Perimeter and Area
NCERT Class 6 Mathematics Chapter 6: Perimeter and Area (Pages 129–150)
Perimeter and Area at a Glance
Board
CBSE
Class
Class 6
Subject
Mathematics
Book
Ganita Prakash
Chapter
6
Pages
129–150
Resources
7 study resources
Perimeter and Area is a chapter in the CBSE Class 6 Mathematics syllabus from Ganita Prakash. This chapter hub brings together revision notes, practice questions, worksheets, flashcards, formula sheet to help students learn, practice, and revise Perimeter and Area effectively.
Scroll down to find Perimeter and Area notes, practice questions, worksheets, and revision resources — all in one place. Use the sidebar to jump to any section, or browse the full page below.
Perimeter and Area Revision Guide
Download the Perimeter and Area revision guide with key points, summaries, and quick revision notes for CBSE Class 6 Mathematics.
Key Points
1
Define Perimeter.
Perimeter is the total distance around a closed shape. It's calculated by adding the lengths of all sides.
2
Perimeter of a rectangle formula.
Perimeter = 2 × (length + breadth). For a rectangle with length 12 cm and breadth 8 cm, it's 40 cm.
3
Perimeter of a square formula.
Perimeter = 4 × side length. For a square photo frame with side 1 m, it's 4 m.
4
Perimeter of a triangle formula.
Perimeter = sum of all sides. For sides 4 cm, 5 cm, and 7 cm, it totals 16 cm.
5
Use case for rectangles in real life.
Finding the fencing needed for a rectangular garden involves calculating its perimeter.
6
Calculate missing dimensions.
If given perimeter, you can find missing dimensions using formulas, e.g., for rectangles.
7
Perimeter of composite shapes.
Add the perimeters of individual shapes (e.g., rectangles and triangles) to find the total.
8
Understanding closed plane figures.
A closed plane figure has no gaps; examples include triangles, squares, and rectangles.
9
Units of measurement in perimeter.
Perimeter is measured in linear units like cm, m, or km. Always keep units consistent.
10
Real-world applications of perimeter.
Used in construction, landscaping, and designing areas to determine material needs.
11
Common misconceptions about perimeter.
Students often confuse perimeter with area; remember, perimeter is the distance around the shape.
12
Practice with different shapes.
Calculate the perimeter of various shapes to strengthen understanding and confidence.
13
Lace example in triangles.
For a triangle with lengths of 4 cm, 5 cm, and 7 cm, lace required for trimming is 16 cm.
14
Perimeter affects cost in projects.
Calculate total fencing cost by multiplying perimeter by cost per unit length of fencing.
15
Identifying regular vs irregular shapes.
Regular shapes have equal sides (e.g., squares), while irregular shapes do not.
16
Using shapes for art projects.
Calculate perimeter to determine material length required in arts and crafts.
17
Understanding perimeter in circular shapes.
While traditional perimeter applies to polygons, circles have a circumference (C = 2πr).
18
Visualizing problems with diagrams.
Draw shapes to visualize and calculate perimeter. Diagrams aid in retention and understanding.
19
Juggling shapes in word problems.
Break down complex problems involving multiple shapes into simpler components to solve.
20
Create a perimeter-related project.
Design a small garden plot and calculate perimeter for fencing and layout optimization.
21
Memory hacks for formulas.
Remember formula patterns: rectangles double their sides, while squares multiply by four.
Perimeter and Area Practice Questions & Answers
Practice important questions and exam-style problems from Perimeter and Area. These questions cover key topics from the CBSE Class 6 Mathematics syllabus.
How to practice: Start with the questions below to test your understanding of Perimeter and Area. Use the revision guide to review concepts you find difficult, then come back and retry the questions for better retention.
Q1
What is the formula to calculate the perimeter of a rectangle?
Single Answer MCQ
Q-00140719
Q2
A rectangle has a length of 10 cm and a breadth of 5 cm. What is its perimeter?
Single Answer MCQ
Q-00140721
Q3
If a rectangle’s perimeter is 50 cm and the length is 20 cm, what is the breadth?
Single Answer MCQ
Q-00140723
Q4
A rectangle has a perimeter of 64 cm and a breadth of 12 cm. What is its length?
Single Answer MCQ
Q-00140725
Q5
How will the perimeter change if each side of a rectangle is doubled?
Single Answer MCQ
Q-00140727
Q6
If the length of a rectangle is halved, how does that affect the perimeter?
Single Answer MCQ
Q-00140729
Q7
Which of the following polygons has the same perimeter as a rectangle with Length 6 cm and Breadth 4 cm.
Single Answer MCQ
Q-00140731
Q8
A rectangle has a length that is twice its breadth. If the perimeter is 48 cm, what is the breadth?
Single Answer MCQ
Q-00140732
View all 111 Perimeter and Area questionsView all 111 Perimeter and Area questions
Q9
What will be the perimeter of a rectangle if both the length and breadth are multiplied by 3?
