NCERT Solutions for Class 6 Maths Chapter 6 Perimeter and Area

NCERT Solutions for Class 6 Maths Chapter 6 Perimeter and Area provide step-by-step answers to the questions and activities in Ganita Prakash. This chapter explains how to find the perimeter and area of different shapes and how these measurements are used in situations such as fencing, flooring, gardening and planning spaces.

Nivedita Dar28 Sept, 2026

Students also learn to find the perimeter of rectangles, squares, triangles and regular polygons, calculate the area of rectangles and squares, estimate the area of irregular shapes using grids, and understand how area and perimeter can change independently.

This page includes Class 6 Perimeter and Area questions with answers, extra questions, worksheet-style practice and important formulas for revision.

Class 6 Maths Chapter 6 Perimeter and Area Questions and Answers

What is Perimeter?

The perimeter of a closed figure is the total distance around its boundary.

For example, if you walk once around a rectangular park, the distance you cover is the perimeter of the park.

For common shapes:

Perimeter of a rectangle = 2 × (length + breadth)

Perimeter of a square = 4 × side

Perimeter of an equilateral triangle = 3 × side

Perimeter of a regular polygon = number of sides × length of one side

Perimeter is measured in units such as cm, m and km.

6.1 Perimeter

Question 1. Find the missing terms.

(a) Perimeter of a rectangle = 14 cm, breadth = 2 cm. Find the length.

Solution:

Perimeter of a rectangle:

P = 2 × (length + breadth)

14 = 2 × (length + 2)

7 = length + 2

Length = 5 cm

Answer: 5 cm

(b) Perimeter of a square = 20 cm. Find the side.

Solution:

Perimeter of a square:

P = 4 × side

20 = 4 × side

Side = 20 ÷ 4

Side = 5 cm

Answer: 5 cm

(c) Perimeter of a rectangle = 12 m, length = 3 m. Find the breadth.

Solution:

12 = 2 × (3 + breadth)

6 = 3 + breadth

Breadth = 3 m

Answer: 3 m

Question 2. A rectangle with side lengths 5 cm and 3 cm is made using a piece of wire. The wire is straightened and then bent to form a square. What is the length of one side of the square?

Solution:

The length of the wire is equal to the perimeter of the rectangle.

Perimeter:

= 2 × (5 + 3)

= 2 × 8

= 16 cm

The same wire is used to form a square.

A square has four equal sides.

Side of square:

= 16 ÷ 4

= 4 cm

Answer: 4 cm

Question 3. Find the length of the third side of a triangle with a perimeter of 55 cm and two sides measuring 20 cm and 14 cm.

Solution:

Perimeter = Sum of all three sides

55 = 20 + 14 + third side

Third side = 55 - 34

= 21 cm

Answer: 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 metre?

Solution:

Perimeter of the park:

= 2 × (150 + 120)

= 2 × 270

= 540 m

Cost of fencing:

= 540 × ₹40

= ₹21,600

Answer: ₹21,600

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

A square has 4 equal sides.

Side = 36 ÷ 4

= 9 cm

Answer: 9 cm

(b) an equilateral triangle

An equilateral triangle has 3 equal sides.

Side = 36 ÷ 3

= 12 cm

Answer: 12 cm

(c) a regular hexagon

A regular hexagon has 6 equal sides.

Side = 36 ÷ 6

= 6 cm

Answer: 6 cm

Question 6. A farmer has a rectangular field 230 m long and 160 m wide. He wants to fence it with 3 rounds of rope. What is the total length of rope needed?

Solution:

Perimeter of the field:

= 2 × (230 + 160)

= 2 × 390

= 780 m

For 3 rounds:

= 780 × 3

= 2340 m

Answer: 2340 m of rope

Running Track Questions

Akshi runs on a rectangular track measuring 70 m × 40 m, while Toshi runs on another rectangular track measuring 60 m × 30 m.

Question 1. Find the total distance Akshi covers in 5 rounds.

Solution:

Perimeter of Akshi's track:

= 2 × (70 + 40)

= 220 m

Distance in 5 rounds:

= 5 × 220

= 1100 m

Answer: 1100 m

Question 2. Find the total distance Toshi covers in 7 rounds. Who ran the longer distance?

Solution:

Perimeter of Toshi's track:

= 2 × (60 + 30)

= 180 m

Distance in 7 rounds:

= 7 × 180

= 1260 m

Akshi covered 1100 m.

Toshi covered 1260 m.

Answer: Toshi ran the longer distance.

