Question 1

Find the missing terms:
(a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?.
(b) Perimeter of a square = 20 cm; length of a side = ?.
(c) Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?.

Accepted Answer

(a) Given, perimeter of rectangle =14 cm, breadth = 2 cmPerimeter of rectangle = 2 (length + breadth)⇒ 14 cm = 2 (length + 2 cm)⇒ 7 cm = length + 2 cm⇒ length = 5 cm(b) Given, perimeter of a square = 20 cm⇒ 4 × side = 20 cm⇒ side = 5 cmTherefore, length of a side = 5 cm(c) Perimeter of a rectangle = 12 m⇒ 2 (length + breadth) = 12 m⇒ 3 m + breadth = 6 m⇒ breadth = 3 m

Question 2

A rectangle having side lengths 5 cm and 3 cm is made using a piece of wire. If the wire is straightened and then bent to form a square, what will be the length of a side of the square?

Accepted Answer

Given, length of rectangle = 5 cm and breadth = 3 cmWe know thatperimeter of rectangle = 2 × (length × breadth)= 2 × (5 + 3) = 16 cmNow, if we bend the wire to form a square, the total length of the wire (16 cm) will be divided equally among the four sides of the square.So, each side of the square = $\frac{\text { Perimeter }}{4}$= $\frac{16}{4}$ = 4 cm

Question 3

Find the length of the third side of a triangle with a perimeter of 55 cm and two sides of length 20 cm and 14 cm, respectively.

Accepted Answer

Let ABC be the given triangle such that AB = 20 cm, BC = 14 cmSo, perimeter = AB + BC + CA = 55 cm⇒ 55 = 20 + 14 + CA⇒ CA = 55 – (20 + 14)⇒ CA = 21 cm∴ the length of the third side of the triangle = 21 cm.

Question 4

What would be the cost of fencing a rectangular park whose length is 150 m and breadth is 120 m if the fence costs ₹ 40 per meter?

Accepted Answer

The length of the fence is the perimeter of the rectangular park.Given that the length of the rectangular park = 150 m and breadth = 120 m∴ Perimeter = 2(l + b)= 2(150 + 120)= 2(270)= 540 mNow cost of fencing per meter = ₹ 40Cost of fencing the rectangular park = ₹ 40 × 540 = ₹ 21600

Question 5

A piece of string is 36 cm long. What will be the length of each side, if it is used to form:
(a) A square,
(b) A triangle with all sides of equal length, and
(c) A hexagon (a six sided closed figure) with sides of equal length?

Accepted Answer

Length of piece of string = 36 cm(a) Length of side of a square = $\frac{36}{4}$ cm = 9 cm(b) Length of side of a triangle when all sides are equal = $\frac{36}{3}$cm = 12 cm(c) Length of a side of a hexagon when all sides are equal= $\frac{36}{6}$cm = 6 cm

Question 6

A farmer has a rectangular field having length 230 m and breadth 160 m. He wants to fence it with 3 rounds of rope as shown. What is the total length of rope needed?

Accepted Answer

Perimeter of a rectangular field = 2 (length + breadth)= 2 (230 m + 160 m)= 780 mThe farmer wants 3 rounds of rope to fence.Total length of rope needed = 780 m × 3= 2340 m6.1 Perimeter Figure it Out (Page No. 133 – 134)Matha Pachchi!Each track is a rectangle. Akshi’s track has length 70 m and breadth 40 m. Running one complete round on this track would cover 220 m, i.e., 2 × (70 + 40) m = 220 m. This is the distance covered by Akshi in one round.

Question 7

Find out the total distance Akshi has covered in 5 rounds.

Accepted Answer

Akshi runs on a rectangular track with a length of 70 metres and a breadth of 40 metres.∴ Perimeter of track = 2 × (length + breadth)= 2 × (70 + 40) = 220 mSince, the distance covered in one round = 220 m∴ Total distance covered in 5 rounds = 5 × 220 m= 1100 m

Question 8

Find out the total distance Toshi has covered in 7 rounds.
Who ran a longer distance?

