NCERT Solutions Class 6 Maths Chapter 6 Perimeter and Area Exercise 6.2

Exercise 6.2 of Class 6 Math Chapter 6 – Perimeter and Area – is about finding the area of shapes such as squares and rectangles. It consists of simple questions that teach you how much space a shape takes up.

This exercise has been made according to the latest NCERT syllabus and are designed to help establish your basics in geometry and measurements that would help you in higher classes in the future. 

You can access the complete NCERT Solutions for Class 6 Maths Chapter 6 Exercise 6.2 in a free pdf format on this page. The solutions have been explained simply in easy steps, so you could learn at your pace. You can use these solutions to revise the chapter and understand the methods used to solve the questions.

1.0Download NCERT Solutions Class 6 Maths Chapter 6 Perimeter and Area Exercise 6.2: Free PDF

Exercise 6.2 is about using standard formulas to calculate the area of squares and rectangles. It reinforces the concepts of basic geometry and measurement. You can find the entire NCERT Solutions for Class 6 Maths Chapter 6 Exercise 6.2 and download the free PDF to help with preparation for exams.

2.0NCERT Solutions Class 6 Chapter 6 Perimeter and Area: All Exercises

3.0NCERT Class 6 Maths Chapter 6 Perimeter and Area Exercise 6.2: Detailed Solutions

6.2 Area

1. The area of a rectangular garden 25 m long is 300 sq m . What is the width of the garden? Sol. Given, area of rectangular garden $=300$ sq. m And length $=25\mathrm{m}$ Area of rectangular field $=\ell \times b$ $\Rightarrow 300=25\times \mathrm{b}$
   
   $\Rightarrow \mathrm{b}=12\mathrm{m}$
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?
   
   Sol. Length $=500$ and breadth $=200\mathrm{m}$ Hence the area of the rectangular plot $=$ length $\times$ breadth $=500\times 200$ $=1,00,000{\mathrm{m}}^2$ Now cost of tilling a rectangular plot $=\frac{8}{100}$ Hence the cost of tilling $1,00,000$ sq. m of rectangular plot $=\frac{8}{100}\times 100000=₹8,000$
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?
   
   Sol. Area of rectangular coconut grove $=100\times 50=5000$ sq. m Given each coconut tree requires 25 sq. m Then the maximum number of trees that can be planted in this grove $=\frac{5000}{25}=200$ trees
4. By splitting the following figures into rectangles, find their areas (all measures are given in metres):
   
   Sol. (a) Area of the figure $=$ Area of sq. $A+$ Area of sq. $B+$ Area of sq. $C+$ Area of sq. $D$ $=(3\times 3)+(1\times 7)+(5\times 2)+(1\times 2)$ $=9+7+10+2$ $=28{\mathrm{m}}^2$
   
   (b) Area of the figure $=$ Area of rectangle $\mathrm{E}+$ Area of rectangle $\mathrm{F}+$ Area of rectangle G $=(1\times 2)+(1\times 5)+(1\times 2)$ $=2+5+2$ $=9{\mathrm{m}}^2$
   
   Cut out the tangram pieces given at the end of your textbook.
   
5. Explore and figure out how many pieces have the same area. Sol. There are two pieces ( A and B ) that have the same area.
6. How many times bigger is Shape D as compared to Shape C? What is the relationship between Shapes C, D and E? Sol. Shape D is two times bigger than shape C . Clearly from the figure, the area of shapes C and E is equal to the area of shape $D$.
7. Which shape has more area: Shape D or F? Give reasons for your answer. Sol. Since the medium triangle and the square are each made up of two small tangram triangles, they each have an area $2x$ that of the small triangle. Hence both have the same area.
8. Which shape has more area: Shape F or G? Give reasons for your answer. Sol. Since the medium triangle and the rhomboid are each made up of two small tangram triangles, they each have an area 2x that of the small triangle. Hence both have the same area.
9. 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. Sol. Shape A has twice the area of shape G.
10. Can you now figure out the area of the big square formed with all seven pieces in terms of the area of Shape C? Sol. Let's say the area of $\mathrm{C}=\mathrm{x}$ Area of $D=$ Area of $2C=2x$ Area of $\mathrm{E}=$ Area of $\mathrm{C}=\mathrm{x}$ Area of $F=$ Area of $2C=2x$ Area of $\mathrm{G}=$ Area of $2\mathrm{C}=2\mathrm{x}$ Area of $A=$ Area of $2F=2\times 2x=4x$ Area of $B=$ Area of $A=4x$ Hence total area of big shape $=$ Area of $\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}+\mathrm{E}+\mathrm{F}+\mathrm{G}$ $=4x+4x+x+2x+x+2x+2x$ $=16\mathrm{x}$ $=16\mathrm{C}$ That means the area of a big square is 16 times the area of shape $C$.
11. 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. Sol. The tangram rectangle with all 7 pieces is a tangram square with 5 pieces extended with two big triangles. All seven tans fit together to form a rectangle. Hence area of this rectangle in terms of Shape C is 16 small triangles.
12. Are the perimeters of the square and the rectangle formed from these 7 pieces different or the same? Give an explanation for your answer. Sol. The perimeter of the square is equal to the square formed from these 7 pieces because these are the arrangements of pieces.

4.0Key Features and Benefits for Class 6 Maths Chapter 6 Exercise 6.2

• This exercise Includes questions on finding areas of squares and rectangles with easy-to-recall formulas.
• All questions are based on the latest NCERT syllabus for Class 6 as prescribed by the CBSE.
• It allows students to understand accurately how to measure space inside flat shapes.
• Practicing NCERT solutions will help you have better accuracy and confidence in preparation for your maths exam and other exams like the Olympiads.
• Students can use the step-by-step solutions in order to learn easily and know precise methods of problem-solving.