to half the product of its altitude and sum of its parallel sides.

Theory

  1. Trapezium is a quadrilateral with one pair of opposite sides parallel.

  2. A quadrilateral is a parallelogram if a pair of its opposite sides are parallel and equal to each other.

  3. The parallel sides are called "bases" of the trapezium and the other two sides are called the "legs" of trapezium.

  4. Area of parallelogram = base(b) X height(h)

Proof:

Consider trapezium ABCD. AB and DC are the bases (parallel sides) and h is the height of trapezium ABCD.

Theory - Area of Trapezium is Equal to half the Product of its Altitude & sum of its parallel Sides Class 9 Notes | EduRev

A parallelogram can be formed by creating a copy of trapezium ABCD and placing it inverted touching side BC as shown in figure below:

 

Theory - Area of Trapezium is Equal to half the Product of its Altitude & sum of its parallel Sides Class 9 Notes | EduRev    

We observe that parallelogram ASPD is formed by combining two trapeziums ABCD and BSPC.

∴ Area of trapezium ABCD  = 1/2 X Area of parallelogram ASPD
= ½ X DP X h
= 1/2 X (DC+CP) X h
=1/2 X (b1 + b2) X h
= ½ X (AB + DC) X h

Thus, area of a trapezium is equal to half the product of its altitude and sum of its parallel sides.

 Example:-

Find the area of the following trapezium.

 

Theory - Area of Trapezium is Equal to half the Product of its Altitude & sum of its parallel Sides Class 9 Notes | EduRev

Solution:-

Given,

b1= 5 cm
b2= 11 cm
h= 8 cm

Area of trapezium = 1/2(b1+b2) X h

=1/2(11+5) X 8

=64 cm2

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