Accepted Answer

Toshi runs on a rectangular track with a length of 60 m and breadth of 30 m.∴ Perimeter of track = 2 × (length + breadth)= 2 × (60 + 30) = 180 mSince, the distance covered in ope round = 180 m∴ Total distance covered in 7 rounds = 7 × 180 m= 1260 mSo, Toshi ran a longer distance.

Question 9

Think and mark the positions as directed:
(a) Mark ‘A’ at the point where Akshi will be after she runs 250 m.
(b) Mark ‘B’ at the point where Akshi will be after she runs 500 m.
(c) Now, Akshi ran 1000 m. How many full rounds has she finished running around her track? Mark her position as ‘C’.
(d) Mark ‘X’ at the point where Toshi will be after she runs 250 m.
(e) Mark ‘Y’ at the point where Toshi will be after she runs 500 m.
(f) Now, Toshi ran 1000 m. How many full rounds has she finished runn

Accepted Answer

(a) Distance covered by Akshi in 1 complete round = 220 m.so, to cover ‘250 m Akshi have to move 30 m more = 220 + 30 = 250 m.(b) Since the perimeter of the outer rectangle is 220 m, it implies that the distance covered till the starting point in 2 rounds will be 2 × 220 = 440 mNow, the point where Akshi will cover 500 m will be 60 m away from this point.(c) Distance covered by Akshi = 1000 mNo. of rounds = $\frac{1000}{220}$ = 4 complete rounds and 120 m more.Thus, she’ll be 120 m away from the starting point.(d) Distance covered by Toshi in 1 round = 180 mSo, to cover 250 m, she’ll be 70 m away from the starting point.(e) Since, the perimeter of the inner rectangle is 180 m, so to cover 500 m, Toshi will be taking 2 complete rounds and then she’ll have to move 140 m more i.e. 140 m away from the starting point.(f) For 1000 m, Toshi will be covering $\frac{1000}{180}$ = 5 complete rounds and 100 m more.This means that she’ll be 100 m away from the starting point.6.2 Area Figure it Out (Page No. 138)

Question 10

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

Accepted Answer

Length of a rectangular garden = 25 mArea of rectangular garden = length × width300 sq m = 25 m × width⇒ Width of the garden = $\frac{300 \mathrm{sqm}}{25 \mathrm{~m}}$ = 12 m

Source: This question is from Perimeter and Area, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Perimeter and Area: Area, Rectangular, Garden, Long, Width, Perimeter and Area. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
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Question 11

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?

Accepted Answer

Length of rectangular plot = 500 mBreadth of rectangular plot = 200 mArea of rectangular plot = 500 m × 200 m = 1,00,000 sq mThe cost of tiling the plot is given ₹ 8 per hundred sq m.So, we will convert area into per hundred sq m$\frac{1,00,000}{100}$ = 1,000 (in hundred sq m)The cost of tiling per hundred sq m = ₹ 8∴ The cost of tiling rectangular plot = 1,000 × ₹ 8 = ₹ 8,000

Question 12

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?

Accepted Answer

Area of rectangular coconut grove = 100 × 50 = 5000 sq. mGiven each coconut tree requires 25 sq. mthen the maximum no. of trees that can be planted in this grove = $\frac{5000}{25}$ = 200

Question 13

By splitting the following figures into rectangles, find their areas (all measures are given in meters):

Accepted Answer

(a) Splitting the given figure into I, II, III, and IV rectangles as shown in the figure below, we getHere, the area of rectangle I = length × breadth= 4 cm × 3 cm= 12 sq. cmArea of rectangle II = length × breadth= 3 cm × 2 cm= 6 sq. cmArea of rectangle III = length × breadth= 4 cm × 1 cm= 4 sq. cmArea of rectangle IV = length × breadth= 3 cm × 2 cm= 6 sq. cmThe total area of the whole figure = 12 sq. cm + 6 sq. cm + 4 sq. cm + 6 sq. cm = 28 sq. cm.Therefore, the total area of Figure (a) is 28 sq. cm.(b) Similarly, by splitting figure (b) into I, II, and III rectangles as shown in the figure below, we getArea of the rectangle I = length × breadth= 3 cm × 1 cm= 3 sq. cmArea of rectangle II = length × breadth= 3 cm × 1 cm= 3 sq. cmArea of rectangle III = length × breadth= 3 cm × 1 cm= 3 sq. cmThe total area of the figure = 3 sq. cm + 3 sq. cm + 3 sq. cm = 9 sq. cm.Therefore, the total area of Figure (b) is 9 sq. cm.6.2 Area Figure it Out (Page No. 139)Cut out the tangram pieces given at the end of your textbook.

