Areas Of Parallelograms And Triangles Class 9 Notes: Chapter 9

CBSE Class 9 Maths Areas Of Parallelograms And Triangles Notes:-Download PDF Here

Areas of parallelograms and triangles for class 9 notes are given here. Here, we are going to discuss some of the geometrical figures. A detailed explanation of areas of parallelograms and triangles are explained below with many theorems and proofs. Go through the below article and get the complete notes here to learn in an easy way.

Introduction

The area represents the amount of planar surface being covered by a closed geometric figure.

Areas Of Parallelograms And Triangles Class 9-1

Areas of closed figures

Figures on the Common Base and Between the Same Parallels

Two shapes are stated to be on the common base and between the same parallels if:
a) They have a common side.
b) The sides parallel to the common base and vertices opposite the common side lie on the same straight line parallel to the base.

Areas Of Parallelograms And Triangles Class 9-2

For example Parallelogram  ABCD, Rectangle ABEF and Triangles ABP and ABQ

Area of a parallelogram

Areas Of Parallelograms And Triangles Class 9-3

Parallelogram

Area of a parallelogram = b×h

Where b is the base and h is the corresponding altitude(Height).

Area of a triangle

Areas Of Parallelograms And Triangles Class 9-4

Area of triangle

Area of a triangle = (1/2)×b×h

Where “b” is the base and “h” is the corresponding altitude.

Theorems

Parallelograms on the Common Base and Between the Same Parallels

Two parallelograms are said to be on the common/same base and between the same parallels if
a) They have a common side.
b) The sides parallel to the common side lie on the same straight line.

Areas Of Parallelograms And Triangles Class 9-5

Parallelogram ABCD and ABEF

Theorem: Parallelograms that lie on the common base and between the same parallels are said to have equal in area.
Here, ar(parallelogram ABCD)=ar(parallelogram ABEF)

Triangles on the common base and between the same Parallels

Two triangles are said to be on the common base and between the same parallels if
a) They have a common side.
b) The vertices opposite the common side lie on a straight line parallel to the common side.

Areas Of Parallelograms And Triangles Class 9-6

Triangles ABC and ABD

Theorem: Triangles that lie on the same or the common base and also between the same parallels are said to have an equal area.
Here, ar(ΔABC)=ar(ΔABD)

Two triangles having the common base & equal areas

If two triangles have the same base and are equal in area, then, their corresponding altitudes are equal.

Areas Of Parallelograms And Triangles Class 9-7

-If two triangles have equal bases and are equal in area, then their corresponding altitudes are equal.

A Parallelogram and a triangle between the same parallels

A triangle and a parallelogram are said to be on the same base and between the same parallels if
a) They have a common side.
b) The vertices opposite the common side lie on a straight line parallel to the common side.

Areas Of Parallelograms And Triangles Class 9-8

A triangle ABC and a parallelogram ABDE

Theorem: If a triangle and a parallelogram are on the common base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram.
Here ar(ΔABC)=(1/2)ar(parallelogarm ABDE)

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