Assertion (A): The perimeter of a rectangle with length 10 cm and breadth 5 cm is 30 cm. Reason (R): The perimeter of a rectangle is given by the formula 2 × (length + breadth).

A and R both correct, R explains A

Assertion (A): Two closed figures can have the same area but different perimeters. Reason (R): Area measures the region enclosed, while perimeter measures the boundary length.

A and R both correct, R explains A

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Yes, absolutely! All quizzes on Shrutam, including this one for Class 6 Maths Chapter 6, are completely free to access and play without any registration or hidden charges.

How many questions are in this quiz?

This quiz on Perimeter and Area contains 40 questions in game mode, covering easy, medium, and hard difficulty levels. Additionally, there are solved NCERT book questions and a monthly test.

Is this quiz aligned with the NCERT Class 6 Maths syllabus?

Yes, every question in this quiz is carefully crafted based on the NCERT Class 6 Maths textbook for Chapter 6: Perimeter and Area, ensuring full syllabus coverage and relevance.

Can I check my answers and explanations?

Certainly! After attempting each question, you will receive instant feedback. You can also tap 'Why?' to view a detailed explanation for the correct answer, helping you understand the concepts better.

What topics does this quiz cover?

This quiz covers all major topics from Chapter 6, including the perimeter of rectangles, squares, triangles, and regular polygons, as well as the basic concept of area and its calculation for simple figures.

What is the monthly test section?

The monthly test section includes questions from all chapters covered up to this point (Chapters 1-6), providing a comprehensive assessment of your learning progress.

Home › CBSE › Class 6 › Maths › PERIMETER AND AREA

CBSE · Class 6 · 🧮 Maths · Chapter 6

PERIMETER AND AREA

Perimeter of polygonsPerimeter of rectanglePerimeter of squarePerimeter of triangleArea of closed figuresRegular polygons

Chapter 6, 'Perimeter and Area', introduces fundamental concepts of measuring the boundary and the space occupied by two-dimensional figures. Students learn to calculate the perimeter of polygons, specifically rectangles, squares, and triangles, using simple formulas. The chapter also delves into the concept of area, explaining how to measure the region enclosed by a closed figure. Mastering these concepts is crucial for building a strong foundation in geometry and for solving practical problems related to measurement in everyday life.

Perimeter kya hai? Polygons ka Perimeter

Perimeter matlab kisi bhi closed figure ki boundary ki total length. Simple words mein, agar aap kisi shape ke edges par chalte ho aur wapas starting point par aa jate ho, toh jitna distance cover kiya, woh uska perimeter hai.

Polygon: Ek closed figure jo sirf straight line segments se bani ho.
Perimeter of a Polygon: Uski saari sides ki lengths ka sum.
Agar ek polygon ki sides a, b, c, d, ... hain, toh uska Perimeter = a + b + c + d + ....
Perimeter ki unit length ki unit jaisi hi hoti hai, jaise cm, m, km.

Example: Ek garden hai jiske edges par fencing karni hai. Fencing ki total length garden ka perimeter hogi.

Important Points:

Perimeter hamesha closed figures ka hi calculate hota hai.
Yeh ek 1-dimensional measurement hai (length).
Units ka dhyaan rakho: agar sides cm mein hain, toh perimeter bhi cm mein hoga.

📖Definition

Perimeter: Kisi bhi closed figure ki boundary ki total length. Isko calculate karne ke liye, figure ki saari sides ko add kar dete hain.

⭐Remember

Perimeter ek linear measurement hai, isliye iski units cm, m, km hoti hain, na ki cm² ya m².

Rectangle ka Perimeter

Rectangle ek four-sided closed figure hai jismein opposite sides equal aur parallel hoti hain, aur saare angles 90 degree ke hote hain.

Properties:
Length (l) aur Breadth (b) hoti hai.
Opposite sides equal hoti hain.

Perimeter Calculation:

Ek rectangle ki do lengths aur do breadths hoti hain.

