# NCERT Solutions for Class 6 Maths Chapter 10 Mensuration (Ex 10.3) Exercise 10.3

## NCERT Solutions for Class 6 Maths Chapter 10 Mensuration (Ex 10.3) Exercise 10.3

The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 cover all the concepts of perimeter and area. The distance travelled along a boundary that forms a closed figure when it is circled is known as the perimeter. The area of a closed figure is the total area that it encloses. Regular closed figures are those that have equal sides and angles.

The following topics are covered in the first section of the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3:

1. A rectangle’s perimeter equals 2 (length plus breadth).
2. A square’s perimeter equals 4 times its side length
3. An equilateral triangle’s perimeter equals three times its side length.

In the following section, the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 highlights the topic Area. The first method described is square-counting area calculation.

The following conventions are used in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 to determine a figure’s area using squared paper:

• One square is considered to have an area of one square (sq). If the sheet is one-centimetre square, one square centimetre equals one square centimetre.
• Ignore any areas that are a fraction of a square.
• If a region occupies more than half of a square. It is a single square.
• Take the area of the square as 1/2 square unit if exactly half of it is counted.

The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 can be used to evaluate these topics. There is only one question in Exercise 10.2, which is a brief exercise. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 include solved examples to help the students comprehend each concept clearly. At the conclusion of the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 Mensuration, a summary of all significant points is provided.

### Access Other Exercises of Class 6 Maths Chapter 10

 Chapter 10 – Mensuration Exercises Exercise 10.1 17 Questions & Solutions Exercise 10.2 1 Questions & Solutions

## NCERT Solutions for Class 6 Maths Chapter 10 Mensuration (Ex 10.3) Exercise 10.3

The primary themes covered in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 are important formulas and procedures to follow when calculating the areas of rectangles and squares. Additionally, Extramarks offers a number of examples that assist students in analysing the types of challenges associated with the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 and are crucial for the examinations. These NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 aid students in developing their problem-solving skills, which are crucial for success in the examinations.

There are a total of 12 questions in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3, 7 of which are brief and 3 of which are moderately difficult. Simple language is used in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 to assist students in understanding the concepts. The links on the Extramarks website and mobile application can take students to the detailed PDF file of the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3.

Problems concerned with finding the area of squares and rectangles are in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. The formulas for the area of a square and a rectangle’s derivation are also provided in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 with the use of illustrations.

Students can learn how to find the areas by putting values on graph paper and counting the number of squares through NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. To derive the formulas, the same method is applied. All the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 questions and examples must be thoroughly practised by students.

## Access NCERT Solutions for Class 6 Math Chapter 10 – Mensuration

Class 6 maths is one of the most challenging subjects in the NCERT curriculum. Complex and difficult concepts may be tough for students to comprehend. Students must study from the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 for the same. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3,are designed by Extramarks subject-matter experts with years of experience in the discipline of Maths.

The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 provide students with detailed explanations for every question. Students can access the linked article on the Extramarks website and mobile application to access the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3.

The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 must be solved in order for a student to successfully complete the concerned course. Students can review the exercise outline listed on the Extramarks website before proceeding to read and study  NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 in more detail.

It is difficult and demanding to complete the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. A significant amount of time is typically spent by students on this exercise. Hence, it is imperative that students access the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. Students benefit from having a firm understanding of the subject and quickly mastering it with the help of the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. The Class 6th Math 10.3 can be challenging, but students can improve their preparation by referring to the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3.

The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 is an essential component of the NCERT curriculum because it teaches students how to calculate the areas of rectangles and triangles. The exercises aid students in laying a solid Mathematical foundation.

The topic of calculating and determining the area of shapes like rectangles and triangles is covered in NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. In this exercise, students learn what an area is and how to calculate it for a variety of shapes and figures. Additionally, students will learn how to use figures to generate formulas for a square and a rectangle’s area with the help of the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3.

## NCERT Solutions For Class 6 Maths Chapter 10 Mensuration Exercise 10.3

Mensuration refers to the measurement of figures. Students are introduced to the measurement of various forms and figures in NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 discusses measurement, focusing on the development and application of algebraic formulas to calculate the various properties, the volume, and the surface area of geometric figures. Additionally, students may discover how to compare two or more things based on the measuring terminology as well as concepts like borders and perimeters of planar figures through the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 are crucial since they aid students in understanding ideas given in higher classes, such as the measurement of solid figures.

In the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3, students learn about unique concepts and ideas that help them strengthen their mathematical foundations. Several topics covered in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 are:-

• Perimeter Definitions
• Calculating the edges of various shapes, such as Squares, Rectangles, and Equilateral Triangles
• Calculating a Square’s Area
• Calculating a Triangle’s Surface Area
• Calculating a Rectangle’s Area

Students can gain a number of advantages and benefit from studying the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 available on Extramarks are created for the advantage of the students, so they may quickly grasp difficult ideas and ace their examinations with little difficulty.