Single Answer MCQ
Q-00140733
Q10
A rectangle has a length of 15 cm. If the perimeter is 50 cm, what is the breadth?
Single Answer MCQ
Q-00140734
Q11
If the perimeter of a rectangle is equal to the perimeter of a square with side 10 cm, what is the maximum length of one side of the rectangle?
Single Answer MCQ
Q-00140735
Q12
A rectangle has a perimeter of 72 cm. If the breadth is decreased by 4 cm, how does that affect the perimeter?
Single Answer MCQ
Q-00140736
Q13
What is the perimeter of a rectangle that is 1 meter long and 1 meter wide?
Single Answer MCQ
Q-00140737
Q14
What is the perimeter of a square with a side length of 5 cm?
Single Answer MCQ
Q-00140769
Q15
If a rectangle has a length of 10 cm and a breadth of 4 cm, what is its perimeter?
Single Answer MCQ
Q-00140770
Q16
The sides of a triangle are 6 cm, 8 cm, and 10 cm. What is its perimeter?
Single Answer MCQ
Q-00140771
Q17
What is the formula to calculate the perimeter of a square?
Single Answer MCQ
Q-00140772
Q18
A rectangular garden measures 15 m by 10 m. How much fencing is needed to enclose it?
Single Answer MCQ
Q-00140773
Q19
If the length of one side of a square is 5 cm, what is its perimeter?
Single Answer MCQ
Q-00140774
Q20
What is the perimeter of a rectangle with length 12 cm and width 5 cm?
Single Answer MCQ
Q-00140775
Q21
A square has a perimeter of 28 cm. What is the length of one side?
Single Answer MCQ
Q-00140776
Q22
If the perimeter of a square is 36 cm, what is the length of one side?
Single Answer MCQ
Q-00140777
Q23
If a square's side length is doubled, how does the perimeter change?
Single Answer MCQ
Q-00140778
Q24
A triangle has sides measuring 3 cm, 4 cm, and 5 cm. What is its perimeter?
Single Answer MCQ
Q-00140779
Q25
Which of the following represents the perimeter of a square with a side length of x?
Single Answer MCQ
Q-00140780
Q26
What is the perimeter of a polygon with 5 equal sides, each measuring 7 cm?
Single Answer MCQ
Q-00140781
Q27
If two squares have side lengths of 3 cm and 5 cm, what is the difference in their perimeters?
Single Answer MCQ
Q-00140782
Q28
A rectangular field is 20 meters long and 15 meters wide. What is the perimeter?
Single Answer MCQ
Q-00140783
Q29
What would be the perimeter of a square if one side is represented by the expression (2a + 3) cm?
Single Answer MCQ
Q-00140784
Q30
A square has a perimeter of 48 cm. What is the area of the square?
Single Answer MCQ
Q-00140785
Q31
Debojeet has a square photo frame with a side measuring 2 m. How much tape does he need to cover the perimeter?
Single Answer MCQ
Q-00140786
Q32
The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its breadth?
Single Answer MCQ
Q-00140787
Q33
The perimeter of a square is 40 cm. What can you conclude about the side length?
Single Answer MCQ
Q-00140788
Q34
If the sides of a polygon are 4 cm, 5 cm, and 6 cm, what is the perimeter?
Single Answer MCQ
Q-00140789
Q35
If a square has a perimeter of 64 m, what is the length of each side?
Single Answer MCQ
Q-00140790
Q36
Which of the following has the smallest perimeter? A square of side 4 cm, a rectangle of 2 cm by 5 cm, a triangle with sides 3 cm, 4 cm, and 5 cm.
Single Answer MCQ
Q-00140791
Q37
Which square has the largest perimeter if square A has a side length of 3 cm, square B has a side length of 4 cm, and square C has a side length of 5 cm?
Single Answer MCQ
Q-00140792
Q38
What is the perimeter of a diamond shape with side lengths of 6 cm each?
Single Answer MCQ
Q-00140793
Q39
If 5 squares each with a side of 4 cm are lined up, what is the total perimeter?
Single Answer MCQ
Q-00140794
Q40
A park is in the shape of a rectangle measuring 50 m by 30 m. What is the perimeter of the park?
Single Answer MCQ
Q-00140795
Q41
A runner runs around a square track with each side measuring 100 m. How far does the runner complete in one lap?
Single Answer MCQ
Q-00140796
Q42
What is the formula for the perimeter of a rectangle?
Single Answer MCQ
Q-00140797
Q43
A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is its perimeter?
Single Answer MCQ
Q-00140798
Q44
If a square has a side length of 5 cm, what is its perimeter?
Single Answer MCQ
Q-00140799
Q45
How do you find the perimeter of a regular pentagon with each side measuring 4 cm?
