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Page 1
6.1 Perimeter
Do you remember what the perimeter of a closed plane ??gure is?
Let us refresh our understanding!
The perimeter of any closed plane ??gure is the distance covered
along its boundary when you go around it once. For a polygon, i.e.,
a closed plane ??gure made up of line segments, the perimeter is
simply the sum of the lengths of its all sides, i.e., the total distance
along its outer boundary.
The perimeter of a polygon = the sum of the lengths of its all sides.
Let us revise the formulas for the perimeter of rectangles, squares,
and triangles.
Perimeter of a rectangle
Consider a rectangle ABCD whose length and breadth are 12 cm and
8 cm, respectively. What is its perimeter?
Perimeter of the rectangle = Sum of the lengths of its four sides
= AB + BC + CD + DA
A 12 cm B
8 cm
D C
PERIMETER AND AREA
6
Chapter 6_Perimeter and Area.indd 129 13-08-2024 16:16:29
Reprint 2026-27
Page 2
6.1 Perimeter
Do you remember what the perimeter of a closed plane ??gure is?
Let us refresh our understanding!
The perimeter of any closed plane ??gure is the distance covered
along its boundary when you go around it once. For a polygon, i.e.,
a closed plane ??gure made up of line segments, the perimeter is
simply the sum of the lengths of its all sides, i.e., the total distance
along its outer boundary.
The perimeter of a polygon = the sum of the lengths of its all sides.
Let us revise the formulas for the perimeter of rectangles, squares,
and triangles.
Perimeter of a rectangle
Consider a rectangle ABCD whose length and breadth are 12 cm and
8 cm, respectively. What is its perimeter?
Perimeter of the rectangle = Sum of the lengths of its four sides
= AB + BC + CD + DA
A 12 cm B
8 cm
D C
PERIMETER AND AREA
6
Chapter 6_Perimeter and Area.indd 129 13-08-2024 16:16:29
Reprint 2026-27
Ganita Prakash | Grade 6
130
= AB + BC + AB + BC
= 2 × AB + 2 × BC
= 2 × (AB + BC)
= 2 × (12 cm + 8 cm)
= 2 × (20 cm)
= 40 cm.
From this example, we see that —
Perimeter of a rectangle = length + breadth + length + breadth.
Perimeter of a rectangle = 2 × (length + breadth).
The perimeter of a rectangle is twice the sum of its length and breadth.
Perimeter of a square
Debojeet wants to put coloured tape all around
a square photo frame of side 1m as shown.
What will be the length of the coloured tape
he requires? Since Debojeet wants to put the
coloured tape all around the square photo
frame, he needs to ??nd the perimeter of the
photo frame.
Thus, the length of the tape required =
perimeter of the square
= sum of the lengths of all four sides of the square
= 1 m + 1 m + 1 m + 1 m = 4 m.
Now, we know that all four sides of a square are equal in length.
Therefore, in place of adding the lengths of each side, we can simply
multiply the length of one side by 4.
Thus, the length of the tape required = 4 × 1 m = 4 m.
From this example, we see that
Perimeter of a square = 4 × length of a side.
The perimeter of a square is quadruple the length of its side.
Opposite sides of a
rectangle are always
equal. So, AB = CD and
AD = BC
1 m
Chapter 6_Perimeter and Area.indd 130 13-08-2024 16:16:29
Reprint 2026-27
Page 3
6.1 Perimeter
Do you remember what the perimeter of a closed plane ??gure is?
Let us refresh our understanding!
The perimeter of any closed plane ??gure is the distance covered
along its boundary when you go around it once. For a polygon, i.e.,
a closed plane ??gure made up of line segments, the perimeter is
simply the sum of the lengths of its all sides, i.e., the total distance
along its outer boundary.
The perimeter of a polygon = the sum of the lengths of its all sides.
Let us revise the formulas for the perimeter of rectangles, squares,
and triangles.
Perimeter of a rectangle
Consider a rectangle ABCD whose length and breadth are 12 cm and
8 cm, respectively. What is its perimeter?
Perimeter of the rectangle = Sum of the lengths of its four sides
= AB + BC + CD + DA
A 12 cm B
8 cm
D C
PERIMETER AND AREA
6
Chapter 6_Perimeter and Area.indd 129 13-08-2024 16:16:29
Reprint 2026-27
Ganita Prakash | Grade 6
130
= AB + BC + AB + BC
= 2 × AB + 2 × BC
= 2 × (AB + BC)
= 2 × (12 cm + 8 cm)
= 2 × (20 cm)
= 40 cm.
From this example, we see that —
Perimeter of a rectangle = length + breadth + length + breadth.
Perimeter of a rectangle = 2 × (length + breadth).
The perimeter of a rectangle is twice the sum of its length and breadth.