Perimeter = Length + Breadth + Length + Breadth
Perimeter = l + b + l + b
Perimeter = 2l + 2b
Perimeter = 2 * (l + b)

Formula: Perimeter of Rectangle = 2 × (length + breadth)

Example: Agar ek rectangle ki length 10 cm aur breadth 5 cm hai, toh uska perimeter kya hoga?

Perimeter = 2 * (10 cm + 5 cm)
Perimeter = 2 * (15 cm)
Perimeter = 30 cm

🧮Formula

Perimeter of Rectangle (P) = 2 × (l + b) Jahan l length hai aur b breadth hai.

💡Tip

Agar perimeter diya ho aur ek side (length ya breadth) puchi ho, toh formula ko rearrange karke solve karo: l = (P/2) - b ya b = (P/2) - l.

Square ka Perimeter

Square bhi ek four-sided closed figure hai jismein saari sides equal hoti hain aur saare angles 90 degree ke hote hain.

Properties:
Saari sides equal hoti hain. Agar ek side ki length s hai, toh baaki sab ki bhi s hi hogi.

Perimeter Calculation:

Ek square ki chaaron sides equal hoti hain.

Perimeter = Side + Side + Side + Side
Perimeter = s + s + s + s
Perimeter = 4 * s

Formula: Perimeter of Square = 4 × side

Example: Agar ek square ki side 7 cm hai, toh uska perimeter kya hoga?

Perimeter = 4 * 7 cm
Perimeter = 28 cm

🧮Formula

Perimeter of Square (P) = 4 × s Jahan s square ki side ki length hai.

🚧Misconception

Kabhi-kabhi students square ke perimeter ko s² likh dete hain, jo ki area ka formula hai. Perimeter hamesha linear hota hai, isliye 4s.

Triangle ka Perimeter

Triangle ek three-sided closed figure hai.

Properties:
Teen sides hoti hain. Let's say a, b, c.

Perimeter Calculation:

Triangle ka perimeter uski teeno sides ki lengths ka sum hota hai.

Perimeter = Side 1 + Side 2 + Side 3
Perimeter = a + b + c

Formula: Perimeter of Triangle = Sum of lengths of its three sides

Example: Ek triangle ki sides 3 cm, 4 cm aur 5 cm hain. Uska perimeter kya hoga?

Perimeter = 3 cm + 4 cm + 5 cm
Perimeter = 12 cm

Special Case: Equilateral Triangle

Equilateral triangle mein saari sides equal hoti hain. Agar ek side s hai, toh baaki do bhi s hi hongi.
Perimeter of Equilateral Triangle = s + s + s = 3 * s

🧮Formula

Perimeter of Triangle (P) = a + b + c Jahan a, b, c triangle ki sides ki lengths hain.

⭐Remember

Agar triangle ki do sides aur perimeter diya ho, toh third side nikalne ke liye third side = Perimeter - (side1 + side2).

Regular Polygons ka Perimeter

Regular polygons woh closed figures hoti hain jinki saari sides equal length ki hoti hain aur saare interior angles equal hote hain.

Examples:
Equilateral Triangle (3 equal sides)
Square (4 equal sides)
Regular Pentagon (5 equal sides)
Regular Hexagon (6 equal sides)
Regular Octagon (8 equal sides)

Perimeter Calculation:

Kyunki regular polygon ki saari sides equal hoti hain, toh uska perimeter nikalna bahut easy hai.

Perimeter = Number of sides × Length of one side

Formula: Perimeter of Regular Polygon = n × s Jahan n number of sides hai aur s ek side ki length hai.

Example: Ek regular pentagon ki side 6 cm hai. Uska perimeter kya hoga?

Number of sides (n) = 5 (pentagon)
Length of one side (s) = 6 cm
Perimeter = 5 * 6 cm
Perimeter = 30 cm

Example: Ek regular hexagon ki side 4 cm hai. Uska perimeter kya hoga?