Single Answer MCQ
Q-00140800
Q46
What is the perimeter of a rectangle with a length of 10 cm and a width of 4 cm?
Single Answer MCQ
Q-00140801
Q47
What is the perimeter of a triangle with sides measuring 8 cm, 5 cm, and 7 cm?
Single Answer MCQ
Q-00140802
Q48
If a hexagon has a perimeter of 36 cm, what is the length of one side?
Single Answer MCQ
Q-00140803
Q49
A rectangular garden measures 10 m in length and 6 m in width. What is its perimeter?
Single Answer MCQ
Q-00140804
Q50
A rectangle has a perimeter of 50 cm. If the length is twice the width, what is the width?
Single Answer MCQ
Q-00140805
Q51
If a rectangular track is 40 m long and 30 m wide, how far would a runner go after completing one lap?
Single Answer MCQ
Q-00140806
Q52
The perimeter of a square is 40 cm. What is the length of one side?
Single Answer MCQ
Q-00140807
Q53
Akshi wants to frame a photo that is 12 cm wide and 18 cm long. How much framing material does she need?
Single Answer MCQ
Q-00140808
Q54
Which of the following has a greater perimeter: a rectangle with length 8 cm and width 4 cm, or a triangle with sides 5 cm, 5 cm, and 6 cm?
Single Answer MCQ
Q-00140809
Q55
The length of a rectangular table is twice its width. If the width is 4 m, what is the perimeter of the table?
Single Answer MCQ
Q-00140810
Q56
How can the perimeter of a regular octagon be found if one side is 3 cm?
Single Answer MCQ
Q-00140811
Q57
A rectangular pool has a length of 15 m and width of 10 m. How much fencing is required to enclose it?
Single Answer MCQ
Q-00140812
Q58
If you fold a rectangular sheet of paper whose sides measure 8 cm x 12 cm, what will be the perimeter of the folded shape assuming you fold it into halves?
Single Answer MCQ
Q-00140813
Q59
Toshi jogs around a square park with each side measuring 50 m. How far does Toshi jog in one complete round?
Single Answer MCQ
Q-00140814
Q60
What would be the perimeter of a regular dodecagon, knowing that each side measures 2 cm?
Single Answer MCQ
Q-00140815
Q61
What is the area of a rectangular field that is 20 m long and 15 m wide?
Single Answer MCQ
Q-00140816
Q62
If the perimeter of a hexagon is 60 cm, what will be the length of one side assuming it's regular?
Single Answer MCQ
Q-00140817
Q63
If a rectangular room measures 5 m by 4 m, what is the area available for carpet?
Single Answer MCQ
Q-00140818
Q64
What is the area of a triangle with a base of 10 cm and a height of 5 cm?
Single Answer MCQ
Q-00140819
Q65
A farmer needs to fence a circular field with a radius of 14 m. What is the length of the fence needed?
Single Answer MCQ
Q-00140820
Q66
If one side of a square garden is increased from 5 m to 7 m, how does the area change?
Single Answer MCQ
Q-00140821
Q67
An artist wants to paint a rectangular mural that is 4 m high and 3 m wide. How much area will be painted?
Single Answer MCQ
Q-00140822
Q68
A rectangular plot of land measures 30 m by 40 m. What will be the area in square meters?
Single Answer MCQ
Q-00140823
Q69
What is the perimeter of a triangle with sides measuring 4 cm, 5 cm, and 7 cm?
Single Answer MCQ
Q-00140824
Q70
What is the formula for the perimeter of a rectangle?
Single Answer MCQ
Q-00140825
Q71
If a triangle has sides of length 10 cm, 6 cm, and 8 cm, what is its perimeter?
Single Answer MCQ
Q-00140826
Q72
If a square has a side length of 5 cm, what is its perimeter?
Single Answer MCQ
Q-00140827
Q73
Which of the following correctly describes the perimeter of a triangle?
Single Answer MCQ
Q-00140828
Q74
A triangle has sides measuring 6 cm, 8 cm, and 10 cm. What is its perimeter?
Single Answer MCQ
Q-00140829
Q75
A triangle's three sides are 9 cm, 12 cm, and 5 cm. How do you calculate its perimeter?
Single Answer MCQ
Q-00140830
Q76
Which of the following is true for the perimeter of a rectangle?
Single Answer MCQ
Q-00140831
Q77
If a triangle has one side of 15 cm and the other two sides each measure 7 cm, what is its perimeter?
Single Answer MCQ
Q-00140832
Q78
What is the perimeter of a square park with each side measuring 100 m?
Single Answer MCQ
Q-00140833
Q79
A triangle with sides measuring 13 cm, 16 cm, and 10 cm has a perimeter that is how much greater than 20 cm?
Single Answer MCQ
Q-00140834
Q80
A rectangle's length is 12 cm, and its perimeter is 50 cm. What is its breadth?