The following are some advantages that students may gain when using the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3:

• The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 are accurate since they follow the most recent CBSE guidelines.
• The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 have been created by Extramarks subject-matter experts.
• Every in-text question is answered with a thorough explanation in Extramarks’ comprehensive NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3, which helps students comprehend them in-depth.
• Since the questions in the exams are taken from NCERT textbooks, the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 are of paramount importance, and students may greatly benefit from referring to them.

Through the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 students can measure the area and perimeter of various forms, such as rectangles and squares, by using measurement formulas. The practise of measuring figures is known as Mensuration. In particular,  Class 6 Maths Chapter 10 Exercise 10.3 emphasises the development of skills required for the application of algebraic formulas to calculate the areas, volumes, and properties of geometric shapes. The NCERT Class 6 Maths Chapter 10 Exercise 10.3 by Extramarks also has many real-world practical applications in people’s daily lives, thus mastering the Class 6 Maths Chapter 10 Exercise 10.3 Solution is crucial. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 focus mostly on flat figures, laying the foundation for students to measure solid figures in higher classes.

Students are introduced to the concepts of borders and perimeters of planar figures in the Ex 10.3 Class 6 solutions of Chapter 10 by Extramarks. They also learn how to compare two or more things based on the terminology used for measurement. The Class 6th Math Chapter 10.3 is available in PDF format, and the questions in the Maths Class 6 Chapter 10 Exercise 10.3 are selected by subject specialists to ensure a thorough understanding of the concerned chapter topics. Using the links provided on the Extramarks website and mobile application, one can access the PDF of  Math Class 6 Ex 10.3.

In order to comprehend how formulas are derived, students must be able to recall the idea of plane forms from earlier lectures and review the properties related to each shape. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 focus especially on Equilateral Triangles, Squares, and Rectangles. Some activity-based problems based on the comparison of planar figures using a wire or string are included in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 as well.

Students may be able to increase their knowledge and their grades by using the readily available links on the Extramarks website. By practising engaging exercises and solving problems, the NCERT solutions provided by Extramarks assist students in developing a solid understanding of the topics discussed. It is likely that students will be more able to relate to these problems if they calculate the size of their own backyard or garden and the perimeter of their fence. The following is an exercise-by-exercise analysis of NCERT Solutions Class 6 Maths Chapter 10 Mensuration:

• Class 6 Maths Chapter 10 Ex 10.1 – 17 Questions
• Class 6 Maths Chapter 10 Ex 10.2 – 1 Question
• Class 6 Maths Chapter 10 Ex 10.3 – 12 Questions

The definition of the Perimeter of various shapes like Squares, Rectangles, and Equilateral Triangles, as well as the Area of Rectangles and Squares, are the topics discussed in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3. The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 include detailed explanations of the questions pertaining to each of these areas, supported by illustrations.

The NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 consists of 13 key issues in Mensuration divided into simple, medium, and complex sums. Students are suggested to study and understand all the topics covered in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 and get prepared for their Maths examination by practising the problems.

There are some key formulas in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 that students learn how to use to calculate the area and perimeter of various shapes in their immediate classes. Students can measure the area and perimeter of geometric objects like Squares, Rectangles, and Equilateral Triangles using Mensuration formulas. These formulas can be reviewed by students one at a time:

• The perimeter of a rectangle is equal to 2 (length + width).
• The perimeter of a square is equal to four times the length of its sides.
• An equilateral triangle’s perimeter is equal to three times its side length.
• Length times width equals the area of a rectangle.
• Square area equals side by side.

The Chapter 10 examples in the NCERT Solutions Class 6 Maths Chapter 10 Exercise 10.3 help students create a practical approach to problem-solving. The topics addressed in this chapter have various use cases in our day-to-day lives. For instance, while installing flooring, the area is measured, and the area of the tiles to be used is compared, providing an estimate of the number of tiles needed. Therefore, the NCERT solutions are crucial not only for our everyday lives, but also from a mathematical perspective.

Q.1 Find the areas of the rectangles whose sides are:
(a) 3 cm and 4 cm (b) 12 m and 21 m
(c) 2 km and 3 km (d) 2 m and 70 cm

Ans.

