NCERT Textbook - Perimeter and Area Class 7 Notes | EduRev

Mathematics (Maths) Class 7

Created by: Praveen Kumar

Class 7 : NCERT Textbook - Perimeter and Area Class 7 Notes | EduRev

 Page 1


PERIMETER AND AREA 205 205 205 205 205
11.1  INTRODUCTION
In Class VI, you have already learnt perimeters of plane figures and areas of squares and
rectangles. Perimeter is the distance around a closed figure while area is the part of plane or
region occupied by the closed figure.
In this class, you will learn about perimeters and areas of a few more plane figures.
11.2  SQUARES AND RECTANGLES
A yush and Deeksha made pictures. A yush made his picture on a rectangular sheet of length
60 cm and breadth 20 cm while Deeksha made hers on a rectangular sheet of length 40 cm
and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for framing, if the cost of framing is ` 3.00 per cm?
If the cost of lamination is ` 2.00 per cm
2
, who has to pay more for lamination?
For finding the cost of framing, we need to find perimeter and then multiply it by the rate
for framing. For finding the cost of lamination, we need to find area and then multiply it by the
rate for lamination.
What would you need to find, area or perimeter, to answer the following?
1. How much space does a blackboard occupy?
2. What is the length of a wire required to fence a rectangular flower bed?
3. What distance would you cover by taking two rounds of a triangular park?
4. How much plastic sheet do you need to cover a rectangular swimming pool?
Do you remember,
Perimeter of a regular polygon = number of sides × length of one side
Perimeter of a square = 4 × side
Chapter  11
Perimeter and
Area
TRY THESE
Page 2


PERIMETER AND AREA 205 205 205 205 205
11.1  INTRODUCTION
In Class VI, you have already learnt perimeters of plane figures and areas of squares and
rectangles. Perimeter is the distance around a closed figure while area is the part of plane or
region occupied by the closed figure.
In this class, you will learn about perimeters and areas of a few more plane figures.
11.2  SQUARES AND RECTANGLES
A yush and Deeksha made pictures. A yush made his picture on a rectangular sheet of length
60 cm and breadth 20 cm while Deeksha made hers on a rectangular sheet of length 40 cm
and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for framing, if the cost of framing is ` 3.00 per cm?
If the cost of lamination is ` 2.00 per cm
2
, who has to pay more for lamination?
For finding the cost of framing, we need to find perimeter and then multiply it by the rate
for framing. For finding the cost of lamination, we need to find area and then multiply it by the
rate for lamination.
What would you need to find, area or perimeter, to answer the following?
1. How much space does a blackboard occupy?
2. What is the length of a wire required to fence a rectangular flower bed?
3. What distance would you cover by taking two rounds of a triangular park?
4. How much plastic sheet do you need to cover a rectangular swimming pool?
Do you remember,
Perimeter of a regular polygon = number of sides × length of one side
Perimeter of a square = 4 × side
Chapter  11
Perimeter and
Area
TRY THESE
MATHEMATICS 206 206 206 206 206
Perimeter of a rectangle = 2 × (l + b)
Area of a rectangle = l × b, Area of a square = side × side
Tanya needed a square of side 4 cm for completing a collage. She had a
rectangular sheet of length 28 cm and breadth 21 cm (Fig 11. 1). She cuts off
a square of side 4 cm from the rectangular sheet. Her friend saw the remaining
sheet (Fig 11.2) and asked T anya, “Has the perimeter of the sheet  increased
or decreased now?”
Has the total length of side AD increased after cutting off the square?
Has the area increased or decreased?
Tanya cuts off one more square from the opposite side (Fig 11.3).
Will the perimeter of the remaining sheet increase further?
Will the area increase or decrease further?
So, what can we infer from this?
It is clear that the increase of perimeter need not lead to increase in area.
1. Experiment with several such shapes and cut-outs. Y ou might find it useful to draw
these shapes on squared sheets and compute their areas and perimeters.
Y ou have seen that increase in perimeter does not mean that area will also increase.
2. Give two examples where the area increases as the perimeter increases.
3. Give two examples where the area does not increase when perimeter increases.
EXAMPLE 1 A door-frame of dimensions 3 m × 2 m is fixed on the wall of dimension
10 m × 10 m. Find the total labour charges for painting the wall if the
labour charges for painting 1 m
2 
of the wall is ` 2.50.
SOLUTION Painting of the wall has to be done excluding the area of the door.
Area of the door = l × b
=3 × 2 m
2
  = 6 m
2
Area of wall including door = side × side = 10 m × 10 m = 100 m
2
Area of wall excluding door = (100 - 6) m
2
 = 94 m
2
Total labour charges for painting the wall = ` 2.50 × 94 = ` 235
EXAMPLE 2 The area of a rectangular sheet is 500 cm
2
. If the length of the sheet is
25 cm, what is its width? Also find the perimeter of the rectangular sheet.
SOLUTION Area of the rectangular sheet = 500 cm
2
Length (l) = 25 cm
Fig 11.2
B
A D
C
Fig 11.3
A
D
B C
Fig 11.1
TRY THESE
Fig 11. 4
Page 3