Perimeter of a square
Debojeet wants to put coloured tape all around
a square photo frame of side 1m as shown.
What will be the length of the coloured tape
he requires? Since Debojeet wants to put the
coloured tape all around the square photo
frame, he needs to ??nd the perimeter of the
photo frame.
Thus, the length of the tape required =
perimeter of the square
= sum of the lengths of all four sides of the square
= 1 m + 1 m + 1 m + 1 m = 4 m.
Now, we know that all four sides of a square are equal in length.
Therefore, in place of adding the lengths of each side, we can simply
multiply the length of one side by 4.
Thus, the length of the tape required = 4 × 1 m = 4 m.
From this example, we see that
Perimeter of a square = 4 × length of a side.
The perimeter of a square is quadruple the length of its side.
Opposite sides of a
rectangle are always
equal. So, AB = CD and
AD = BC
1 m
Chapter 6_Perimeter and Area.indd 130 13-08-2024 16:16:29
Reprint 2026-27
Perimeter and Area
131
Perimeter of a triangle
Consider a triangle having three given sides of
lengths 4 cm, 5 cm and 7 cm. Find its perimeter.
Perimeter of the triangle = 4 cm + 5 cm + 7 cm
= 16 cm.
Perimeter of a triangle = sum of the lengths of its three sides.
Example: Akshi wants to put lace all around a
rectangular tablecloth that is 3 m long and 2 m
wide. Find the length of the lace required.
Solution
Length of the rectangular table cover = 3 m.
Breadth of the rectangular table cover = 2 m.
Akshi wants to put lace all around the
tablecloth.
Therefore, the length of the lace required will be the perimeter of the
rectangular tablecloth.
Now, the perimeter of the rectangular tablecloth = 2 × (length + breadth)
= 2 × (3 m + 2 m)
= 2 × 5 m = 10 m.
Hence, the length of the lace required is 10 m.
Example: Find the distance travelled by Usha if she takes three rounds of
a square park of side 75 m.
Solution
Perimeter of the square park = 4 × length
of a side = 4 × 75 m = 300 m.
Distance covered by Usha in one
round = 300 m.
Therefore, the total distance travelled by
Usha in three rounds = 3 × 300 m = 900 m.
5 cm
4 cm
7 cm
Chapter 6_Perimeter and Area.indd 131 12-12-2024 11:04:16
Reprint 2026-27
Page 4
6.1 Perimeter
Do you remember what the perimeter of a closed plane ??gure is?
Let us refresh our understanding!
The perimeter of any closed plane ??gure is the distance covered
along its boundary when you go around it once. For a polygon, i.e.,
a closed plane ??gure made up of line segments, the perimeter is
simply the sum of the lengths of its all sides, i.e., the total distance
along its outer boundary.
The perimeter of a polygon = the sum of the lengths of its all sides.
Let us revise the formulas for the perimeter of rectangles, squares,
and triangles.
Perimeter of a rectangle
Consider a rectangle ABCD whose length and breadth are 12 cm and
8 cm, respectively. What is its perimeter?
Perimeter of the rectangle = Sum of the lengths of its four sides
= AB + BC + CD + DA
A 12 cm B
8 cm
D C
PERIMETER AND AREA
6
Chapter 6_Perimeter and Area.indd 129 13-08-2024 16:16:29
Reprint 2026-27
Ganita Prakash | Grade 6
130
= AB + BC + AB + BC
= 2 × AB + 2 × BC
= 2 × (AB + BC)
= 2 × (12 cm + 8 cm)
= 2 × (20 cm)
= 40 cm.
From this example, we see that —
Perimeter of a rectangle = length + breadth + length + breadth.
Perimeter of a rectangle = 2 × (length + breadth).
The perimeter of a rectangle is twice the sum of its length and breadth.
Perimeter of a square
Debojeet wants to put coloured tape all around
a square photo frame of side 1m as shown.
What will be the length of the coloured tape
he requires? Since Debojeet wants to put the
coloured tape all around the square photo
frame, he needs to ??nd the perimeter of the
photo frame.
Thus, the length of the tape required =
perimeter of the square
= sum of the lengths of all four sides of the square
= 1 m + 1 m + 1 m + 1 m = 4 m.
Now, we know that all four sides of a square are equal in length.
Therefore, in place of adding the lengths of each side, we can simply
multiply the length of one side by 4.
Thus, the length of the tape required = 4 × 1 m = 4 m.
From this example, we see that
Perimeter of a square = 4 × length of a side.
The perimeter of a square is quadruple the length of its side.
Opposite sides of a
rectangle are always
equal. So, AB = CD and
AD = BC
1 m
Chapter 6_Perimeter and Area.indd 130 13-08-2024 16:16:29
Reprint 2026-27
Perimeter and Area
131
Perimeter of a triangle
Consider a triangle having three given sides of
lengths 4 cm, 5 cm and 7 cm. Find its perimeter.
