CBSE Class 5 Mathematics Chapter 11: Area and its Boundary NCERT Solutions

Reviewed by · Updated on

NCERT Solutions PDF Class 5 PDF

CBSE Class 5 Mathematics Chapter 11, 'Area and its Boundary,' introduces young learners to the essential geometric concepts of perimeter and area. These NCERT Solutions offer a clear, step-by-step guide to understanding how to measure the boundary of shapes and the space they cover. Using relatable examples, such as comparing pieces of aam paapad, students will learn to visually and practically assess the size of various two-dimensional figures. The chapter emphasizes the use of unit squares as a tool for calculating the area of rectangles, helping students grasp the concept of area measurement and differentiate between shapes with varying areas. This foundational knowledge in geometry is vital for developing problem-solving skills in measurement and spatial reasoning, preparing students effectively for future mathematical challenges and assessments.

Home

Quick info

BoardCBSE
ClassClass 5
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 11

Chapter summary

Chapter 11 of the CBSE Class 5 Mathematics curriculum, 'Area and its Boundary,' focuses on introducing the concepts of area and perimeter. The NCERT Solutions guide students through practical methods of comparing the sizes of shapes, primarily using the concept of unit squares to calculate area. Students will learn to find the area of rectangular pieces by counting squares and understand how to determine which piece is larger and by how much. This chapter lays the groundwork for understanding spatial measurement.

Learning outcomes

  • Understand the concept of area as the space occupied by a 2D shape.
  • Learn to measure area using unit squares.
  • Calculate the area of rectangular shapes by multiplying length and width.
  • Compare the areas of different shapes to determine which is larger.
  • Calculate the difference in area between two shapes.

Topics covered

Paper topics

  • Area
  • Boundary
  • Unit Squares
  • Measuring Area
  • Comparing Areas
  • Rectangular Shapes
  • Length
  • Width
  • Area Calculation

Important topics

  • Understanding Area
  • Calculating Area using Unit Squares
  • Area of Rectangles
  • Comparing Areas of Shapes

PDF preview

Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.

Loading document …
Page of
Loading page …

Questions and Solutions

Question 1

Parth and Gini bought aam paapad (dried mango slice) from a shop. Their pieces looked like these.

Piece A has dimensions 6 cm by 5 cm.

Piece B has dimensions 11 cm by 3 cm.

Both could not make out whose piece was bigger.

Suggest some ways to find out whose piece is bigger. Discuss.

A friend of Parth and Gini showed one way, using small squares.

The length of piece A is 6 cm. So 6 squares of side 1 cm can be arranged along its length. The width of piece A is 5 cm. So 5 squares can be arranged along its width.

  • Altogether how many squares can be arranged on it?
  • So the area of piece A = _____ square cm

In the same way find the area of piece B.

Who had the bigger piece? How much bigger?

Solution:

To determine whose piece of aam paapad is bigger, we need to compare their areas. The area of a shape tells us the amount of space it covers.

Ways to find out whose piece is bigger:

  1. Visual Comparison: Place the two pieces side-by-side and visually estimate which one covers more space. This is not always accurate.
  2. Using Unit Squares: Cover each piece with small squares of the same size (e.g., 1 cm × 1 cm squares) and count how many squares fit on each piece. The piece that fits more squares has a larger area.
  3. Using a Formula: If the pieces are rectangular, we can calculate their area by multiplying their length and width.

Let's use the unit square method and the formula method as shown in the problem.

For Piece A:

The length of Piece A is 6 cm. This means we can arrange 6 squares of side 1 cm along its length.

The width of Piece A is 5 cm. This means we can arrange 5 squares of side 1 cm along its width.

• Altogether, the total number of 1 cm squares that can be arranged on Piece A is the product of the number of squares along the length and the number of squares along the width.

Number of squares = 6 squares × 5 squares = 30 squares.

• So, the area of Piece A = 30 square cm.

For Piece B:

The length of Piece B is 11 cm.

The width of Piece B is 3 cm.

Using the same method, we can find the area of Piece B:

Area of Piece B = Length × Width

Area of Piece B = 11 \text{ cm} \times 3 \text{ cm} = 33 \text{ square cm}

Comparison:

Area of Piece A = 30 square cm

Area of Piece B = 33 square cm

• Comparing the two areas, we see that 33 square cm is greater than 30 square cm.

• Therefore, Piece B is bigger than Piece A.

How much bigger?

To find out how much bigger Piece B is, we calculate the difference between their areas:

Difference in area = Area of Piece B - Area of Piece A

Difference in area = 33 \text{ square cm} - 30 \text{ square cm} = 3 \text{ square cm}

Answer:

• Altogether, 30 squares can be arranged on Piece A.

• So, the area of Piece A = 30 square cm.

• The area of Piece B = 33 square cm.

• Piece B had the bigger piece. It was bigger by 3 square cm.

Common mistakes

  • Confusing area with perimeter.
  • Incorrectly counting unit squares.
  • Errors in multiplication when calculating area.
  • Misinterpreting 'how much bigger' to mean perimeter difference instead of area difference.

Revision tips

  • Visualize area by imagining covering the shape with unit squares.
  • Practice calculating the area of different rectangles using the formula: Area = Length × Width.
  • Always ensure units are consistent (e.g., cm with square cm).
  • Pay close attention to the question asked: 'area' vs. 'boundary' and 'how much bigger' in terms of area.

Practice MCQs

Q1. What does 'area' measure in a shape?

Q2. If a piece of paper is 5 cm long and 4 cm wide, how many 1 cm squares can fit on it?

Q3. Piece A is 6 cm × 5 cm and Piece B is 11 cm × 3 cm. Which piece has a larger area?

Q4. How much larger is the area of Piece B compared to Piece A?

Frequently asked questions

What is the main concept covered in CBSE Class 5 Maths Chapter 11?

Chapter 11, 'Area and its Boundary,' introduces students to the concept of area, which is the amount of space a two-dimensional shape covers, and how to measure it using unit squares.

How do these NCERT Solutions help students understand area?

The solutions break down the process of calculating area for rectangular shapes by using unit squares, making it easy for students to visualize and compute the space occupied by different pieces.

What is the difference between area and boundary?

The boundary refers to the length of the outline of a shape (perimeter), while the area refers to the total space enclosed within that boundary.

How can students compare the sizes of different pieces using these solutions?

Students can compare sizes by calculating the area of each piece using unit squares and then finding the difference between their areas to see which one is larger and by how much.

Are the questions in this chapter about real-life objects?

Yes, the chapter uses relatable examples like pieces of 'aam paapad' to help students connect mathematical concepts to everyday situations.

Important links

Content reviewed by the NCERT Help team. Editorial Team and update policy

NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.