PERIMETER AND AREA 205 205 205 205 205
11.1  INTRODUCTION
In Class VI, you have already learnt perimeters of plane figures and areas of squares and
rectangles. Perimeter is the distance around a closed figure while area is the part of plane or
region occupied by the closed figure.
In this class, you will learn about perimeters and areas of a few more plane figures.
11.2  SQUARES AND RECTANGLES
A yush and Deeksha made pictures. A yush made his picture on a rectangular sheet of length
60 cm and breadth 20 cm while Deeksha made hers on a rectangular sheet of length 40 cm
and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for framing, if the cost of framing is ` 3.00 per cm?
If the cost of lamination is ` 2.00 per cm
2
, who has to pay more for lamination?
For finding the cost of framing, we need to find perimeter and then multiply it by the rate
for framing. For finding the cost of lamination, we need to find area and then multiply it by the
rate for lamination.
What would you need to find, area or perimeter, to answer the following?
1. How much space does a blackboard occupy?
2. What is the length of a wire required to fence a rectangular flower bed?
3. What distance would you cover by taking two rounds of a triangular park?
4. How much plastic sheet do you need to cover a rectangular swimming pool?
Do you remember,
Perimeter of a regular polygon = number of sides × length of one side
Perimeter of a square = 4 × side
Chapter  11
Perimeter and
Area
TRY THESE
MATHEMATICS 206 206 206 206 206
Perimeter of a rectangle = 2 × (l + b)
Area of a rectangle = l × b, Area of a square = side × side
Tanya needed a square of side 4 cm for completing a collage. She had a
rectangular sheet of length 28 cm and breadth 21 cm (Fig 11. 1). She cuts off
a square of side 4 cm from the rectangular sheet. Her friend saw the remaining
sheet (Fig 11.2) and asked T anya, “Has the perimeter of the sheet  increased
or decreased now?”
Has the total length of side AD increased after cutting off the square?
Has the area increased or decreased?
Tanya cuts off one more square from the opposite side (Fig 11.3).
Will the perimeter of the remaining sheet increase further?
Will the area increase or decrease further?
So, what can we infer from this?
It is clear that the increase of perimeter need not lead to increase in area.
1. Experiment with several such shapes and cut-outs. Y ou might find it useful to draw
these shapes on squared sheets and compute their areas and perimeters.
Y ou have seen that increase in perimeter does not mean that area will also increase.
2. Give two examples where the area increases as the perimeter increases.
3. Give two examples where the area does not increase when perimeter increases.
EXAMPLE 1 A door-frame of dimensions 3 m × 2 m is fixed on the wall of dimension
10 m × 10 m. Find the total labour charges for painting the wall if the
labour charges for painting 1 m
2 
of the wall is ` 2.50.
SOLUTION Painting of the wall has to be done excluding the area of the door.
Area of the door = l × b
=3 × 2 m
2
  = 6 m
2
Area of wall including door = side × side = 10 m × 10 m = 100 m
2
Area of wall excluding door = (100 - 6) m
2
 = 94 m
2
Total labour charges for painting the wall = ` 2.50 × 94 = ` 235
EXAMPLE 2 The area of a rectangular sheet is 500 cm
2
. If the length of the sheet is
25 cm, what is its width? Also find the perimeter of the rectangular sheet.
SOLUTION Area of the rectangular sheet = 500 cm
2
Length (l) = 25 cm
Fig 11.2
B
A D
C
Fig 11.3
A
D
B C
Fig 11.1
TRY THESE
Fig 11. 4
PERIMETER AND AREA 207 207 207 207 207
Area of the rectangle = l × b  (where  b = width of the sheet)
Therefore, width b =
Area
l
 = 
500
25
 = 20 cm
Perimeter of sheet = 2 × (l + b) = 2 × (25 + 20) cm = 90 cm
So, the width of the rectangular sheet is 20 cm and its perimeter is 90 cm.
EXAMPLE 3 Anu wants to fence the garden in front of her
house (Fig 11.5), on three sides with lengths
20 m, 12 m and 12 m. Find the cost of fencing
at the rate of ` 150 per metre.
SOLUTION The length of the fence required is the perimeter
of the garden (excluding one side) which is
equal to 20 m + 12 m + 12 m, i.e.,  44 m.
Cost of fencing = ` 150 × 44 = ` 6,600.
EXAMPLE 4 A wire is in the shape of a square of side 10 cm. If the wire is
rebent into a rectangle of length 12 cm, find its breadth. Which encloses
more area, the square or the rectangle?
SOLUTION Side of the square = 10 cm
Length of the wire = Perimeter of the square = 4 × side = 4 × 10 cm
= 40 cm
Length of the rectangle, l = 12 cm. Let b be the breadth of the rectangle.
Perimeter of rectangle = Length of wire = 40 cm
Perimeter of the rectangle = 2 (l + b)
Thus, 40 = 2 (12 + b)
or
40
2
 = 12 + b
Therefore, b =20 - 12 = 8 cm
The breadth of the rectangle is 8 cm.
Area of the square = (side)
2
= 10 cm × 10 cm = 100 cm
2
Area of the rectangle = l × b
= 12 cm × 8 cm = 96 cm
2
So, the square encloses more area even though its perimeter is the same as that of the rectangle.
EXAMPLE 5 The area of a square and a rectangle are equal. If the side of the square is
40 cm and the breadth of the rectangle is 25 cm, find the length of the
rectangle. Also, find the perimeter of the rectangle.
SOLUTION Area of square = (side)
2
= 40 cm × 40 cm = 1600 cm
2
Fig 11.5
Page 4


