*Note: As per the revised CBSE curriculum, this chapter has been removed from the syllabus for the 2020-21 academic session.*

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

### Area of a parallelogram

The area of a parallelogram is the product of any of its sides and the corresponding altitude.

Area of a parallelogram = b×h

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

### Area of a 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

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

**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**.

### Triangles on the Common Base and Between the Same Parallels

**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** 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**.

### Two Triangles Having the Common Base & Equal Areas

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

**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.**

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**.