Ncert Solutions Class 6 Maths Chapter 6 Exercise 6 2

Exercise 6.2

Figure it Out

1. The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden? 

Ans:

Given:

Length of the garden $ l = 25 \, \text{m} $

Area of the garden $ A = 300 \, \text{sq m} $

Formula:

$A = l \times w$

Where:

$ A $ is the area,

$ l $ is the length,

$ w $ is the width.

Solution:

$300 = 25 \times w$

Divide both sides by 25:

$w = \frac{300}{25} = 12 \, \text{m}$

Answer: The width of the garden is 12 metres.

2. 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:

Given:

Length of the plot $ l = 500 \, \text{m} $

Width of the plot $ w = 200 \, \text{m} $

Rate of tiling $ \text{₹} 8 $ per 100 square metres.

Formula:

The area of the plot is:

$A = l \times w$

Total cost of tiling is:

$\text{Cost} = \left( \frac{A}{100} \right) \times \text{Rate per 100 sq m}$

Solution:

Calculate the area of the plot:

$A = 500 \times 200 = 100,000 \, \text{sq m}$

Now calculate the cost:

$\text{Cost} = \left( \frac{100,000}{100} \right) \times 8 = 1000 \times 8 = \text{₹} 8000$

Answer: The cost of tiling the plot is ₹ 8000.

3. A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m, what is the maximum number of trees that can be planted in this grove? 

Ans:

Given:

Length of the grove $ l = 100 \, \text{m} $

Width of the grove $ w = 50 \, \text{m} $

Area required for each coconut tree $ = 25 \, \text{sq m} $

Formula:

The area of the grove is:

$A = l \times w$

The number of trees that can be planted is:

$\text{Number of trees} = \frac{\text{Total area of grove}}{\text{Area per tree}}$

Solution:

Calculate the area of the grove:

$A = 100 \times 50 = 5000 \, \text{sq m}$

Now calculate the number of trees:

$\text{Number of trees} = \frac{5000}{25} = 200$

Answer: The maximum number of trees that can be planted is 200.

4. By splitting the following figures into rectangles, find their areas (all measures are given in metres).

Ans: To solve these problems, we will split each figure into smaller rectangles, calculate the area of each rectangle, and then sum the areas to get the total area for each figure.

(a) Figure a

We can split the figure into three smaller rectangles as follows:

1. Rectangle 1 (top-right rectangle):

   - Length = 3 metres

   - Width = 1 metre

   - Area = $ 3 \times 1 = 3 \, \text{sq metres} $

2. Rectangle 2 (middle rectangle):

   - Length = 4 metres

   - Width = 2 metres

   - Area = $ 4 \times 2 = 8 \, \text{sq metres} $

3. Rectangle 3 (bottom-left rectangle):

   - Length = 3 metres

   - Width = 3 metres

   - Area = $ 3 \times 3 = 9 \, \text{sq metres} $

Total area for figure (a):

$\text{Total area} = 3 + 8 + 9 = 20 \, \text{sq metres}$

(b) Figure b

We can split this figure into two rectangles as follows:

1. Rectangle 1 (outer rectangle):

   - Length = 5 metres

   - Width = 3 metres

   - Area = $ 5 \times 3 = 15 \, \text{sq metres} $

2. Rectangle 2 (inner cut-out rectangle):

   - Length = 3 metres

   - Width = 2 metres

   - Area = $ 3 \times 2 = 6 \, \text{sq metres} $

Total area for figure (b):

$\text{Total area} = \text{Area of outer rectangle} - \text{Area of inner cut-out}$

$\text{Total area} = 15 - 6 = 9 \, \text{sq metres}$

 Final Answers:

- Total area for figure (a): 20 sq metres

- Total area for figure (b): 9 sq metres

Figure it Out

Cut out the tangram pieces given at the end of your textbook.

1. Explore and figure out how many pieces have the same area. 

Ans: Shapes C, E, and F have the same area. These are all triangles of equal size.

2. How many times bigger is Shape D as compared to Shape C? What is the relationship between Shapes C, D and E? 

Ans: Shape D is twice the area of Shape C (or E). Shapes C and E have the same area, while Shape D is exactly double their area.

3. Which shape has more area: Shape D or F? Give reasons for your answer. 

Ans: Shape D has more area than Shape F. This is because Shape D is twice the area of Shape C (or E), while Shape F has the same area as Shape C and E.

4. Which shape has more area: Shape F or G? Give reasons for your answer. 

Ans: Shape G has more area than Shape F. Shape G is a square, and its area is larger than the area of Shape F, which is one of the smaller triangles.

5. What is the area of Shape A as compared to Shape G? Is it twice as big? Four times as big? 

Hint: In the tangram pieces, by placing the shapes over each other, we can find out that Shapes A and B have the same area, Shapes C and E have the same area. You would have also figured out that Shape D can be exactly covered using Shapes C and E, which means Shape D has twice the area of Shape C or shape E, etc. 

Ans: Shape A is exactly four times the area of Shape G. This can be deduced by the relative size of the pieces and the way they fit together.

6. Can you now figure out the area of the big square formed with all seven pieces in terms of the area of Shape C? 

Ans: The big square formed by all seven pieces has an area that is 8 times the area of Shape C. This is because the combined areas of the tangram pieces form a large square, and when you calculate the pieces' relative sizes, you find that the total area is 8 times the area of one Shape C.

7. Arrange these 7 pieces to form a rectangle. What will be the area of this rectangle in terms of the area of Shape C now? Give reasons for your answer. 

Ans: When the 7 pieces are arranged to form a rectangle, the area of the rectangle will still be 8 times the area of Shape C. The total area of the pieces remains constant regardless of the shape they form (whether a square or rectangle).

8. Are the perimeters of the square and the rectangle formed from these 7 pieces different or the same? Give an explanation for your answer.

Ans: The perimetres of the square and the rectangle formed by the 7 pieces will be different. Although the areas remain the same, the shape of the perimeter changes when you rearrange the pieces into different arrangements, changing the overall perimeter.

Benefits of NCERT Solutions for Class 6 Maths Chapter 1 Exercise 6.2 Perimeter and Area

• The solutions provide step-by-step explanations, ensuring students grasp the key concepts of calculating the area of squares and rectangles.

• By working through real-life examples, students develop practical problem-solving skills that they can apply in day-to-day situations involving measurements.

• These solutions reinforce important area formulas like area of a rectangle and square, helping students remember and apply them easily.

• The NCERT solutions help students practise efficiently, preparing them well for exams by covering essential types of questions that are likely to appear.

• The NCERT Solutions PDF Free is accessible anytime, allowing students to study and practice at their own pace without requiring internet access.

• Step-by-step methods enhance students' accuracy in solving area-related problems, reducing errors and building confidence.

• Mastering area calculation in this exercise strengthens the students' foundation, which is crucial for higher-level geometry concepts.

Class 6 Maths Chapter 1: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 6 - Perimeter and Area

Conclusion

In Chapter 6, Exercise 6.2 of Class 6 Maths, students are introduced to the critical concepts of calculating the area of squares and rectangles. Through the NCERT Solutions, students gain a clear understanding of the formulas and methods required to solve real-life problems involving area. These solutions not only help in building a strong foundation in geometry but also enhance problem-solving skills that are essential for future math topics. By practising with the free PDF solutions, students can strengthen their understanding, improve accuracy, and prepare effectively for exams, ensuring a confident approach to mathematical challenges.

Chapter-Specific NCERT Solutions for Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Maths Class 6

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.