PERIMETER AND AREA 205 205 205 205 205
11.1  INTRODUCTION
In Class VI, you have already learnt perimeters of plane figures and areas of squares and
rectangles. Perimeter is the distance around a closed figure while area is the part of plane or
region occupied by the closed figure.
In this class, you will learn about perimeters and areas of a few more plane figures.
11.2  SQUARES AND RECTANGLES
A yush and Deeksha made pictures. A yush made his picture on a rectangular sheet of length
60 cm and breadth 20 cm while Deeksha made hers on a rectangular sheet of length 40 cm
and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for framing, if the cost of framing is ` 3.00 per cm?
If the cost of lamination is ` 2.00 per cm
2
, who has to pay more for lamination?
For finding the cost of framing, we need to find perimeter and then multiply it by the rate
for framing. For finding the cost of lamination, we need to find area and then multiply it by the
rate for lamination.
What would you need to find, area or perimeter, to answer the following?
1. How much space does a blackboard occupy?
2. What is the length of a wire required to fence a rectangular flower bed?
3. What distance would you cover by taking two rounds of a triangular park?
4. How much plastic sheet do you need to cover a rectangular swimming pool?
Do you remember,
Perimeter of a regular polygon = number of sides × length of one side
Perimeter of a square = 4 × side
Chapter  11
Perimeter and
Area
TRY THESE
MATHEMATICS 206 206 206 206 206
Perimeter of a rectangle = 2 × (l + b)
Area of a rectangle = l × b, Area of a square = side × side
Tanya needed a square of side 4 cm for completing a collage. She had a
rectangular sheet of length 28 cm and breadth 21 cm (Fig 11. 1). She cuts off
a square of side 4 cm from the rectangular sheet. Her friend saw the remaining
sheet (Fig 11.2) and asked T anya, “Has the perimeter of the sheet  increased
or decreased now?”
Has the total length of side AD increased after cutting off the square?
Has the area increased or decreased?
Tanya cuts off one more square from the opposite side (Fig 11.3).
Will the perimeter of the remaining sheet increase further?
Will the area increase or decrease further?
So, what can we infer from this?
It is clear that the increase of perimeter need not lead to increase in area.
1. Experiment with several such shapes and cut-outs. Y ou might find it useful to draw
these shapes on squared sheets and compute their areas and perimeters.
Y ou have seen that increase in perimeter does not mean that area will also increase.
2. Give two examples where the area increases as the perimeter increases.
3. Give two examples where the area does not increase when perimeter increases.
EXAMPLE 1 A door-frame of dimensions 3 m × 2 m is fixed on the wall of dimension
10 m × 10 m. Find the total labour charges for painting the wall if the
labour charges for painting 1 m
2 
of the wall is ` 2.50.
SOLUTION Painting of the wall has to be done excluding the area of the door.
Area of the door = l × b
=3 × 2 m
2
  = 6 m
2
Area of wall including door = side × side = 10 m × 10 m = 100 m
2
Area of wall excluding door = (100 - 6) m
2
 = 94 m
2
Total labour charges for painting the wall = ` 2.50 × 94 = ` 235
EXAMPLE 2 The area of a rectangular sheet is 500 cm
2
. If the length of the sheet is
25 cm, what is its width? Also find the perimeter of the rectangular sheet.
SOLUTION Area of the rectangular sheet = 500 cm
2
Length (l) = 25 cm
Fig 11.2
B
A D
C
Fig 11.3
A
D
B C
Fig 11.1
TRY THESE
Fig 11. 4
PERIMETER AND AREA 207 207 207 207 207
