CBSE Class 5 Mathematics Chapter 3: How Many Squares NCERT Solutions

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NCERT Solutions PDF Class 5 PDF

This chapter, 'How Many Squares,' for CBSE Class 5 Mathematics, focuses on understanding the concepts of area and perimeter through practical examples involving squares and rectangles. Students will learn to measure sides, construct different shapes using a fixed number of squares, and compare the perimeters of these shapes. The solutions provide step-by-step guidance on how to find the number of squares that fit into a shape (area) and the total length of its boundary (perimeter). This chapter is crucial for developing spatial reasoning and foundational geometry skills, aiding students in visualizing and solving problems related to tiling and measurement. These NCERT Solutions are designed to help students grasp these concepts effectively and prepare for their exams by offering clear explanations and visual aids.

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Quick info

BoardCBSE
ClassClass 5
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3

Chapter summary

Chapter 3, 'How Many Squares,' of the CBSE Class 5 Mathematics curriculum introduces students to the fundamental concepts of area and perimeter. The exercises focus on calculating the area of irregular shapes by counting unit squares and determining the perimeter of various rectangles formed using a specific number of squares. Students will explore how different arrangements of the same number of squares can result in shapes with varying perimeters, highlighting the relationship between area and perimeter. These NCERT Solutions offer clear, step-by-step methods to solve problems related to tiling and measurement.

Learning outcomes

  • Understand the concept of area by counting unit squares.
  • Calculate the perimeter of rectangles formed using a given number of squares.
  • Differentiate between shapes with the same area but different perimeters.
  • Construct different rectangles using a fixed number of unit squares.
  • Measure the side length of squares and apply it to form rectangles.

Topics covered

Paper topics

  • Area
  • Perimeter
  • Unit Squares
  • Rectangles
  • Tiling
  • Measurement
  • Spatial Reasoning

Important topics

  • Calculating Area by Counting Squares
  • Finding Perimeter of Rectangles
  • Comparing Perimeters of Shapes with Same Area
  • Constructing Rectangles from Unit Squares

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Questions and Solutions

Question 1

Measure the side of the red square on the dotted sheet. Draw here as many rectangles as possible using 12 such squares. How many rectangles could you make? Which of these rectangles has the longest perimeter? Which of these rectangles has the smallest perimeter?
Solution:

First, measure the side of the red square on the dotted sheet. Let's assume the side of the red square is 1 cm. This means the area of one red square is 1 \times 1 = 1 square cm.

We need to make rectangles using 12 such squares. This means the area of each rectangle will be 12 square cm. To find the possible rectangles, we need to find the pairs of factors of 12.

The factors of 12 are 1, 2, 3, 4, 6, and 12. We can form the following rectangles:

  • 1 cm x 12 cm (Length = 12 cm, Width = 1 cm)
  • 2 cm x 6 cm (Length = 6 cm, Width = 2 cm)
  • 3 cm x 4 cm (Length = 4 cm, Width = 3 cm)

We can make 3 different rectangles using 12 squares. If we consider the orientation, we can also have 12 cm x 1 cm, 6 cm x 2 cm, and 4 cm x 3 cm. So, in total, there are 6 possible arrangements if we consider length and width distinctly.

Now, let's calculate the perimeter for each rectangle. The formula for the perimeter of a rectangle is P = 2 \times (Length + Width).

  • For the 1 cm x 12 cm rectangle: Perimeter = 2 \times (1 + 12) = 2 \times 13 = 26 cm.
  • For the 2 cm x 6 cm rectangle: Perimeter = 2 \times (2 + 6) = 2 \times 8 = 16 cm.
  • For the 3 cm x 4 cm rectangle: Perimeter = 2 \times (3 + 4) = 2 \times 7 = 14 cm.

Comparing the perimeters:

  • The longest perimeter is 26 cm, which corresponds to the 1 cm x 12 cm rectangle.
  • The smallest perimeter is 14 cm, which corresponds to the 3 cm x 4 cm rectangle.

Answer: We can make 3 distinct rectangles (or 6 if orientation matters). The rectangle with dimensions 1 cm x 12 cm has the longest perimeter (26 cm). The rectangle with dimensions 3 cm x 4 cm has the smallest perimeter (14 cm).

Question 1

Look at these interesting stamps. How many squares of one centimetre side does stamp A cover? And stamp B?
Solution:

To find out how many squares of one centimetre side each stamp covers, we need to count the number of unit squares within the boundary of each stamp. This count represents the area of the stamp in square centimetres.

For Stamp A: By carefully counting the squares shown in the figure for Stamp A, we find that it covers 16 squares, each with a side of 1 cm. Therefore, the area of Stamp A is 16 square cm.

For Stamp B: Similarly, by counting the unit squares within Stamp B, we find that it covers 12 squares, each with a side of 1 cm. Therefore, the area of Stamp B is 12 square cm.

Answer: Stamp A covers 16 squares of one centimetre side. Stamp B covers 12 squares of one centimetre side.

Common mistakes

  • Confusing area (number of squares inside) with perimeter (length of the boundary).
  • Incorrectly counting the total number of squares used to form a shape.
  • Errors in calculating the perimeter by not adding all sides correctly.
  • Assuming that all rectangles made from the same number of squares will have the same perimeter.

Revision tips

  • Practice drawing different rectangles using the same number of squares to visualize varying perimeters.
  • Carefully count the unit squares to determine the area of each shape.
  • Double-check perimeter calculations by adding all four sides of each rectangle.
  • Use graph paper to draw the shapes and verify the solutions visually.

Practice MCQs

Q1. If a rectangle is made using 12 unit squares, which of the following dimensions would result in the smallest perimeter?

Q2. What is the area of a rectangle formed by 12 unit squares?

Q3. Which measurement represents the perimeter of a shape?

Q4. If stamp A covers 16 squares of one centimetre side, what is its area?

Frequently asked questions

What is the main concept taught in CBSE Class 5 Maths Chapter 3?

Chapter 3, 'How Many Squares,' focuses on understanding and calculating the area of shapes by counting unit squares and determining the perimeter of rectangles.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each problem, helping students understand how to find areas and perimeters, and how different arrangements of squares affect the perimeter.

What is the difference between area and perimeter?

Area is the measure of the space inside a two-dimensional shape (counted in square units), while perimeter is the total length of the boundary of the shape.

Can different rectangles have the same area but different perimeters?

Yes, as shown in the chapter, different rectangles can be formed using the same number of squares (same area), but they can have different lengths of boundaries (perimeters).

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