Question 3. Akshi runs 250 m. How far beyond one complete round is she?

Solution:

One round = 220 m

Remaining distance:

250 - 220 = 30 m

Answer: Akshi is 30 m beyond the starting point after completing one full round.

Question 4. Akshi runs 500 m. How far beyond two complete rounds is she?

Solution:

Two rounds:

2 × 220 = 440 m

Remaining:

500 - 440 = 60 m

Answer: 60 m beyond the starting point after two full rounds.

Question 5. Akshi runs 1000 m. How many complete rounds does she finish?

Solution:

1000 ÷ 220 = 4 complete rounds with 120 m remaining.

Answer: 4 complete rounds and 120 m more.

Question 6. Toshi runs 250 m. How far beyond one complete round is she?

Solution:

One round = 180 m

250 - 180 = 70 m

Answer: 70 m beyond the starting point.

Question 7. Toshi runs 500 m. How far beyond two complete rounds is she?

Solution:

Two rounds:

2 × 180 = 360 m

Remaining:

500 - 360 = 140 m

Answer: 140 m beyond the starting point.

Question 8. Toshi runs 1000 m. How many complete rounds does she finish?

Solution:

1000 ÷ 180 = 5 complete rounds with 100 m remaining.

Answer: 5 complete rounds and 100 m more.

Perimeter of a Regular Polygon

For a regular polygon, all sides have equal length.

Perimeter = Number of sides × Length of one side

Examples

Square

4 × side

Equilateral triangle

3 × side

Regular hexagon

6 × side

For example, a regular hexagon with each side measuring 10 cm has:

6 × 10 = 60 cm

perimeter.

6.2 Area

The area of a closed figure is the amount of surface enclosed by it.

Area is measured in square units, such as:

cm²
m²
km²

For a rectangle:

Area = length × breadth

For a square:

Area = side × side

Question 1. The area of a rectangular garden is 300 m² and its length is 25 m. Find its width.

Solution:

Area = length × breadth

300 = 25 × breadth

Breadth = 300 ÷ 25

= 12 m

Answer: 12 m

Question 2. Find the cost of tiling a rectangular plot 500 m long and 200 m wide if the cost is ₹8 per 100 m².

Solution:

Area of the plot:

= 500 × 200

= 100,000 m²

Number of 100 m² units:

= 100,000 ÷ 100

= 1000

Total cost:

= 1000 × ₹8

= ₹8,000

Answer: ₹8,000

Question 3. A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 m², what is the maximum number of trees that can be planted?

Solution:

Area of grove:

= 100 × 50

= 5000 m²

Area required by one tree = 25 m²

Number of trees:

= 5000 ÷ 25

= 200

Answer: 200 trees

Tangram and Area Questions

A tangram contains seven pieces that can be rearranged to form different shapes. The important idea is that rearranging the pieces does not change their total area.

Question 1. How many times bigger is Shape D compared with Shape C?

Answer:

Shape D has twice the area of Shape C.

So:

Area of D = 2 × Area of C

Question 2. What is the relationship between Shapes C, D and E?

Answer:

Shape D can be formed by combining Shapes C and E.

Therefore:

Area of D = Area of C + Area of E

Shapes C and E have equal areas, so Shape D has twice the area of either one.

Question 3. Which has more area, Shape D or Shape F?

Answer:

Shapes D and F have equal areas.

Answer: Their areas are the same.

Question 4. Which has more area, Shape F or Shape G?

Answer:

Shapes F and G have equal areas.

Answer: Their areas are the same.

Question 5. What is the area of Shape A compared with Shape G?

Answer:

Shape A has twice the area of Shape G.

Question 6. Find the area of the large square formed using all seven pieces in terms of the area of Shape C.

Solution:

Let the area of Shape C = x.

Then:

C = x
E = x
D = 2x
F = 2x
G = 2x
A = 4x
B = 4x

Total:

4x + 4x + x + 2x + x + 2x + 2x

= 16x

Therefore:

Area of the large square = 16 × area of Shape C

Question 7. If the seven tangram pieces are arranged to form a rectangle, what will be its area in terms of Shape C?

Answer:

Rearranging the pieces does not change the total area.

Therefore:

Area of rectangle = 16 × area of Shape C

Question 8. Are the perimeters of the square and rectangle formed using the seven pieces the same?

Answer:

No.

Although the two shapes have the same area, their perimeters can be different.

This shows an important idea from the chapter:

Two shapes can have the same area but different perimeters.