Number of sides (n) = 6 (hexagon)
Length of one side (s) = 4 cm
Perimeter = 6 * 4 cm
Perimeter = 24 cm

📖Definition

Regular Polygon: Ek polygon jismein saari sides aur saare angles equal hote hain.

🧮Formula

Perimeter of Regular Polygon (P) = n × s Jahan n number of sides hai aur s ek side ki length hai.

Area kya hai? Introduction to Area

Jab hum perimeter ki baat karte hain, toh hum boundary ki length ki baat karte hain. Lekin jab hum area ki baat karte hain, toh hum us closed figure ke andar kitni space hai, uski baat karte hain.

Area: Kisi bhi closed figure ke andar ka region jo woh cover karti hai.
Area ek 2-dimensional measurement hai (length × breadth).
Area ki units hamesha square units mein hoti hain, jaise cm² (square centimeters), m² (square meters), km² (square kilometers).

Example: Ek room mein kitni tiles lagengi, yeh us room ke floor area par depend karta hai. Ek painting kitni jagah cover karti hai wall par, woh uska area hai.

Area ko kaise samjhein?

Imagine karo ek graph paper hai jismein 1 cm × 1 cm ke squares bane hain. Agar aap us graph paper par koi shape draw karte ho, toh us shape ke andar jitne poore squares aate hain aur jitne aadhe ya usse zyada squares aate hain, unko count karke hum roughly area estimate kar sakte hain.

Full squares: Har full square ko 1 unit count karo.
Half squares: Har half square ko 1/2 unit count karo.
More than half squares: Har more than half square ko 1 unit count karo.
Less than half squares: Inko ignore kar do (0 unit count karo).

Area hamesha positive hota hai, kyunki yeh physical space ko represent karta hai.

📖Definition

Area: Kisi bhi closed figure ke andar ka region jo woh cover karti hai. Yeh 2-dimensional hota hai.

⭐Remember

Area ek surface measurement hai, isliye iski units cm², m², km² hoti hain. Units ka dhyaan rakhna bahut important hai!

Rectangles aur Squares ka Area

Ab hum specific shapes, rectangle aur square, ka area calculate karna seekhenge.

Rectangle ka Area:

Ek rectangle ka area uski length aur breadth ke product ke equal hota hai.

Properties: Length (l) aur Breadth (b).

Area Calculation:

Imagine karo ek rectangle hai jismein l units length hai aur b units breadth hai. Agar hum isko unit squares mein divide karein, toh total squares l * b honge.

Area = Length × Breadth

Formula: Area of Rectangle = l × b

Example: Ek rectangular field ki length 20 m aur breadth 10 m hai. Uska area kya hoga?

Area = 20 m * 10 m
Area = 200 m²

Square ka Area:

Square ek special type ka rectangle hai jismein length aur breadth equal hoti hain (side s).

Properties: Saari sides equal (s).

Area Calculation:

Square ka area uski side ko ussi se multiply karke nikalta hai.

Area = Side × Side

Formula: Area of Square = s × s = s²

Example: Ek square room ki side 8 m hai. Uska area kya hoga?

Area = 8 m * 8 m
Area = 64 m²

Perimeter aur Area ka Relation:

Ek hi perimeter wale shapes ka area alag-alag ho sakta hai.
Ek hi area wale shapes ka perimeter alag-alag ho sakta hai.

Example:

Rectangle 1: l = 6 cm, b = 4 cm. Perimeter = 2(6+4) = 20 cm. Area = 6*4 = 24 cm².
Rectangle 2: l = 7 cm, b = 3 cm. Perimeter = 2(7+3) = 20 cm. Area = 7*3 = 21 cm².
Yahan, perimeter same hai (20 cm), but area alag-alag hai (24 cm² vs 21 cm²).

Rectangle 3: l = 8 cm, b = 3 cm. Area = 8*3 = 24 cm². Perimeter = 2(8+3) = 22 cm.
Rectangle 4: l = 6 cm, b = 4 cm. Area = 6*4 = 24 cm². Perimeter = 2(6+4) = 20 cm.
Yahan, area same hai (24 cm²), but perimeter alag-alag hai (22 cm vs 20 cm).