Question 14

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

Accepted Answer

Here, we can see that some shapes have identical areas.SpecificallyShapes A and B These shapes are identical, meaning they cover the same amount of space, so they have the ^ same area.Shapes C and E These shapes also have the same area because they are identical in size and shape.

Question 15

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

Accepted Answer

Shape D is twice as big as shape C. This means that if you place two shape C pieces together. Then, they exactly cover shape D.The relationship between these shapesShape D can be completely filled by combining shape C and shape E. So, area of shape D is equal to the sum of the area of shape C and E.Each of shapes C and E has half the area of shape D.

Question 16

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

Accepted Answer

Solution:From the figure, we can see that two times Shape C forms Shape D. Similarly two times Shape C forms Shape F. Thus, both Shape D and F are equal.

Source: This question is from Perimeter and Area, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Perimeter and Area: Shape, Area, Perimeter and Area, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Perimeter and AreaQ1: Find the missing terms: (a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?. (b)...
Q11: What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹ 8...
Q12: A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m,...
Q13: By splitting the following figures into rectangles, find their areas (all measures are given in...
Q14: Explore and figure out how many pieces have the same area.
Practice more questions from Perimeter and Area &mdash; Mathematics, Class 6 CBSE

Question 17

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

Accepted Answer

Solution: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.

Source: This question is from Perimeter and Area, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Perimeter and Area: Shape, Area, Perimeter and Area, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Perimeter and AreaQ1: Find the missing terms: (a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?. (b)...
Q11: What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹ 8...
Q12: A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m,...
Q13: By splitting the following figures into rectangles, find their areas (all measures are given in...
Q14: Explore and figure out how many pieces have the same area.
Practice more questions from Perimeter and Area &mdash; Mathematics, Class 6 CBSE

Question 18

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, and 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.]

Accepted Answer

Shape A has twice the area of shape G.

Source: This question is from Perimeter and Area, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Perimeter and Area: Area, Shape, Compared, Twice, Big, Times. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Perimeter and AreaQ1: Find the missing terms: (a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?. (b)...
Q11: What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹ 8...
Q12: A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m,...
Q13: By splitting the following figures into rectangles, find their areas (all measures are given in...
Q14: Explore and figure out how many pieces have the same area.
Practice more questions from Perimeter and Area &mdash; Mathematics, Class 6 CBSE

Question 19

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

Accepted Answer

Let’s say the area of C = xArea of D = Area of 2C = 2xArea of E = Area of C = xArea of F = Area of 2C = 2xArea of G = Area of 2C = 2xArea of A = Area of 2F = 2 × 2x = 4xArea of B = Area of A = 4xHence total area of big shape = Area of A + B + C + D + E + F + G= 4x + 4x + x + 2x + x + 2x + 2x= 16x= 16CThat means the area of a big square is 16 times the area of shape C.

Question 20

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

Accepted Answer

Solution:When arranging the 7 pieces to form a rectangle, the area of the rectangle will be the same as that of area of square.Area of rectangle = 16 × area of shape C.

Source: This question is from Perimeter and Area, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Perimeter and Area: Arrange, Pieces, Form, Rectangle, Area, Terms. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Perimeter and AreaQ1: Find the missing terms: (a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?. (b)...
Q11: What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹ 8...
Q12: A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m,...
Q13: By splitting the following figures into rectangles, find their areas (all measures are given in...
Q14: Explore and figure out how many pieces have the same area.
Practice more questions from Perimeter and Area &mdash; Mathematics, Class 6 CBSE