CBSE Notes Class 6 Maths Chapter 6 Perimeter and Area

Perimeter is the total distance around the edge of a shape. To find it, we add the lengths of all the sides. Area is the amount of space inside a shape, measured in square units like cm² or m². To calculate area, we use different formulas depending on the shape. For example, the area of a rectangle is length × width, and the perimeter is the sum of all sides. Understanding these concepts helps us solve real-life problems like measuring land or building materials.

1.0What is Perimeter? 

The Perimeter of a shape is the total length of the boundary or the distance around the shape. 

To find the perimeter, you simply add up the lengths of all the sides of the shape. Let’s look at some common shapes and how we calculate their perimeters

Perimeter of a Rectangle 

A Rectangle is a shape with four sides, where opposite sides are equal in length. To find the perimeter of a rectangle, we use this formula:

Perimeter of Rectangle = 2 × (Length + Breadth)

For example, if a rectangle has a length of 8 cm and a breadth of 5 cm, the perimeter will be:

Perimeter = 2 × (8 + 5) = 2 × 13 = 26 cm

Perimeter of a Square

A Square is a special kind of rectangle where all four sides are equal in length. To calculate the perimeter of a square, you simply multiply the length of one side by 4:

Perimeter of Square = 4 × Side

For example, if one side of a square is 5 cm, the perimeter will be:

Perimeter = 4 × 5 = 20 cm

Perimeter of a Triangle

A Triangle has three sides. To find the perimeter of a triangle, simply add up the lengths of all three sides:

Perimeter of Triangle = a + b + c

For example, if a triangle has sides measuring cm, 8 cm, and 10 cm, the perimeter will be:

Perimeter = 5 + 8 + 10 = 23 cm

Perimeter of a Regular Polygon

A Regular Polygon is a polygon in which all sides are equal in length. To find the perimeter of a regular polygon, you multiply the length of one side by the total number of sides:

Perimeter of Regular Polygon = Number of sides × Length of one side

For example, for a regular hexagon (a polygon with 6 sides) with each side measuring 2 cm, the perimeter will be:

Perimeter = 6 × 2 = 12 cm

Perimeter of an Equilateral Triangle

An Equilateral Triangle is a triangle where all three sides are of equal length. To find its perimeter, simply multiply the length of one side by 3:

Perimeter of Equilateral Triangle = 3 × Side

For example, if one side of an equilateral triangle is 4 cm, the perimeter will be:

Perimeter = 3 × 4 = 12 cm

2.0What is Area?

While Perimeter measures the distance around the boundary of a shape, Area measures the amount of space inside the shape. It tells us how much surface a shape covers. We measure area in square units like square centimeters (cm²), square meters (m²), or square inches (in²).

Now, let’s look at how to calculate the area of some common shapes:

Area of a Triangle

To calculate the Area of a Triangle, we use the formula:

$\text{ Area of Triangle }=\frac{1}{2}\times \text{ Base }\times \text{ Height }$

For example, if a triangle has a base of 6 cm and a height of 4 cm, the area will be:

$\text{ Area }=\frac{1}{2}\times 6\times 4=12{\mathrm{cm}}^2$