Class 6 Maths Chapter 6 Perimeter and Area NCERT Solutions (Complete Explanation, Step-by-Step Answers & Solved Questions | Ganita Prakash)

📘 Class 6 Ganita Prakash Chapters

• Chapter 1: Knowing Our Numbers
• Chapter 2: Lines and Angles
• Chapter 3: Whole Numbers
• Chapter 4: Data Handling
• Chapter 5: Prime Time
• Chapter 6: Perimeter and Area
• Chapter 7: Fractions
• Chapter 8: Playing with Constructions
• Chapter 9: Symmetry
• Chapter 10: The Other Side of Zero

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Introduction

In daily life we often need to measure the boundary of objects and the space they occupy.

For example:

• fencing a garden

• putting a border around a playground

• measuring the floor area of a room

Mathematics helps us calculate these measurements using two important ideas:

Perimeter
Area

In this chapter, students learn how to calculate these for different shapes.

Understanding these concepts helps in solving real life problems easily.

Key Terms and Definitions

1. Perimeter

The perimeter of a closed figure is the total length of its boundary.

Example

If a square field has sides of 10 m each

Perimeter = 10 + 10 + 10 + 10
Perimeter = 40 m

Formula

Square
Perimeter = 4 × side

Rectangle
Perimeter = 2 × (length + breadth)

2. AreaThe area of a figure is the amount of surface it covers.

It is measured in square units.

Examples

cm²
m²
km²

Example

If a square has side 5 cm

Area = side × side
Area = 5 × 5 = 25 cm²

3. Unit Square

A unit square is a square whose side is 1 unit.

Area of unit square = 1 square unit

Students often find the area of shapes by counting unit squares.

Understanding Perimeter with Example

Suppose a rectangular garden has

Length = 8 m
Breadth = 5 m

Perimeter = 2 × (Length + Breadth)

Step 1
Perimeter = 2 × (8 + 5)

Step 2
Perimeter = 2 × 13

Step 3
Perimeter = 26 m

So fencing needed = 26 meters

Understanding Area with Example

Suppose a rectangle has

Length = 7 cm
Breadth = 4 cm

Area = length × breadth

Step 1
Area = 7 × 4

Step 2
Area = 28

Area = 28 cm²

Section Questions with Step-by-Step SolutionsQuestion 1

Find the perimeter of a square whose side is 9 cm.

Solution

Side = 9 cm

Perimeter of square = 4 × side

Step 1
Perimeter = 4 × 9

Step 2
Perimeter = 36

Answer
Perimeter = 36 cm

Question 2

Find the perimeter of a rectangle whose

Length = 12 cm
Breadth = 7 cm

Solution

Formula

Perimeter = 2 × (Length + Breadth)

Step 1
Perimeter = 2 × (12 + 7)

Step 2
Perimeter = 2 × 19

Step 3
Perimeter = 38

Answer
Perimeter = 38 cm

Question 3

Find the area of a square whose side is 6 cm.

Solution

Formula

Area = side × side

Step 1
Area = 6 × 6

Step 2
Area = 36

Answer
Area = 36 cm²

Question 4

Find the area of a rectangle whose

Length = 10 cm
Breadth = 4 cm

Solution

Area = length × breadth

Step 1
Area = 10 × 4

Step 2
Area = 40

Answer
Area = 40 cm²

Real Life Application

Perimeter and area are used in many real situations:

Fencing a field
Carpeting a room
Painting a wall
Designing gardens
Building houses

Understanding these helps students connect mathematics with everyday life.

Common Mistakes Students Make

Students often confuse perimeter and area.

Perimeter measures boundary length
Area measures surface covered

Remember:

Perimeter → units like cm, m
Area → square units like cm², m²

Quick Summary

Perimeter = total boundary length

Area = space covered inside a figure

Square

Perimeter = 4 × side
Area = side × side

Rectangle

Perimeter = 2 × (length + breadth)
Area = length × breadth

Practice Questions

1 Find the perimeter of a square with side 11 cm
2 Find the area of a rectangle with length 8 cm and breadth 5 cm
3 A square park has side 20 m. Find its perimeter.
4 Find the area of a rectangle with length 15 m and breadth 6 m.

Conclusion

Perimeter and area are basic but powerful mathematical concepts.
Once students understand these ideas, they can easily solve many real life problems.

Practicing NCERT questions regularly helps build strong mathematical skills.

For more Class 6 Maths explanations and NCERT solutions, keep visiting

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Previous Chapter: Chapter 5 – Prime Time
Next Chapter: Chapter 7 – Fractions

Q1. What is the perimeter of a rectangle?

Perimeter of a rectangle = 2 × (length + breadth). Example: length = 12 cm, breadth = 8 cm → perimeter = 2 × (12+8) = 40 cm.

Q2. What is the perimeter of a square?

Perimeter of a square = 4 × side length. Example: side = 1 m → perimeter = 4 × 1 = 4 m.

Q3. How do we find the perimeter of a triangle?

Perimeter of a triangle = sum of all three sides. Example: sides = 4 cm, 5 cm, 7 cm → perimeter = 16 cm.

Q4. How to calculate fencing cost of a rectangular park?

Step 1: Find perimeter = 2 × (length + breadth). Step 2: Multiply perimeter by cost per metre. Example: length = 150 m, breadth = 120 m → perimeter = 540 m. Cost = 540 × ₹40 = ₹21,600.

Q5. How to find side length if perimeter is given?

For a square: side = perimeter ÷ 4. Example: perimeter = 20 cm → side = 20 ÷ 4 = 5 cm.

Q6. How to calculate area of a rectangle?

Area = length × breadth. Example: length = 5 m, breadth = 4 m → area = 20 sq m.

Q7. How to calculate area of a square?

Area = side × side. Example: side = 3 m → area = 9 sq m.

Q8. How to find area not carpeted in a room?

Step 1: Find area of floor = length × breadth. Step 2: Find area of carpet. Step 3: Subtract carpet area from floor area. Example: floor = 20 sq m, carpet = 9 sq m → uncovered area = 11 sq m.

Q9. How to calculate maximum number of trees in a grove?

Step 1: Find area of grove = length × breadth. Step 2: Divide by area required per tree. Example: grove = 100 × 50 = 5000 sq m, each tree = 25 sq m → 200 trees.

Q10. What is the formula for area of a triangle?

Area of a triangle = ½ × base × height. Example: base = 10 cm, height = 6 cm → area = 30 sq cm.

Q11. Can two figures have same area but different perimeters?

Yes. Example: A square of side 4 cm → area = 16 sq cm, perimeter = 16 cm. A rectangle of 8 × 2 cm → area = 16 sq cm, perimeter = 20 cm.

Q12. How to estimate area using graph paper?

Count full squares as 1 sq unit, ignore less than half squares, count more than half as 1 sq unit, and half squares as ½ sq unit.

Q13. Why is area measured in square units?

Because squares can be packed without gaps or overlaps, making them ideal for measuring regions accurately.

Q14. How to find perimeter of a regular polygon?

Perimeter = number of sides × length of one side. Example: hexagon with side 6 cm → perimeter = 6 × 6 = 36 cm.

Q15. How to calculate tiling cost of land?

Step 1: Find area = length × breadth. Step 2: Multiply by cost per unit area. Example: land = 500 × 200 = 100,000 sq m. Cost = (100,000 ÷ 100) × ₹8 = ₹8000.