CBSE Class 6 Mathematics Chapter 10: Mensuration NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Mathematics Chapter 10: Mensuration introduces the basic ideas of measuring geometric shapes. The NCERT Solutions for this chapter focus on understanding and calculating the perimeter of different polygons. Students will learn what perimeter means – the total distance around a shape – and how to find it by adding up the lengths of all its sides. The solutions also show how this concept is used in real life, like figuring out how much tape is needed to go around a box or how much wood is required to frame a picture. These clear, step-by-step explanations help build a solid understanding of geometry and make solving mensuration problems easier for exams.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 10: Mensuration

Chapter summary

Chapter 10, Mensuration, for Class 6 Mathematics NCERT Solutions focuses on the concept of perimeter. It explains how to calculate the perimeter of different shapes by adding the lengths of all their sides. The exercises involve finding the perimeter of irregular polygons and applying this concept to real-world scenarios like framing a photograph or sealing a box. These solutions provide clear, step-by-step guidance for students to master perimeter calculations.

Learning outcomes

  • Understand the concept of perimeter as the total length of the boundary of a shape.
  • Calculate the perimeter of various irregular polygons by summing the lengths of their sides.
  • Apply the perimeter formula to solve real-world problems involving rectangular shapes.
  • Convert measurements between centimeters and meters when calculating perimeter.

Topics covered

Paper topics

  • Perimeter
  • Perimeter of irregular polygons
  • Perimeter of rectangles
  • Perimeter of squares
  • Sum of sides
  • Unit conversion (cm to m)
  • Mensuration basics

Important topics

  • Calculating perimeter by summing all sides
  • Perimeter of rectangles
  • Real-world applications of perimeter
  • Unit consistency in calculations

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Questions and Solutions

Question 1

Find the perimeter of each of the following figures:

(a) (b) (c) (d) (e) (f)

Solution:

The perimeter of a figure is the total length of its boundary. To find the perimeter, we sum the lengths of all its sides.

  1. (a) The sides are 4 cm, 2 cm, 1 cm, and 5 cm.

    Perimeter = 4 cm + 2 cm + 1 cm + 5 cm = 12 cm.

  2. (b) The sides are 23 cm, 35 cm, 40 cm, and 35 cm.

    Perimeter = 23 cm + 35 cm + 40 cm + 35 cm = 133 cm.

  3. (c) The sides are 15 cm, 15 cm, 15 cm, and 15 cm.

    Perimeter = 15 cm + 15 cm + 15 cm + 15 cm = 60 cm.

  4. (d) The sides are 4 cm, 4 cm, 4 cm, 4 cm, and 4 cm.

    Perimeter = 4 cm + 4 cm + 4 cm + 4 cm + 4 cm = 20 cm.

  5. (e) The sides are 1 cm, 4 cm, 0.5 cm, 2.5 cm, 2.5 cm, 0.5 cm, and 4 cm.

    Perimeter = 1 cm + 4 cm + 0.5 cm + 2.5 cm + 2.5 cm + 0.5 cm + 4 cm = 15 cm.

  6. (f) The sides are 4 cm, 1 cm, 3 cm, 2 cm, 3 cm, 4 cm, 1 cm, 3 cm, 2 cm, 3 cm, 4 cm, 1 cm, 3 cm, 2 cm, and 3 cm.

    Perimeter = 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 = 52 cm.

Question 2

The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?
Solution:

The length of the tape required to seal the lid all around is equal to the perimeter of the rectangular lid.

Given: Length = 40 cm, Breadth = 10 cm.

The formula for the perimeter of a rectangle is P = 2 \times (\text{length} + \text{breadth}).

Substituting the given values:

P = 2 \times (40 \text{ cm} + 10 \text{ cm})

P = 2 \times (50 \text{ cm})

P = 100 \text{ cm}

Since 100 cm is equal to 1 meter, the length of the tape required is 100 cm or 1 m.

Thus, the total length of tape required is 100 cm or 1 m.

Question 3

A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?
Solution:

First, we need to express the length and breadth in the same unit. Let's convert them to meters.

Length of the table top = 2 m 25 cm. Since 100 cm = 1 m, 25 cm = 0.25 m. So, Length = 2 m + 0.25 m = 2.25 m.

Breadth of the table top = 1 m 50 cm. Since 50 cm = 0.50 m. So, Breadth = 1 m + 0.50 m = 1.50 m.

The formula for the perimeter of a rectangle is P = 2 \times (\text{length} + \text{breadth}).

Substituting the values:

P = 2 \times (2.25 \text{ m} + 1.50 \text{ m})

P = 2 \times (3.75 \text{ m})

P = 7.50 \text{ m}

Thus, the perimeter of the table top is 7.5 m.

Question 4

What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?
Solution:

The length of the wooden strip required to frame the photograph is equal to the perimeter of the photograph.

Given: Length = 32 cm, Breadth = 21 cm.

The formula for the perimeter of a rectangle is P = 2 \times (\text{length} + \text{breadth}).

Substituting the given values:

P = 2 \times (32 \text{ cm} + 21 \text{ cm})

P = 2 \times (53 \text{ cm})

P = 106 \text{ cm}

Thus, the length of the wooden strip required is 106 cm.

Common mistakes

  • Forgetting to add all sides when calculating the perimeter of an irregular shape.
  • Errors in unit conversion between centimeters and meters.
  • Calculation mistakes when adding multiple side lengths.
  • Confusing perimeter with area.

Revision tips

  • Practice calculating the perimeter of different shapes by drawing them and measuring sides.
  • Focus on understanding the definition of perimeter before applying formulas.
  • Work through the real-world application problems to see how perimeter is used.
  • Ensure accuracy in addition and unit conversions.

Practice MCQs

Q1. What is the perimeter of a shape?

Q2. If a rectangle has a length of 10 cm and a breadth of 5 cm, what is its perimeter?

Q3. How do you find the perimeter of an irregular polygon?

Q4. A square has a side length of 5 cm. What is its perimeter?

Q5. Which unit is commonly used for measuring perimeter in this chapter?

Frequently asked questions

What is Mensuration in Class 6 Maths?

Mensuration is the branch of mathematics concerned with measuring geometric figures. In Class 6, Chapter 10 focuses on understanding and calculating the perimeter of various shapes.

How is the perimeter of an irregular shape calculated?

The perimeter of an irregular shape is found by adding the lengths of all its individual sides together.

What is the formula for the perimeter of a rectangle?

The perimeter of a rectangle is calculated using the formula: Perimeter = 2 * (length + breadth).

Why is it important to convert units in Mensuration problems?

It is crucial to convert units (e.g., from cm to m) to ensure consistency in calculations and to provide the final answer in the required unit, preventing errors.

How do these NCERT Solutions help with exam preparation?

These solutions provide clear, step-by-step explanations for each problem, helping students understand the methods and practice calculations, which is essential for exam revision and confidence building.

Important links

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