Single Answer MCQ
Q-00140835
Q81
If a triangle's perimeter is 36 cm and two of its sides are 12 cm and 14 cm, what is the length of the third side?
Single Answer MCQ
Q-00140836
Q82
The perimeter of a triangular garden is 30 m. If two sides are 10 m and 12 m, what is the length of the third side?
Single Answer MCQ
Q-00140837
Q83
Which set of side lengths cannot form a triangle if they have a perimeter of 30 cm?
Single Answer MCQ
Q-00140838
Q84
How does the perimeter of a circle differ from that of a polygon?
Single Answer MCQ
Q-00140839
Q85
A triangle has a perimeter of 48 cm. If two of its sides are equal, and the third side is 18 cm, what is the length of each of the equal sides?
Single Answer MCQ
Q-00140840
Q86
If a square has a perimeter of 36 cm, what is the length of one side?
Single Answer MCQ
Q-00140841
Q87
What is the perimeter of a triangle with one side measuring 24 cm and the other two sides each measuring 15 cm?
Single Answer MCQ
Q-00140842
Q88
What will be the perimeter of a rectangle that has a length of 15 m and a breadth of 5 m?
Single Answer MCQ
Q-00140843
Q89
How do you determine if a triangle is equilateral using its sides lengths?
Single Answer MCQ
Q-00140844
Q90
A rectangular field's length is 200 m, and the width is half of the length. What is the perimeter?
Single Answer MCQ
Q-00140845
Q91
If the perimeter of a triangle is 60 cm and one side is 20 cm, what is the maximum possible length of the other two sides?
Single Answer MCQ
Q-00140846
Q92
Which shape has equal length sides and requires the least material for a fixed perimeter?
Single Answer MCQ
Q-00140847
Q93
If a triangle has a perimeter of 90 cm and two sides are in the ratio 2:3, what are the sides?
Single Answer MCQ
Q-00140848
Q94
If the perimeter of a square is equal to 40 m, then what will be the total area of the square?
Single Answer MCQ
Q-00140849
Q95
A triangle has sides of 5 cm, 12 cm, and what must be the minimum value of the third side to form a triangle?
Single Answer MCQ
Q-00140850
Q96
If a rectangular tablecloth has a length of 4 m and a breadth of 3 m, what is the length of lace needed to cover it entirely?
Single Answer MCQ
Q-00140851
Q97
What does it mean if the perimeter of a triangle is 0 cm?
Single Answer MCQ
Q-00140852
Q98
What is the area of a triangle with a base of 10 cm and a height of 5 cm?
Single Answer MCQ
Q-00140868
Q99
A triangle has an area of 36 cm² and a base of 12 cm. What is the height of the triangle?
Single Answer MCQ
Q-00140869
Q100
What is the area of a triangle with vertices at (0, 0), (4, 0), and (4, 3)?
Single Answer MCQ
Q-00140870
Q101
If a triangle has an area of 48 cm² and a height of 8 cm, what is the length of the base?
Single Answer MCQ
Q-00140871
Q102
What is the area of an equilateral triangle with a side length of 6 cm?
Single Answer MCQ
Q-00140872
Q103
A triangle has sides of lengths 8 cm, 10 cm, and 12 cm. What is its semi-perimeter?
Single Answer MCQ
Q-00140873
Q104
What is the area of a right triangle with legs measuring 5 cm and 12 cm?
Single Answer MCQ
Q-00140874
Q105
If the base of a triangle is doubled and the height remains constant, how does the area change?
Single Answer MCQ
Q-00140875
Q106
What is the area of a triangle formed by the points (0, 0), (6, 0), and (3, 4)?
Single Answer MCQ
Q-00140876
Q107
What is the area of a triangle with a base of 9 cm and an angle of 60° between the base and height of 7 cm?
Single Answer MCQ
Q-00140877
Q108
A triangle has a perimeter of 36 cm. If two sides measure 10 cm and 12 cm, how long is the third side?
Single Answer MCQ
Q-00140878
Q109
If the sides of a triangle are increased by 50%, what happens to the area?
Single Answer MCQ
Q-00140879
Q110
A triangle has an area of 24 cm² and a base of 6 cm. What is the height?
Single Answer MCQ
Q-00140880
Q111
Determine the area of a triangle whose vertices are at (1, 3), (5, 11), and (9, 3).
Single Answer MCQ
Q-00140881
Perimeter and Area Practice Worksheets
Download and practice Perimeter and Area worksheets to improve problem-solving accuracy and speed for CBSE Class 6 Mathematics exams.
Perimeter and Area - Practice Worksheet
This worksheet covers essential long-answer questions to help you build confidence in Perimeter and Area from Ganita Prakash for Class 6 (Mathematics).
Practice
Questions
1
What is the perimeter of a rectangle and how can it be calculated? Give an example.