Estimating Area on a Grid

The area of an irregular shape can be estimated by placing it on squared paper.

The basic idea is:

Count complete squares.
Combine suitable parts of squares.
Ignore very small parts according to the estimation method used in the textbook.
Add the counted areas.

This helps estimate the area of shapes that do not have simple formulas.

For example, if a figure covers 7 complete squares and approximately 3 additional square units, its estimated area is about:

10 square units

Area of a Triangle

A triangle can be understood by comparing it with rectangles.

When a triangle and a suitable rectangle have the same base and height, the triangle occupies half the area of that rectangle.

Therefore:

Area of a triangle = ½ × base × height

For example, if:

Base = 8 cm
Height = 5 cm

Then:

Area = ½ × 8 × 5

= 20 cm²

Finding the Area of Composite Figures

Some figures cannot be measured using one simple formula.

In such questions, divide the figure into smaller rectangles and triangles.

Then:

Area of whole figure = Sum of the areas of its parts

This method is useful for irregular or composite shapes.

Area and Perimeter Can Behave Differently

One important idea in Chapter 6 is that area and perimeter are different measurements.

Two figures can have:

the same area but different perimeters
the same perimeter but different areas

For example, rectangles measuring 4 × 6 and 3 × 8 both have area 24 square units.

But their perimeters are:

4 × 6 rectangle:

2 × (4 + 6) = 20 units

3 × 8 rectangle:

2 × (3 + 8) = 22 units

So, the areas are equal but the perimeters are different.

Class 6 Perimeter and Area Questions With Answers

Question 1. A rectangle has length 12 cm and breadth 5 cm. Find its perimeter.

Answer:

2 × (12 + 5)

= 2 × 17

= 34 cm

Question 2. A square has a side of 9 cm. Find its perimeter.

Answer:

4 × 9 = 36 cm

Question 3. Find the area of a rectangle measuring 15 m × 8 m.

Answer:

15 × 8 = 120 m²

Question 4. Find the area of a square with side 12 cm.

Answer:

12 × 12 = 144 cm²

Question 5. A triangular garden has sides 8 m, 10 m and 12 m. Find its perimeter.

Answer:

8 + 10 + 12 = 30 m

Question 6. A rectangular floor is 10 m long and 6 m wide. Find its area.

Answer:

10 × 6 = 60 m²

Question 7. A square has a perimeter of 48 cm. Find its side.

Answer:

Side = 48 ÷ 4

= 12 cm

Question 8. A rectangle has a perimeter of 30 cm and length 10 cm. Find its breadth.

Answer:

30 = 2 × (10 + breadth)

15 = 10 + breadth

Breadth = 5 cm

Perimeter and Area Class 6 Extra Questions

These questions are useful for additional practice after completing the NCERT exercises.

Q1. A rectangular playground is 45 m long and 25 m wide. Find its perimeter.

Answer:

2 × (45 + 25)

= 140 m

Q2. Find the area of the playground in Question 1.

Answer:

45 × 25

= 1125 m²

Q3. A square has an area of 144 cm². Find its side.

Answer:

12 × 12 = 144

Therefore, side = 12 cm

Q4. Find the perimeter of this square.

Answer:

4 × 12 = 48 cm

Q5. A wire 60 cm long is bent into a regular hexagon. Find the length of each side.

Answer:

60 ÷ 6 = 10 cm

Q6. A rectangular garden has an area of 240 m² and a length of 20 m. Find its breadth.

Answer:

Breadth = 240 ÷ 20

= 12 m

Q7. A rectangle measures 18 cm × 7 cm. Find both its area and perimeter.

Answer:

Area:

18 × 7 = 126 cm²

Perimeter:

2 × (18 + 7) = 50 cm

Q8. Can two shapes have the same area but different perimeters?

Answer:
Yes.

For example:

4 × 6 rectangle:

Area = 24 square units
Perimeter = 20 units

3 × 8 rectangle:

Area = 24 square units
Perimeter = 22 units

The areas are the same but the perimeters are different.

Q9. Can two shapes have the same perimeter but different areas?

Answer:
Yes.

For example:

A square with side 5 units has:

Perimeter = 20 units
Area = 25 square units

A rectangle measuring 4 × 6 units has:

Perimeter = 20 units
Area = 24 square units

So the perimeters are the same but the areas are different.

Q10. A rectangular field is 80 m long and 50 m wide. Find the cost of fencing it at ₹25 per metre.