Perimeter of the triangle = 4 cm + 5 cm + 7 cm
= 16 cm.
Perimeter of a triangle = sum of the lengths of its three sides.
Example: Akshi wants to put lace all around a
rectangular tablecloth that is 3 m long and 2 m
wide. Find the length of the lace required.
Solution
Length of the rectangular table cover = 3 m.
Breadth of the rectangular table cover = 2 m.
Akshi wants to put lace all around the
tablecloth.
Therefore, the length of the lace required will be the perimeter of the
rectangular tablecloth.
Now, the perimeter of the rectangular tablecloth = 2 × (length + breadth)
= 2 × (3 m + 2 m)
= 2 × 5 m = 10 m.
Hence, the length of the lace required is 10 m.
Example: Find the distance travelled by Usha if she takes three rounds of
a square park of side 75 m.
Solution
Perimeter of the square park = 4 × length
of a side = 4 × 75 m = 300 m.
Distance covered by Usha in one
round = 300 m.
Therefore, the total distance travelled by
Usha in three rounds = 3 × 300 m = 900 m.
5 cm
4 cm
7 cm
Chapter 6_Perimeter and Area.indd 131 12-12-2024 11:04:16
Reprint 2026-27
Ganita Prakash | Grade 6
132
Figure it Out
1. Find the missing terms:
a. Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?.
b. Perimeter of a square = 20 cm; side of a length = ?.
c. Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?.
2. A rectangle having sidelengths 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?
3. Find the length of the third side of a triangle having a perimeter
of 55 cm and having two sides of length 20 cm and 14 cm,
respectively.
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?
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 ??gure) with sides of equal
length?
6. A farmer has a rectangular ??eld 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?
Chapter 6_Perimeter and Area.indd 132 13-08-2024 16:16:30
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Page 5
6.1 Perimeter
Do you remember what the perimeter of a closed plane ??gure is?
Let us refresh our understanding!
The perimeter of any closed plane ??gure is the distance covered
along its boundary when you go around it once. For a polygon, i.e.,
a closed plane ??gure made up of line segments, the perimeter is
simply the sum of the lengths of its all sides, i.e., the total distance
along its outer boundary.
The perimeter of a polygon = the sum of the lengths of its all sides.
Let us revise the formulas for the perimeter of rectangles, squares,
and triangles.
Perimeter of a rectangle
Consider a rectangle ABCD whose length and breadth are 12 cm and
8 cm, respectively. What is its perimeter?
Perimeter of the rectangle = Sum of the lengths of its four sides
= AB + BC + CD + DA
A 12 cm B
8 cm
D C
PERIMETER AND AREA
6
Chapter 6_Perimeter and Area.indd 129 13-08-2024 16:16:29
Reprint 2026-27
Ganita Prakash | Grade 6
130
= AB + BC + AB + BC
= 2 × AB + 2 × BC
= 2 × (AB + BC)
= 2 × (12 cm + 8 cm)
= 2 × (20 cm)
= 40 cm.
From this example, we see that —
Perimeter of a rectangle = length + breadth + length + breadth.
Perimeter of a rectangle = 2 × (length + breadth).
The perimeter of a rectangle is twice the sum of its length and breadth.
Perimeter of a square
Debojeet wants to put coloured tape all around
a square photo frame of side 1m as shown.
What will be the length of the coloured tape
he requires? Since Debojeet wants to put the
coloured tape all around the square photo
frame, he needs to ??nd the perimeter of the
photo frame.
Thus, the length of the tape required =
perimeter of the square
= sum of the lengths of all four sides of the square
= 1 m + 1 m + 1 m + 1 m = 4 m.
Now, we know that all four sides of a square are equal in length.
Therefore, in place of adding the lengths of each side, we can simply
multiply the length of one side by 4.
Thus, the length of the tape required = 4 × 1 m = 4 m.
From this example, we see that
Perimeter of a square = 4 × length of a side.
The perimeter of a square is quadruple the length of its side.
Opposite sides of a
rectangle are always
equal. So, AB = CD and
AD = BC
1 m
Chapter 6_Perimeter and Area.indd 130 13-08-2024 16:16:29
Reprint 2026-27
Perimeter and Area
131
Perimeter of a triangle
Consider a triangle having three given sides of
lengths 4 cm, 5 cm and 7 cm. Find its perimeter.
Perimeter of the triangle = 4 cm + 5 cm + 7 cm
= 16 cm.
Perimeter of a triangle = sum of the lengths of its three sides.
Example: Akshi wants to put lace all around a
rectangular tablecloth that is 3 m long and 2 m
wide. Find the length of the lace required.