The perimeter of a rectangle is defined as the sum of the lengths of all four sides. It can also be calculated using the formula: Perimeter = 2 × (length + breadth). For example, consider a rectangle with a length of 10 cm and a breadth of 5 cm. The perimeter would be calculated as follows: P = 2 × (10 cm + 5 cm) = 2 × 15 cm = 30 cm.
2
Explain how to find the perimeter of a square and provide a simple example.
The perimeter of a square can be found by adding the lengths of all four equal sides. It can also be calculated using the formula: Perimeter = 4 × side length. For instance, if a square has a side length of 3 m, its perimeter would be P = 4 × 3 m = 12 m.
3
What is the procedure to calculate the perimeter of a triangle? Illustrate with an example.
To find the perimeter of a triangle, add the lengths of all three sides. The formula is Perimeter = side1 + side2 + side3. For example, if a triangle has sides of lengths 6 cm, 8 cm, and 10 cm, then its perimeter would be P = 6 cm + 8 cm + 10 cm = 24 cm.
4
Provide a real-life application scenario where calculating the perimeter is essential. Explain.
One common real-life application of calculating perimeter is fencing a garden. For example, if a rectangular garden measures 12 m by 5 m, the total length of fencing required is the perimeter. Using the formula, P = 2 × (length + breadth) = 2 × (12 m + 5 m) = 34 m, the gardener will need 34 m of fencing.
5
How can you find the perimeter of complex shapes, such as a composite figure made of rectangles? Provide an example.
To find the perimeter of complex shapes, break them down into simpler shapes like rectangles or squares, find the perimeter of each and sum them up. For example, consider a shape made of two rectangles; if one rectangle has dimensions 4 m by 3 m and the other 3 m by 2 m, calculate separately and sum up the unique outer lengths to find the overall perimeter.
6
What is the significance of knowing the perimeter in everyday life? Provide examples.
Knowing the perimeter is important in real life for tasks such as installing borders for gardens, creating paths, and using materials efficiently. For example, knowing the perimeter helps a homeowner decide on the amount of paint needed to edge around a yard or the length of trim required for a picture frame.
7
How is the perimeter of a rectangular tablecloth useful when decorating? Explain with a specific use case.
When decorating, knowing the perimeter of a rectangular tablecloth is useful for hanging decorations or placing lace. For instance, if the tablecloth measures 1.5 m by 0.75 m, you can calculate the perimeter as P = 2 × (1.5 + 0.75) = 4.5 m. This helps ensure the right amount of lace is purchased to outline the cloth effectively.
8
Illustrate how the concept of perimeter aids in planning sports activities in a track field.
In sports, knowing the perimeter of a track field is crucial for planning runs and training. For instance, a standard track is often circular or rectangular. If a rectangular track measures 100 m by 50 m, P = 2 × (100 + 50) = 300 m, informing athletes how far they will run in laps.
9
Can perimeter help in construction projects? Discuss with an example.
Yes, the perimeter is essential in construction, especially for foundations. For example, if a building's foundation is rectangular, measuring 20 m by 10 m, the perimeter helps calculate the amount of materials needed for the foundation walls, P = 2 × (20 + 10) = 60 m.
10
What is the relationship between perimeter and area in geometric shapes? Explain with a simple example.
The perimeter is related to the area of geometric shapes, as both are fundamental properties. For instance, while the rectangle's area gives you how much surface space is inside, the perimeter tells you the distance around it. A rectangle of length 5 m and breadth 3 m has an area of 15 m² (Area = length × breadth) and a perimeter of 16 m (P = 2 × (5 + 3)). This illustrates differing importance for various applications.
Perimeter and Area - Mastery Worksheet
This worksheet challenges you with deeper, multi-concept long-answer questions from Perimeter and Area to prepare for higher-weightage questions in Class 6.
Mastery
Questions
1
A rectangular garden has a length of 10 m and a breadth of 6 m. If a pathway of width 1 m surrounds the garden, calculate the perimeter of the entire area including the pathway. Provide a clear explanation of your reasoning.
First, calculate the dimensions of the area including the pathway: Length = 10 m + 2(1 m) = 12 m; Breadth = 6 m + 2(1 m) = 8 m. Then, calculate the perimeter: Perimeter = 2(length + breadth) = 2(12 m + 8 m) = 40 m.
2
If the perimeter of a rectangle is 50 cm and the length is 10 cm, what is the breadth? Additionally, if the length were doubled, what would be the new perimeter? Show your workings.
Perimeter = 2(length + breadth) → 50 = 2(10 cm + breadth) → breadth = 15 cm. If the length doubles: New length = 20 cm; New perimeter = 2(20 cm + 15 cm) = 70 cm.
3
A triangle has sides of lengths 7 cm, 8 cm, and 5 cm. Calculate the perimeter and find out how much longer the perimeter is compared to a square with a side of 6 cm.