Answer:

Perimeter:

2 × (80 + 50)

= 260 m

Cost:

260 × ₹25

= ₹6,500

Perimeter and Area Class 6 Worksheet With Answers

Part A: Fill in the blanks

Perimeter is the total distance around a ________ figure.
Area is measured in ________ units.
Perimeter of a square = ________ × side.
Area of a rectangle = ________ × breadth.
A regular hexagon has ________ equal sides.

Answers

closed
square
4
length
6

Part B: Solve

1. Find the perimeter of a rectangle measuring 18 cm × 6 cm.

Answer:

2 × (18 + 6)

= 48 cm

2. Find the area of the same rectangle.

Answer:

18 × 6

= 108 cm²

3. Find the perimeter of a square with side 15 cm.

Answer:

4 × 15

= 60 cm

4. Find the area of a square with side 15 cm.

Answer:

15 × 15

= 225 cm²

5. A triangle has sides 7 cm, 9 cm and 12 cm. Find its perimeter.

Answer:

7 + 9 + 12

= 28 cm

6. A garden measures 30 m × 20 m. Find its area.

Answer:

30 × 20

= 600 m²

7. Find the missing side of a square whose perimeter is 64 cm.

Answer:

64 ÷ 4 = 16 cm

8. A rectangle has perimeter 50 cm and length 15 cm. Find its breadth.

Answer:

50 = 2 × (15 + breadth)

25 = 15 + breadth

Breadth = 10 cm

Perimeter and Area Worksheet: Multiple Choice Questions

1. The perimeter of a square with side 8 cm is:

a) 16 cm
b) 24 cm
c) 32 cm
d) 64 cm

Answer: c) 32 cm

2. The area of a rectangle measuring 9 cm × 7 cm is:

a) 16 cm²
b) 32 cm²
c) 63 cm²
d) 72 cm²

Answer: c) 63 cm²

3. Which unit is suitable for the area of a classroom floor?

a) cm
b) m
c) m²
d) km

Answer: c) m²

4. Which unit is suitable for the perimeter of a playground?

a) m
b) m²
c) cm²
d) km²

Answer: a) m

5. A regular hexagon has a side of 7 cm. Its perimeter is:

a) 14 cm
b) 21 cm
c) 35 cm
d) 42 cm

Answer: d) 42 cm

Important Formulas for Class 6 Perimeter and Area

Shape	Perimeter	Area
Rectangle	2 × (length + breadth)	length × breadth
Square	4 × side	side × side
Equilateral triangle	3 × side	Depends on base and height
Regular polygon	Number of sides × side	Depends on the shape

Triangle Area

Area = ½ × base × height

Regular Polygon

Perimeter = Number of sides × Length of one side

Perimeter and Area Class 6 Notes

Perimeter

Perimeter measures the boundary of a closed shape.

Think of:

fencing a field
putting a border around a picture
walking around a park
framing a rectangular board

These situations involve perimeter.

Area

Area measures the surface covered by a shape.

Think of:

tiling a floor
planting a field
carpeting a room
painting a surface

These situations involve area.

Remember the Units

Perimeter uses ordinary length units:

cm, m, km

Area uses square units:

cm², m², km²

A common mistake is writing cm² for perimeter or cm for area. Always check what the question is asking.

Also Read: NCERT Solutions for Class 6 Social Science Chapter 9 – Family and Community

Common Mistakes in Perimeter and Area

1. Confusing area and perimeter

Perimeter measures the boundary.

Area measures the enclosed surface.

2. Forgetting to multiply by 2 for a rectangle

The perimeter is:

2 × (length + breadth)

not simply length + breadth.

3. Using square units for perimeter

Perimeter is measured in units such as cm or m.

4. Using ordinary units for area

Area is measured in square units such as cm² or m².

5. Forgetting that a square has four equal sides

If the side is 7 cm:

Perimeter = 4 × 7 = 28 cm

6. Adding areas incorrectly

When a complex shape is divided into smaller shapes, calculate each area carefully and then add them.

Quick Revision: Perimeter and Area

Before a test, remember these points:

Perimeter means distance around a closed figure.
Area means the surface enclosed by a figure.
Rectangle perimeter = 2(l + b).
Square perimeter = 4 × side.
Rectangle area = l × b.
Square area = side × side.
Triangle area = ½ × base × height.
Regular polygon perimeter = number of sides × side.
Perimeter uses units such as cm and m.
Area uses square units such as cm² and m².
Two shapes can have the same area but different perimeters.
Two shapes can have the same perimeter but different areas.
Irregular areas can be estimated using grids or found by splitting the figure into simpler shapes.