NCERT Textbook: Perimeter and Area | Mathematics (Maths) Class 6 PDF Download

 Page 1


6.1  Perimeter
Do you remember what the perimeter of a closed plane figure is?  
Let us refresh our understanding! 
 The perimeter of any closed plane figure is the distance covered 
along its boundary when you go around it once. For a polygon, i.e., 
a closed plane figure 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 09-08-2024   17:09:45
Page 2


6.1  Perimeter
Do you remember what the perimeter of a closed plane figure is?  
Let us refresh our understanding! 
 The perimeter of any closed plane figure is the distance covered 
along its boundary when you go around it once. For a polygon, i.e., 
a closed plane figure 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 09-08-2024   17:09:45
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 find 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 09-08-2024   17:09:45
Page 3


6.1  Perimeter
Do you remember what the perimeter of a closed plane figure is?  
Let us refresh our understanding! 
 The perimeter of any closed plane figure is the distance covered 
along its boundary when you go around it once. For a polygon, i.e., 
a closed plane figure 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 09-08-2024   17:09:45
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 find 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 09-08-2024   17:09:45
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 09-08-2024   17:09:45
Page 4


6.1  Perimeter
Do you remember what the perimeter of a closed plane figure is?  
Let us refresh our understanding! 
 The perimeter of any closed plane figure is the distance covered 
along its boundary when you go around it once. For a polygon, i.e., 
a closed plane figure 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 09-08-2024   17:09:45
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 find 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 09-08-2024   17:09:45
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 09-08-2024   17:09:45
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 figure) with sides of equal 
length?
6.  A farmer has a rectangular field having length 230 m and breadth 
160 m. He wants to fence it with 3 rounds of rope as shown. What 
is the total length of rope needed?
Chapter 6_Perimeter and Area.indd   132 09-08-2024   17:09:45
Page 5


6.1  Perimeter
Do you remember what the perimeter of a closed plane figure is?  
Let us refresh our understanding! 
 The perimeter of any closed plane figure is the distance covered 
along its boundary when you go around it once. For a polygon, i.e., 
a closed plane figure 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 09-08-2024   17:09:45
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 find 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 09-08-2024   17:09:45
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 09-08-2024   17:09:45
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 figure) with sides of equal 
length?
6.  A farmer has a rectangular field having length 230 m and breadth 
160 m. He wants to fence it with 3 rounds of rope as shown. What 
is the total length of rope needed?
Chapter 6_Perimeter and Area.indd   132 09-08-2024   17:09:45
Perimeter and Area
133
Starting Point 
for Toshi
Akshi and Toshi start running along the rectangular 
tracks as shown in the figure. 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 finished 
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 09-08-2024   17:09:46