Solution
Length of the rectangular table cover = 3 m.
Breadth of the rectangular table cover = 2 m.
Akshi wants to put lace all around the
tablecloth.
Therefore, the length of the lace required will be the perimeter of the
rectangular tablecloth.
Now, the perimeter of the rectangular tablecloth = 2 × (length + breadth)
= 2 × (3 m + 2 m)
= 2 × 5 m = 10 m.
Hence, the length of the lace required is 10 m.
Example: Find the distance travelled by Usha if she takes three rounds of
a square park of side 75 m.
Solution
Perimeter of the square park = 4 × length
of a side = 4 × 75 m = 300 m.
Distance covered by Usha in one
round = 300 m.
Therefore, the total distance travelled by
Usha in three rounds = 3 × 300 m = 900 m.
5 cm
4 cm
7 cm
Chapter 6_Perimeter and Area.indd 131 12-12-2024 11:04:16
Reprint 2026-27
Ganita Prakash | Grade 6
132
Figure it Out
1. Find the missing terms:
a. Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?.
b. Perimeter of a square = 20 cm; side of a length = ?.
c. Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?.
2. A rectangle having sidelengths 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?
3. Find the length of the third side of a triangle having a perimeter
of 55 cm and having two sides of length 20 cm and 14 cm,
respectively.
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?
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 ??gure) with sides of equal
length?
6. A farmer has a rectangular ??eld 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?
Chapter 6_Perimeter and Area.indd 132 13-08-2024 16:16:30
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Perimeter and Area
133
Starting Point
for Toshi
Akshi and Toshi start running along the rectangular
tracks as shown in the ??gure. Akshi runs along the
outer track and completes 5 rounds. Toshi runs along
the inner track and completes 7 rounds. Now, they
are wondering who ran more. Find out who ran the
longer distance.
Starting Point
for Akshi
60 m
70 m
30 m
40 m
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.
Figure it Out
1. Find out the total distance Akshi has covered in 5 rounds.
2. Find out the total distance Toshi has covered in 7 rounds. Who ran
a longer distance?
3. Think and mark the positions as directed—
a. Mark ‘A’ at the point where Akshi will be after she ran 250 m.
b. Mark ‘B’ at the point where Akshi will be after she ran 500 m.
c. Now, Akshi ran 1000 m. How many full rounds has she ??nished
running around her track? Mark her position as ‘C’.
d. Mark ‘X’ at the point where Toshi will be after she ran 250 m.
e. Mark ‘Y’ at the point where Toshi will be after she ran 500 m.
Matha Pachchi!
Chapter 6_Perimeter and Area.indd 133 13-08-2024 16:16:30
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Read MoreFAQs on NCERT Textbook: Perimeter and Area
| 1. What's the difference between perimeter and area, and why do both matter? |  |
Ans. Perimeter is the total distance around the outside edge of a shape, while area measures the space covered inside it. Perimeter uses linear units (cm, m), whereas area uses square units (cm², m²). Both are essential for real-world problems like fencing a garden (perimeter) versus painting a wall (area). Understanding this distinction prevents calculation errors in CBSE Class 6 Mathematics.
| 2. How do I calculate the perimeter of different shapes like rectangles and triangles? | |
Ans. Perimeter formulas vary by shape. For rectangles, add all four sides: 2(length + breadth). For triangles, sum all three sides. For squares, multiply one side by four. For irregular polygons, simply add every side length. Students often confuse which measurement to use; refer to flashcards and mind maps on EduRev to visualise these formulas clearly and practise applying them to different figures.
| 3. Why do rectangles and squares have different area formulas when they look similar? | |
Ans. Rectangles and squares actually use the same area formula: length × breadth. A square is simply a special rectangle where all sides are equal, so its formula becomes side × side or side². Both measure the number of square units inside the shape. The difference isn't in the formula but in how side lengths relate to each other in these figures.
| 4. Can two shapes have the same perimeter but different areas? | |
Ans. Yes, absolutely. Two shapes can share identical perimeter measurements yet possess completely different areas-this is a common source of student confusion. For example, a 3cm × 6cm rectangle and a 4cm × 5cm rectangle both have 18cm perimeter but different areas (18cm² versus 20cm²). This concept reinforces why perimeter and area are independent measurements in geometry.
| 5. What's the easiest way to remember area formulas for different shapes in CBSE exams? | |
Ans. Break shapes into familiar categories: rectangles (length × breadth), triangles (½ × base × height), and circles (π × radius²). Create mnemonics or visual associations for each. For Class 6, most questions involve rectangles, squares, and triangles. Use PPTs and detailed notes available on EduRev to see colour-coded diagrams showing how these formulas derive from basic concepts, making memorisation more effective than rote learning.
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