Perimeter of triangle = 7 cm + 8 cm + 5 cm = 20 cm. Perimeter of square = 4 × 6 cm = 24 cm. The triangle's perimeter is 4 cm less than the square's perimeter.
4
A farmer wants to create a square fence around his 400 m² field. How long will each side of the fence be? Also, calculate the perimeter of the fence. Reflect on the relationship between area and perimeter.
Each side of the square = √400 = 20 m. Perimeter = 4 × 20 m = 80 m. Notice how increasing the area affects perimeter.
5
Two circles have radii of 3 m and 5 m respectively. Calculate the perimeter (circumference) of both circles and find how much longer the circumference of the larger circle is compared to the smaller one.
Circumference of Circle 1 = 2π × 3 m; Circumference of Circle 2 = 2π × 5 m. The difference = 10π m - 6π m = 4π m.
6
A rectangular swimming pool is 25 m long and 10 m wide. A walkway of width 2 m is created all around the pool. What is the perimeter of the pool and the walkway combined? Show your calculations.
New length = 25 m + 2(2 m) = 29 m; New width = 10 m + 2(2 m) = 14 m. Perimeter = 2(29 m + 14 m) = 86 m.
7
Calculate the cost to put a fence around a rectangular park with a length of 150 m and a width of 120 m if the cost of fencing is Rs.50 per meter. Determine the total cost.
Perimeter = 2(150 m + 120 m) = 540 m; Total cost = 540 m × Rs.50/m = Rs.27,000.
8
Compare the perimeters of a rectangle with a length of 30 cm and width of 20 cm, and a square whose area is equal to the area of the rectangle. Which shape has a larger perimeter? Explain your reasoning.
Rectangle perimeter = 2(30 cm + 20 cm) = 100 cm; Area = 30 cm × 20 cm = 600 cm². Side of square = √600 cm² ≈ 24.49 cm; Perimeter = 4 × 24.49 cm ≈ 97.96 cm. The rectangle has a larger perimeter.
9
A playground is in the shape of a trapezium with parallel sides 12 m and 20 m, and height 8 m. Calculate its area and the perimeter if the two non-parallel sides measure 10 m each. Relate the area to its dimensions.
Area = (1/2) × (12 m + 20 m) × 8 m = 128 m²; Perimeter = 12 m + 20 m + 10 m + 10 m = 52 m. Reflect on how the shape influences area and perimeter.
10
A rectangular room measures 5 m by 4 m. If all sides are extended by 2 m, calculate the new perimeter and area. How does this change affect the dimensions?
New length = 5 m + 2(2 m) = 9 m; New width = 4 m + 2(2 m) = 8 m. New perimeter = 2(9 m + 8 m) = 34 m; New area = 9 m × 8 m = 72 m². The dimensions were increased by extending both sides.
Perimeter and Area - Challenge Worksheet
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Perimeter and Area in Class 6.
Challenge
Questions
1
Evaluate how the concept of perimeter can be applied in urban planning, specifically in designing parks and recreational areas. What factors must be considered?
Consider physical space, costs, user needs, and environmental impact. Discuss how perimeter affects the overall design and accessibility.
2
A rectangular garden measures 10 m by 6 m. If a path of width 1 m is to be built inside the garden, calculate the new perimeter. Discuss the implications of such modifications.
New lengths and breadths will alter the original perimeter, leading to changes in functional space and design. Evaluate space usability.
3
Compare the perimeter of a square with a side of length 5 m with that of a triangle with sides measuring 4 m, 4 m, and 2 m. What insights can you draw about shape efficiency?
Assess the perimeters and their implications. Discuss area versus perimeter considerations regarding shape choices.
4
If a farmer wants to create a rectangular field for crops with a fixed perimeter of 100 m, which dimensions yield the maximum area? Analyze why this configuration is optimal.
Identify dimensions as 25 m by 25 m, linking perimeter to area. Discuss implications in agricultural planning.
5
Two rectangular fields have the same perimeter but different lengths and widths. Explore how these differences might affect the fields' utility and functionality.
Discuss how aspect ratios impact usability, sunlight exposure, and water drainage.
6
A rectangular swimming pool’s dimensions are 15 m by 10 m. If the goal is to increase the pool's area by 50%, what should be the new dimensions while retaining the rectangular shape? Discuss design considerations.
The new area will be 225 m², leading to dimensions such as 18 m by 12.5 m, considering perimeter effects on surrounding area.
7
Imagine you have a length of fencing material totaling 60 m. Design a perimeter using the material to create different shapes (rectangle, triangle). Discuss which shape maximizes enclosed area.
The rectangle with equal sides (a square) will yield the largest area of 225 m². Contrast this with triangular possibilities.
8
Evaluate the perimeter of a shape formed by connecting four points in different configurations (e.g., square vs. rectangle). How does the arrangement impact perimeter?
Analyze various configurations to find that perimeter can vary based on layout even if area remains constant.
