**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**.

### 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**.

**For example**Â ParallelogramÂ ABCD, Rectangle ABEF and Triangles ABP and ABQ

### Area of a parallelogram

Area of a parallelogram = bÃ—h

Where â€˜bâ€² is the **base** and â€˜hâ€² is the corresponding **altitude**(Height).

### Area of a triangle

Area of a triangle =Â (1/2)Ã—bÃ—h

Where **“b”** is the** base** and “**h”**Â 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**.

**Theorem**:Â Parallelograms that lie on the **common base**Â and **between the same parallels** are said to haveÂ **equal in area**.

Here, ar(parallelogramÂ ABCD)=ar(parallelogramÂ 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**.

**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(Î”ABC)=ar(Î”ABD)

### 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.

-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**.

**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(Î”ABC)=(1/2)ar(parallelogarmÂ ABDE)