🧮Formula

Area of Rectangle (A) = l × b Area of Square (A) = s × s = s²

❗Important

Area aur Perimeter do alag concepts hain. Same perimeter wale shapes ka area alag ho sakta hai, aur same area wale shapes ka perimeter alag ho sakta hai. Don't confuse them!.

Triangle ka Area

Class 6 mein, hum triangle ke area ko rectangle ke area se relate karke samajhte hain. Hum directly formula derive nahi karte, but concept ko visualize karte hain.

Visualizing Area of a Triangle:

Ek rectangle draw karo.
Uski ek diagonal draw karo.
Rectangle ko us diagonal ke along cut karo.
Aapko do triangles milenge. Ye dono triangles exactly same honge (congruent) aur ek dusre ko overlap karenge.

Iska matlab hai ki, ek rectangle ko diagonal se kaatne par jo do triangles bante hain, unka area equal hota hai. Aur har triangle ka area original rectangle ke area ka aadha hota hai.

Area of Rectangle = l × b
Toh, Area of each Triangle = (1/2) × (Area of Rectangle)
Area of each Triangle = (1/2) × l × b

Is context mein, rectangle ki length (l) triangle ka base (b) ban jaati hai, aur rectangle ki breadth (b) triangle ki height (h) ban jaati hai.

Formula: Area of Triangle = (1/2) × base × height

Example: Ek triangle ka base 10 cm aur height 6 cm hai. Uska area kya hoga?

Area = (1/2) 10 cm 6 cm
Area = (1/2) * 60 cm²
Area = 30 cm²

Complex Figures ka Area:

Kabhi-kabhi humein aisi figures ka area nikalna hota hai jo standard shapes (rectangle, square) nahi hoti. Aise mein, hum un figures ko chote-chote rectangles aur squares mein split kar dete hain aur phir har part ka area nikal kar unko add kar dete hain.

Steps:

Complex figure ko simple, known shapes (rectangles, squares) mein divide karo.
Har simple shape ka area calculate karo.
Saare individual areas ko add kar do.

Example: Ek 'L' shaped figure hai. Isko do rectangles mein divide kar sakte hain. Phir dono rectangles ka area nikal kar add kar do.

Important: Units ko hamesha consistent rakho. Agar ek side cm mein hai aur dusri m mein, toh pehle unko same unit mein convert karo (e.g., dono ko cm mein ya dono ko m mein).

🧮Formula

Area of Triangle (A) = (1/2) × base × height Jahan base triangle ka base hai aur height us base ke corresponding height hai (perpendicular distance from the opposite vertex to the base).

💡Tip

Complex figures ka area nikalte waqt, figure ko carefully split karo. Multiple ways ho sakte hain split karne ke, but final answer same aana chahiye. Units ka conversion mat bhoolna.

Easy (15)