9
A park in the center of a city has a perimeter of 200 m. If the park's layout is changed from a rectangle to a circle while maintaining the same perimeter, what benefits could arise?
A circular park may provide equitable access from the center, enhancing usability. Discuss aesthetic and functional improvements.
10
Find the implications of maintaining equal land access for two gardens with the same perimeter. Analyze how garden shape affects sunlight, water collection, and accessibility.
Even with the same perimeter, shapes may provide different characteristics. Discuss factors influencing garden growth and wellness.
Perimeter and Area Formula Sheet
Use this Class 6 Mathematics Perimeter and Area Formula Sheet for quick revision before school exams and CBSE exams. It brings together the important formulas, key concepts, and worked examples in one place so students can revise faster and download a printable PDF for offline study.
Important Formulas
1
Perimeter of a Rectangle: P = 2 × (l + b)
P is the perimeter, l is the length, and b is the breadth. This formula calculates the total distance around the rectangle. Remember: add both dimensions and double the result.
2
Perimeter of a Square: P = 4 × s
P is the perimeter, s is the length of one side. Since all sides are equal, multiply the side length by 4 to find the perimeter.
3
Perimeter of a Triangle: P = a + b + c
P is the perimeter, and a, b, and c are the lengths of the sides. Add the lengths of all three sides to find the perimeter.
4
Area of a Rectangle: A = l × b
A is the area, l is the length, and b is the breadth. Multiply the length by the breadth to find the area.
5
Area of a Square: A = s²
A is the area, and s is the length of one side. Square the side length to calculate the area.
6
Area of a Triangle: A = 1/2 × b × h
A is the area, b is the base, and h is the height. Multiply the base by the height and divide by 2 to find the area.
7
Circumference of a Circle: C = 2πr
C is the circumference, and r is the radius. This formula finds the distance around the circle; multiply the radius by 2 and π (approx. 3.14).
8
Area of a Circle: A = πr²
A is the area and r is the radius. Square the radius and multiply by π to find the area.
9
Total Distance for Multiple Rounds: D = n × P
D is the total distance, n is the number of rounds, and P is the perimeter of the shape. Multiply the perimeter by the number of rounds to calculate the total distance.
10
Cost of Fencing: C = P × rate
C is the total cost, P is the perimeter, and rate is the cost per meter. To find out how much it will cost to fence an area, multiply the perimeter by the rate.
Worked Examples
1
P = 2 × (l + b)
This equation expresses the perimeter of a rectangle in terms of its length and breadth. Useful for calculating fencing needs.
2
P = 4 × s
This formula calculates the perimeter of a square. When all sides are equal, this representation simplifies the calculation.
3
P = a + b + c
This formula shows how to calculate the perimeter of a triangle using the lengths of all three sides.
4
A = l × b
This equation defines how to find the area of a rectangle. Useful for determining the space covered by the rectangle.
5
A = s²
This equation shows how to compute the area of a square by squaring the length of one side.
6
A = 1/2 × b × h
This formula indicates how to calculate the area of a triangle using its base and height.
7
C = 2πr
This equation is used to find the circumference of a circle, linking radius to the total circular distance.
8
A = πr²
This equation enables the calculation of the area of a circle by squaring the radius and multiplying by π.
9
D = n × P
This formula represents how to find the total distance traveled when making multiple rounds of a shape.
10
C = P × rate
This equation calculates the total cost incurred for fencing based on the perimeter and cost per meter.
Explore More Perimeter and Area Resources
Explore more chapter resources to strengthen your understanding and prepare for exams.
Perimeter and Area Frequently Asked Questions
Dive into the fundamental concepts of perimeter and area with engaging explanations and examples. This chapter is designed to strengthen students' understanding of geometry in Class 6 Mathematics.
The perimeter of a closed figure is the total distance around its boundary. For any polygon, it is calculated by summing the lengths of all its sides. Understanding this concept is essential for solving various geometrical problems.
To calculate the perimeter of a rectangle, use the formula P = 2 × (length + breadth). For instance, if a rectangle has a length of 12 cm and a breadth of 8 cm, its perimeter is 40 cm, calculated as 2 × (12 cm + 8 cm).
The formula for the perimeter of a square is P = 4 × side length. Since all four sides of a square are equal, you simply multiply the length of one side by four. For example, if each side is 1 m, the perimeter is 4 m.
The perimeter of a triangle is found by adding the lengths of its three sides. For example, if a triangle has sides measuring 4 cm, 5 cm, and 7 cm, the perimeter is 16 cm, calculated as 4 cm + 5 cm + 7 cm.
The perimeter of a regular polygon can be calculated by multiplying the length of one side by the total number of sides. For example, for a hexagon with each side measuring 6 cm, the perimeter would be 6 cm × 6 = 36 cm.