$\begin{array}{l}\because \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Area}\text{of rectangle}=\mathrm{Length}×\mathrm{Breadth}\\ \left(\mathrm{a}\right)\mathrm{Area}\text{of rectangle}=3\text{\hspace{0.17em}}\mathrm{cm}×4\text{\hspace{0.17em}}\mathrm{cm}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=12{\mathrm{cm}}^{2}\\ \left(\mathrm{b}\right)\mathrm{Area}\text{of rectangle}=12\text{\hspace{0.17em}}\mathrm{cm}×21\text{\hspace{0.17em}}\mathrm{cm}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=252\text{\hspace{0.17em}}{\mathrm{cm}}^{2}\\ \left(\mathrm{c}\right)\mathrm{Area}\text{of rectangle}=2\text{\hspace{0.17em}}\mathrm{km}×3\text{\hspace{0.17em}}\mathrm{km}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=6\text{\hspace{0.17em}}{\mathrm{km}}^{2}\\ \left(\mathrm{d}\right)\mathrm{Length}\text{of rectangle}=2\text{\hspace{0.17em}}\mathrm{m}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=200\text{\hspace{0.17em}}\mathrm{cm}\\ \mathrm{Area}\text{of rectangle}=200\text{\hspace{0.17em}}\mathrm{cm}×70\text{\hspace{0.17em}}\mathrm{cm}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=14000\text{\hspace{0.17em}}{\mathrm{cm}}^{2}\end{array}$

Q.2 Find the areas of the squares whose sides are:

(a) 10 cm (b) 14 cm (c) 5 m

Ans.

Area of square = (side of square)2
(a) Area of square = (10)2

= 100 cm2
(b) Area of square = (14)2
= 196 cm2
(c) Area of square = (5)2

= 25 cm2

Q.3 The length and breadth of three rectangles are as given below:
(a) 9 m and 6 m
(b) 17 m and 3 m
(c) 4 m and 14 m
Which one has the largest area and which one has the smallest?

Ans.

$\begin{array}{l}\text{\hspace{0.17em}}\mathrm{Area}\text{of rectangle}=\mathrm{Length}×\mathrm{Breadth}\\ \left(\mathrm{a}\right)\mathrm{Area}\text{of rectangle}=9\text{\hspace{0.17em}}\mathrm{m}×6\text{\hspace{0.17em}}\mathrm{m}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=54\text{\hspace{0.17em}}{\mathrm{m}}^{2}\\ \left(\mathrm{b}\right)\mathrm{Area}\text{of rectangle}=17\text{\hspace{0.17em}}\mathrm{m}×3\text{\hspace{0.17em}}\mathrm{m}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=51\text{\hspace{0.17em}}{\mathrm{m}}^{2}\\ \left(\mathrm{c}\right)\mathrm{Area}\text{of rectangle}=4\text{\hspace{0.17em}}\mathrm{m}×14\text{\hspace{0.17em}}\mathrm{m}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=56\text{\hspace{0.17em}}{\mathrm{m}}^{2}\\ \text{Rectangle}\left(\text{c}\right)\text{has the largest area and rectangle}\left(\mathrm{b}\right)\text{has the}\\ \text{smallest area.}\end{array}$

Q.4 The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.

Ans.

$\begin{array}{c}\text{Area of rectangular garden}=\text{3}00\text{sq m}\\ \text{Length of rectangular garden}=50\text{\hspace{0.17em}}\mathrm{m}\\ \mathrm{Breadth}\text{of rectangular garden}=\frac{\mathrm{Area}\text{of garden}}{\mathrm{Length}\text{of garden}}\\ =\frac{300}{50}\\ =6\text{\hspace{0.17em}}\mathrm{m}\end{array}$

Q.5 What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹8 per hundred sq m.?

Ans.

Area of rectangular plot = 500 m × 200 m

= 1, 00, 000 sq m
Rate of tilling per sq m = ₹8 per hundred
= ₹(8/100)
Cost of tilling the plot = ₹(8/100) × 1,00,000

= ₹8000

Q.6 A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?

Ans.

Length of table top = 2 m

Breadth of table top = 1 m 50 cm

= (1 + 0.50) m

= 1.5 m

Area of table-top = Length x Breadth

= 2 m x 1.5 m

= 3 sq m

Q.7 A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room?

Ans.

Length of room = 4 m

Breadth of room = 3 m 50 cm

= (3 + 0.50) m

= 3.5 m

Area of floor = Length x Breadth

= 4 m x 3.5 m

= 14 sq m
Therefore, 14 sq m carpet is required to cover the floor of the room.

Q.8 A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.

Ans.

