CBSE Class 6 Maths Chapter 6 Mensuration NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Maths Chapter 6, Mensuration, lays the groundwork for understanding geometric shapes and their measurements. This chapter focuses on the concept of perimeter, defined as the total length around the boundary of a shape. The NCERT Solutions offer clear, step-by-step guidance for solving problems related to finding the perimeter of basic shapes like squares and rectangles. Students will learn to identify these shapes and apply appropriate formulas. The solutions also delve into calculating the perimeter of more complex figures, such as those made up of unit squares, promoting visual understanding and problem-solving skills. Mastering these fundamental mensuration concepts is essential for building a strong mathematical foundation and preparing effectively for exams.

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Quick info

BoardCBSE
ClassClass 6
SubjectMaths Exemplar
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 6

Chapter summary

Chapter 6, Mensuration, for Class 6 Maths NCERT Solutions focuses on understanding and calculating the perimeter of various shapes. It covers problems involving simple figures made of unit squares and composite shapes, requiring students to count the boundary units or apply basic perimeter formulas. The exercises are designed to reinforce the concept of perimeter as the total length around a shape, preparing students for more complex mensuration topics later.

Learning outcomes

  • Understand the concept of perimeter for different shapes.
  • Calculate the perimeter of figures formed by unit squares.
  • Determine the perimeter of a square.
  • Solve problems related to the boundary length of a park.
  • Analyze how changes in side length affect the perimeter of a square.

Topics covered

Paper topics

  • Mensuration
  • Perimeter
  • Unit Squares
  • Composite Figures
  • Square
  • Rectangle
  • Boundary Length
  • Geometric Shapes

Important topics

  • Calculating Perimeter of Composite Figures
  • Perimeter of a Square
  • Understanding Boundary Length
  • Effect of Doubling Side on Perimeter

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Questions and Solutions

Question 1

Following figures are formed by joining six unit squares. Which figure has the smallest perimeter in Fig. 6.4?

The figures provided are: (i) (ii)

(iii)

(iv)

Fig. 6.4

Options are: (A) (ii) (B) (iii) (C) (iv) (D) (i)

Solution:

To find the smallest perimeter, we need to calculate the perimeter of each figure by counting the number of unit square sides on its boundary. Assume each unit square has a side length of 1 cm.

  1. Figure (i) has a boundary formed by 10 sides of the unit squares. Therefore, its perimeter is 10 \times 1 \text{ cm} = 10 \text{ cm}.
  2. Figure (ii) has a boundary formed by 12 sides of the unit squares. Therefore, its perimeter is 12 \times 1 \text{ cm} = 12 \text{ cm}.
  3. Figure (iii) has a boundary formed by 14 sides of the unit squares. Therefore, its perimeter is 14 \times 1 \text{ cm} = 14 \text{ cm}.
  4. Figure (iv) has a boundary formed by 14 sides of the unit squares. Therefore, its perimeter is 14 \times 1 \text{ cm} = 14 \text{ cm}.

Comparing the perimeters: 10 cm, 12 cm, 14 cm, and 14 cm. The smallest perimeter is 10 cm, which corresponds to figure (i).

Thus, option (D) is correct.

Question 2

A square shaped park ABCD has a side of 100m. It has two equal rectangular flower beds each of size 10m x 5m (Fig. 6.5). What is the length of the boundary of the remaining park?

Fig. 6.5 shows a square park with flower beds inside.

Options are: (A) 360m (B) 400m (C) 340m (D) 460m

Solution:

Given:

Side of the square shaped park ABCD = 100 \text{ m}

Size of each rectangular flower bed = 10 \text{ m} \times 5 \text{ m}

The question asks for the length of the boundary of the *remaining* park. The boundary of the park refers to its outer perimeter. The flower beds are located *inside* the park. Therefore, the presence of the flower beds does not change the outer boundary of the square park itself.

The perimeter of the square park is calculated as:

Perimeter = 4 \times \text{side}

Perimeter = 4 \times 100 \text{ m}

Perimeter = 400 \text{ m}

The length of the boundary of the remaining park is the same as the perimeter of the original square park.

Thus, option (B) is correct.

Question 3

The side of a square is 10cm. How many times will the new perimeter become if the side of the square is doubled?

Options are: (A) 2 times (B) 4 times (C) 3 times (D) 8 times

Solution:

Given:

The original side of the square = 10 \text{ cm}

First, calculate the original perimeter of the square:

Original Perimeter = 4 \times \text{side}

Original Perimeter = 4 \times 10 \text{ cm}

Original Perimeter = 40 \text{ cm}

Now, the side of the square is doubled:

New side = 10 \text{ cm} \times 2

New side = 20 \text{ cm}

Next, calculate the new perimeter with the doubled side:

New Perimeter = 4 \times \text{new side}

New Perimeter = 4 \times 20 \text{ cm}

New Perimeter = 80 \text{ cm}

To find how many times the new perimeter has increased, divide the new perimeter by the original perimeter:

Ratio = \frac{\text{New Perimeter}}{\text{Original Perimeter}}

Ratio = \frac{80 \text{ cm}}{40 \text{ cm}}

Ratio = 2

Therefore, the new perimeter will be 2 times the original perimeter.

Thus, option (A) is correct.

Common mistakes

  • Confusing perimeter with area.
  • Incorrectly counting the units for perimeter in composite figures.
  • Errors in applying the perimeter formula for squares.
  • Miscalculating the boundary length when parts of the shape are removed or added.

Revision tips

  • Visualize each shape and trace its boundary to understand perimeter.
  • Practice counting units carefully for irregular shapes made of squares.
  • Memorize the perimeter formula for a square and understand its derivation.
  • Work through all examples and exercises to build confidence.

Practice MCQs

Q1. Which of the following figures, formed by joining six unit squares, has the smallest perimeter?

Q2. If the side of a square is doubled, how many times will its perimeter increase?

Q3. A square park has a side of 100m. If two rectangular flower beds of 10m x 5m are inside it, what is the length of the boundary of the remaining park?

Frequently asked questions

What is Mensuration in Class 6 Maths?

Mensuration is the branch of mathematics concerned with calculating the properties of geometric figures, such as length, area, and volume. In Class 6, it primarily focuses on understanding and calculating the perimeter of various shapes.

How do I calculate the perimeter of a shape made of unit squares?

To find the perimeter of a shape made of unit squares, you need to count the number of sides of the unit squares that lie on the outer boundary of the shape. Each counted side represents one unit of length.

What is the formula for the perimeter of a square?

The perimeter of a square is calculated by adding the lengths of all its four equal sides. If 's' is the length of one side, the formula is Perimeter = 4 × s.

How do these NCERT Solutions help with exam preparation?

These solutions provide clear, step-by-step explanations for each problem, helping you understand the methods and concepts. Practicing with these solutions builds confidence and accuracy for your exams.

What is the difference between perimeter and area?

Perimeter is the total length of the boundary of a two-dimensional shape, while area is the measure of the space enclosed within that boundary.

Important links

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