The area of a rectangle is calculated using the formula A = length × breadth. For instance, a rectangle that is 12 cm long and 8 cm wide has an area of 96 cm², calculated as 12 cm × 8 cm.
The area of a square is calculated using the formula A = side². If the side of a square measures 1 m, then the area is 1 m × 1 m = 1 m².
The area of a triangle can be found using the formula A = 1/2 × base × height. For example, if a triangle has a base of 8 cm and a height of 5 cm, its area would be 20 cm².
Perimeter and area have numerous real-life applications, such as calculating the length of fencing for a yard, determining the amount of paint needed for a wall, or finding out how much carpet to buy for a room. Understanding these concepts assists in practical decision-making.
While perimeter measures the distance around a figure, area measures the space within it. Understanding both concepts is essential for solving problems efficiently, and they often complement each other in applications like landscaping or construction.
Understanding perimeter and area lays the groundwork for advanced geometry and practical applications in fields such as architecture, engineering, and environmental design. It enhances analytical skills and encourages problem-solving.
To find the cost of fencing a rectangular park, first calculate the perimeter using P = 2 × (length + breadth). Then, multiply the perimeter by the cost per meter of fencing. For example, if the length is 150 m, breadth is 120 m, and cost is Rs. 40 per meter, the total cost would be Rs. 10,800.
Students may struggle with remembering formulas or applying them correctly in complex shapes. They might also have difficulties visualizing the figures or making the correct calculations. Regular practice and real-world applications can help overcome these challenges.
Activities like measuring the perimeter of classroom objects, creating shapes with string and measuring the boundaries, or engaging in outdoor projects like garden layout planning can significantly enhance understanding of perimeter and area.
If you make a mistake in calculating perimeter, review each step starting from identifying the dimensions of the shape. Check if you've correctly added the lengths of all sides or applied the formula properly. Practice will help reduce mistakes.
To estimate the perimeter of irregular shapes, you can measure the distances along the edge with a string or a measuring tape and sum these lengths. Alternatively, you can break the shape into smaller polygons, calculate their perimeters, and add them together.
Common tools include rulers, measuring tapes, and grids. For more complex shapes, digital tools like geometry software can also help in calculating and visualizing perimeter and area.
Yes, units are crucial. When calculating perimeter, all lengths should be in the same unit before summing. For area, ensure to square the unit (e.g., cm² for square centimeters) for accurate results.
Regular practice is important. Aim to solve multiple problems weekly to reinforce your understanding. Utilize study guides, worksheets, or math games to keep the learning engaging.
Learning about regular polygons helps to understand symmetry and simplifies the process of calculating both perimeter and area, laying the foundation for geometry concepts encountered in higher grades.
Absolutely! Concepts of perimeter and area can be applied in subjects like physics (light patterns), art (design layouts), and environmental science (land use planning), demonstrating their interdisciplinary significance.
Grasping perimeter and area is foundational for more advanced topics in mathematics such as calculus, where concepts of distance and area develop into integration and coordinate geometry.
Perimeter and Area PDF Downloads
Download worksheets, revision guides, formula sheets, and the official textbook PDF for Perimeter and Area.
Perimeter and Area Official Textbook PDF
Download the official NCERT/CBSE textbook PDF for Class 6 Mathematics.
Official PDFEnglish EditionNCERT Source
Perimeter and Area Revision Guide
Use this one-page guide to revise the most important ideas from Perimeter and Area.
Best for1-page chapter recap
Perimeter and Area Formula Sheet
Download the Perimeter and Area formula sheet PDF with important formulas, worked examples, and quick revision support for exam preparation.
Best forImportant formulas for quick revision
Perimeter and Area Practice Worksheet
Solve basic and application-based questions from Perimeter and Area.
Best forCore practice set
Perimeter and Area Mastery Worksheet
Work through mixed Perimeter and Area questions to improve accuracy and speed.
Best forMixed difficulty set
Perimeter and Area Challenge Worksheet
Try harder Perimeter and Area questions that test deeper understanding.
Best forFor deeper problem solving
Perimeter and Area Question Bank
Download important questions and exam-style prompts from Perimeter and Area.
Best forPrintable question set
Perimeter and Area Flashcards
Revise key terms and definitions from Perimeter and Area with interactive flashcards. Quick recall practice for CBSE Class 6 Mathematics.
These flash cards cover important concepts from Perimeter and Area in Ganita Prakash for Class 6 (Mathematics).
Practice Perimeter and Area with Interactive Duels
Live Academic Duel
Master Perimeter and Area via Live Academic Duels
Challenge your classmates or test your individual retention on the core concepts of CBSE Class 6 Mathematics (Ganita Prakash). Compete in speed-recall question rounds matched explicitly to the latest syllabus milestones for Perimeter and Area.
CBSE-aligned questions
Instant speed-recall rounds
Quick, competitive practice on Perimeter and Area with zero setup.