$\begin{array}{c}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Area}\text{of rectangular floor}=5\mathrm{m}×4\mathrm{m}\\ =20\text{\hspace{0.17em}}{\mathrm{m}}^{2}\\ \text{\hspace{0.17em}}\mathrm{Length}\text{of side of square carpet}=3\text{\hspace{0.17em}}\mathrm{m}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{Area}\text{of square carpet}={\left(3\text{\hspace{0.17em}}\mathrm{m}\right)}^{2}\\ =9\text{\hspace{0.17em}}{\mathrm{m}}^{2}\\ \mathrm{Area}\text{of floor that is not carpeted}=20-9\\ =11{\mathrm{m}}^{2}\end{array}$

Q.9 Five square flower beds each of sides 1 m are dug on a piece of land 5 m long and 4 m wide. What is the area of the remaining part of the land?

Ans.

Area of rectangular land = 5m x 4m

= 20 m2
Area of 1 flower bed = (1m)2
= 1m2
Area of 5 flower beds = 5m2
Area of remaining part of land= 20 – 5
= 15 m2

Q.10 By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).

Ans.

(a)Area of given figure = 3 × 3 + 1 × 2 +3 × 3
+ 2 × 4
= 9 + 2 + 9 + 8

= 28 cm2
(b) Area of given figure = 3 × 1 + 3 × 1 +3 × 1
= 3 + 3 + 3

= 9 cm2

Q.11 Split the following shapes into rectangles and find their areas. (The measures are given in centimeters)

Ans.

(a) Area of given figure = 12 x 2 + 8 x 2

= 24 + 16

= 40 cm2
(b) Area of given figure = 7 x 7 + 7 x 21 +7 x 7
= 49 + 147 + 49

= 245 cm2

(c) Area of given figure = 1 x 5 + 4 x 1
= 5 + 4

= 9 cm2

Q.12 How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to fit in a rectangular region whose length and breadth are respectively:

(a) 100 cm and 144 cm

(b) 70 cm and 36 cm.

Ans.

$\begin{array}{l}\left(\mathrm{a}\right)\text{Number of bricks in wall}=\frac{\mathrm{Area}\text{of rectangular region}}{\mathrm{Area}\text{of surface of brick}}\\ \text{\hspace{0.17em}\hspace{0.17em}}=\frac{100×144}{12×5}\\ \text{\hspace{0.17em}\hspace{0.17em}}=20×12\\ \text{\hspace{0.17em}\hspace{0.17em}}=240\\ \left(\mathrm{b}\right)\text{Number of bricks in wall}=\frac{\mathrm{Area}\text{of rectangular region}}{\mathrm{Area}\text{of surface of brick}}\\ \text{\hspace{0.17em}\hspace{0.17em}}=\frac{70×36}{12×5}\\ \text{\hspace{0.17em}\hspace{0.17em}}=14×3\\ \text{\hspace{0.17em}\hspace{0.17em}}=42\end{array}$

## FAQs (Frequently Asked Questions)

### 1. Is it necessary for students to practice all questions in Class 6 Maths NCERT Solutions Mensuration?

The topics covered by the questions in NCERT Solutions Class 6 Mensuration span from the area of the square and rectangle to the perimeter of shapes like rectangles, squares, and equilateral triangles. Each of the chapter’s questions is distinct and offers students a unique viewpoint. Students should therefore practice all of the Class 6 NCERT Solutions to exercise questions of Chapter 10 Mensuration.

### 2. What Important topics are Covered in Chapter 10 of the Class 6 Maths NCERT Solutions?

The Class 6 Maths Chapter 10 NCERT Solutions aid students in understanding what perimeter and area mean. Additionally, this chapter enables students to investigate the surface of planar figures such as squares, rectangles, and equilateral triangles. In view of the importance of each of these topics to the exam, students should devote the same amount of time to each topic and work through the examples with solutions.

### 3. How many questions are there in Chapter 10 Mensuration of the NCERT Class 6 Maths?

There are a total of 30 problems in the NCERT Class 6 Maths Chapter 10 Mensuration, 15 of which are short-form and the remaining 15 are long-form. The ability to recall both formulas and characteristics of each shape is essential for students in order to accurately answer every question.

### 4. How can CBSE students properly use the NCERT Solutions provided by Extramarks for Class 6 Maths Chapter 10?

The formulas in this chapter should be the students’ main emphasis, and they should pay close attention to the topics that are mentioned in the chapter summary. Students can also create formula notes to periodically review the crucial formulas. Additionally, it is suggested that students thoroughly comprehend the formulas in NCERT Solutions Class 6 Maths Chapter 10.

### 5. Why should students continue to practice the NCERT Solutions for Class 6 Maths Chapter 10?

Each and every question in the NCERT Solutions Class 6 Maths Chapter 10 Mensuration is supported by clear examples and logical and elaborate explanations. Additionally, these NCERT solutions provide illustrations to aid students in understanding ideas like area and object perimeter. Given that the majority of exam questions are derived from the NCERT textbooks, these solutions are the finest study guides for students preparing for the CBSE Maths examination of Class 6.