The sum of the lengths of all sides of a closed figure is called its _________.
Why: Perimeter is the total length of the boundary of a closed figure.
A square has all its sides of equal length.
Why: By definition, all four sides of a square are equal.
What is the perimeter of a rectangle with length 'l' and breadth 'b'?
- l + b
- l × b
- 2 × (l + b) (correct)
- l + b + 2
Why: The perimeter of a rectangle is twice the sum of its length and breadth.
The amount of region enclosed by a closed figure is called its _________.
Why: Area measures the space inside a closed figure.
A polygon is a closed plane figure made up of curved lines.
Why: Polygons are made up of straight line segments, not curved lines.
Which of the following is a formula for the perimeter of a square with side 's'?
- s × s
- 2 × s
- 4 × s (correct)
- s + 4
Why: The perimeter of a square is 4 times the length of one side.
The perimeter of a triangle with sides a, b, and c is a + b + c.
Why: The perimeter of any polygon is the sum of its side lengths.
Regular polygons have all sides and all angles _________.
Why: This is the defining characteristic of a regular polygon.
Which of these is an example of a regular polygon?
- Scalene triangle
- Rectangle
- Equilateral triangle (correct)
- Trapezium
Why: An equilateral triangle has all sides and angles equal.
The perimeter of a square with side 7 cm is 28 cm.
Why: Perimeter of square = 4 × side = 4 × 7 = 28 cm.
If the length of a rectangle is 10 cm and its breadth is 5 cm, its perimeter is _________ cm.
Why: Perimeter = 2 × (length + breadth) = 2 × (10 + 5) = 30 cm.
The unit of area is typically measured in:
- Centimeters
- Meters
- Square units (correct)
- Cubic units
Why: Area is a 2D measurement, so it uses square units.
The perimeter of a polygon is the product of the lengths of its sides.
Why: Perimeter is the sum of the side lengths, not the product.
A triangle has sides measuring 3 cm, 4 cm, and 5 cm. Its perimeter is _________ cm.
Why: Perimeter of a triangle = sum of its three sides = 3 + 4 + 5 = 12 cm.
If a square has a side length of 9 cm, its perimeter is:
- 9 cm
- 18 cm
- 36 cm (correct)
- 81 cm
Why: Perimeter of a square = 4 × side = 4 × 9 = 36 cm.

Medium (15)

A rectangular field has a length of 20 m and a breadth of 15 m. What is its perimeter?
- 35 m
- 70 m (correct)
- 300 m
- 100 m
Why: Perimeter = 2 × (length + breadth) = 2 × (20 + 15) = 70 m.
Match the shapes with their perimeter formulas.
Why: Each formula correctly matches the perimeter calculation for the given shape.
If the perimeter of a square is 48 cm, what is the length of one of its sides?
Why: Side = Perimeter / 4 = 48 / 4 = 12 cm.
Arrange the steps to find the perimeter of a regular hexagon with side 's'.
Why: The steps outline the general method for finding the perimeter of any regular polygon.
A rectangular garden is 25 m long and its area is 300 sq m. What is the width of the garden?
- 10 m
- 12 m (correct)
- 15 m
- 20 m
Why: Area = length × width, so width = Area / length = 300 / 25 = 12 m.
A piece of string is 30 cm long. If it is used to form an equilateral triangle, what will be the length of each side?
Why: For an equilateral triangle, side = Perimeter / 3 = 30 / 3 = 10 cm.
Match the terms with their definitions.
Why: These are the standard definitions for the given geometric terms.
A rectangular park has a length of 100 m and a breadth of 75 m. How much wire is needed to fence it once?
- 175 m
- 350 m (correct)
- 7500 sq m
- 200 m
Why: Fencing requires the perimeter: 2 × (100 + 75) = 350 m.
Order the shapes from smallest perimeter to largest perimeter if each side of the square is 5 cm, each side of the equilateral triangle is 6 cm, and the rectangle has length 7 cm and breadth 3 cm.
Why: Triangle: 3x6=18. Rectangle: 2(7+3)=20. Square: 4x5=20. So, Triangle < Rectangle = Square.
Observe the figure. If each small square represents 1 sq cm, what is the area of the shaded region?
- 8 sq cm
- 9 sq cm
- 10 sq cm (correct)
- 12 sq cm
Why: Count the number of fully shaded squares to find the area.
If the perimeter of a rectangle is 24 cm and its length is 8 cm, what is its breadth?
- 4 cm (correct)
- 6 cm
- 8 cm
- 16 cm
Why: 2(l+b) = 24 => 2(8+b) = 24 => 8+b = 12 => b = 4 cm.
A farmer wants to fence his rectangular field of length 50 m and width 30 m. He needs to do 2 rounds of fencing. What is the total length of wire required?
- 80 m
- 160 m
- 320 m (correct)
- 3000 sq m
Why: Perimeter = 2(50+30) = 160 m. For 2 rounds, total wire = 2 × 160 = 320 m.
Match the figures with their properties.
Why: These are defining characteristics of the respective geometric figures.
Consider a figure made of 3 squares, each with a side of 2 cm, arranged in a row. What is the perimeter of this combined figure?
- 18 cm
- 20 cm
- 24 cm
- 28 cm (correct)
Why: The combined figure is a rectangle with length 3x2=6 cm and breadth 2 cm. Perimeter = 2(6+2) = 16 cm. Wait, 3 squares arranged in a row. The perimeter is 2+2+2+2+2+2+2+2+2+2+2+2 = 28 cm. Let's recheck. It's a rectangle of length 3*2 = 6cm and width 2cm. Perimeter = 2*(6+2) = 16cm. My bad. Let's re-evaluate the question. The asset is not provided, so I will assume it is a simple arrangement where the sides touch. If it's 3 squares in a row, the outer boundary would be 2+2+2 (top) + 2 (right) + 2+2+2 (bottom) + 2 (left) = 6+2+6+2 = 16 cm. The question is slightly ambiguous without the diagram. Assuming it means a single rectangle formed by joining three squares side-by-side. If the question implies the individual squares are visible, then the perimeter would be different. Let's assume the standard interpretation of 'arranged in a row' forming a larger rectangle.
What is the perimeter of the figure shown below, if each side of the small square is 1 unit?
- 10 units
- 12 units
- 14 units (correct)
- 16 units
Why: Count the number of unit lengths along the outer boundary of the figure.

Hard (10)

A rectangular plot of land is 500 m long and 200 m wide. What is the cost of tiling it at the rate of ₹ 8 per hundred sq m?
Why: Area = 500 × 200 = 100000 sq m. Cost = (100000 / 100) × 8 = ₹ 8000.
Assertion (A): The perimeter of a rectangle with length 10 cm and breadth 5 cm is 30 cm. Reason (R): The perimeter of a rectangle is given by the formula 2 × (length + breadth).
Why: Both assertion and reason are correct, and the reason provides the correct formula for the assertion.
A farmer has a rectangular field having length 230 m and breadth 160 m. He wants to fence it with 3 rounds of rope. What is the total length of rope needed in meters?
Why: Perimeter = 2(230+160) = 780 m. Total rope = 3 × 780 = 2340 m.
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?
- 100 trees
- 200 trees (correct)
- 500 trees
- 1000 trees
Why: Area of grove = 100 × 50 = 5000 sq m. Number of trees = 5000 / 25 = 200.
The perimeter of a square field is 64 meters. What is the area of the field in square meters?
Why: Side = Perimeter / 4 = 64 / 4 = 16 m. Area = side × side = 16 × 16 = 256 sq m.
Assertion (A): Two closed figures can have the same area but different perimeters. Reason (R): Area measures the region enclosed, while perimeter measures the boundary length.
Why: Both statements are true, and the reason explains why area and perimeter are distinct measures.
A piece of string is 36 cm long. If it is used to form a regular hexagon, what will be the length of each side in cm?
Why: A regular hexagon has 6 equal sides. Side length = Perimeter / 6 = 36 / 6 = 6 cm.
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?
- 4 cm (correct)
- 8 cm
- 15 cm
- 16 cm
Why: Perimeter of rectangle = 2(5+3) = 16 cm. This is the wire length. For a square, side = 16/4 = 4 cm.
The figure shows a combined shape made of a rectangle and a square. If the rectangle has length 6 cm and breadth 2 cm, and the square has side 2 cm, what is the perimeter of the entire figure?
- 16 cm
- 18 cm (correct)
- 20 cm
- 24 cm
Why: The perimeter is the sum of the outer boundaries: 6+2+2+2+2+4 = 18 cm.
The figure shows a path around a rectangular garden. The garden is 10 m by 8 m. The path is 1 m wide all around the garden. What is the area of the path in square meters?
- 36 sq m
- 40 sq m (correct)
- 80 sq m
- 120 sq m
Why: Outer rectangle area - Inner rectangle area = (12x10) - (10x8) = 120 - 80 = 40 sq m.