Area of the rectangle = l × b  (where  b = width of the sheet)
Therefore, width b =
Area
l
 = 
500
25
 = 20 cm
Perimeter of sheet = 2 × (l + b) = 2 × (25 + 20) cm = 90 cm
So, the width of the rectangular sheet is 20 cm and its perimeter is 90 cm.
EXAMPLE 3 Anu wants to fence the garden in front of her
house (Fig 11.5), on three sides with lengths
20 m, 12 m and 12 m. Find the cost of fencing
at the rate of ` 150 per metre.
SOLUTION The length of the fence required is the perimeter
of the garden (excluding one side) which is
equal to 20 m + 12 m + 12 m, i.e.,  44 m.
Cost of fencing = ` 150 × 44 = ` 6,600.
EXAMPLE 4 A wire is in the shape of a square of side 10 cm. If the wire is
rebent into a rectangle of length 12 cm, find its breadth. Which encloses
more area, the square or the rectangle?
SOLUTION Side of the square = 10 cm
Length of the wire = Perimeter of the square = 4 × side = 4 × 10 cm
= 40 cm
Length of the rectangle, l = 12 cm. Let b be the breadth of the rectangle.
Perimeter of rectangle = Length of wire = 40 cm
Perimeter of the rectangle = 2 (l + b)
Thus, 40 = 2 (12 + b)
or
40
2
 = 12 + b
Therefore, b =20 - 12 = 8 cm
The breadth of the rectangle is 8 cm.
Area of the square = (side)
2
= 10 cm × 10 cm = 100 cm
2
Area of the rectangle = l × b
= 12 cm × 8 cm = 96 cm
2
So, the square encloses more area even though its perimeter is the same as that of the rectangle.
EXAMPLE 5 The area of a square and a rectangle are equal. If the side of the square is
40 cm and the breadth of the rectangle is 25 cm, find the length of the
rectangle. Also, find the perimeter of the rectangle.
SOLUTION Area of square = (side)
2
= 40 cm × 40 cm = 1600 cm
2
Fig 11.5
MATHEMATICS 208 208 208 208 208
It is given that,
The area of the rectangle = The area of the square
Area of the rectangle = 1600 cm
2
, breadth of the rectangle = 25 cm.
Area of the rectangle = l × b
or 1600 = l × 25
or
1600
25
 = l or l = 64 cm
So, the length of rectangle is 64 cm.
Perimeter of the rectangle = 2 (l + b) = 2 (64 + 25) cm
= 2 × 89 cm = 178 cm
So, the perimeter of the rectangle is 178 cm even though its area is the same as that of
the square.
EXERCISE 11.1
1. The length and the breadth of a rectangular piece of land are 500 m and 300 m
respectively . Find
(i) its area (ii) the cost of the land, if 1 m
2
 of the land costs ` 10,000.
2. Find the area of a square park whose perimeter is 320 m.
3. Find the breadth of a rectangular plot of land, if its area is 440 m
2
 and the length is
22 m. Also find its perimeter.
4. The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth.
Also find the area.
5. The area of a square park is the same as of a rectangular park. If the side of the
square park is 60 m and the length of the rectangular park is 90 m, find the breadth of
the rectangular park.
6. A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the
same wire is rebent in the shape of a square, what will be the measure of each side.
Also find which shape encloses more area?
7. The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is
30 cm, find its length. Also find the area of the rectangle.
8. A door of length 2 m and breadth  1m is fitted in a wall. The length of the
wall is 4.5 m and the breadth is 3.6 m (Fig11.6). Find the cost of white
washing the wall, if the rate of white washing the wall is ` 20 per m
2
.
Fig 11.6
Page 5


PERIMETER AND AREA 205 205 205 205 205
11.1  INTRODUCTION
In Class VI, you have already learnt perimeters of plane figures and areas of squares and
rectangles. Perimeter is the distance around a closed figure while area is the part of plane or
region occupied by the closed figure.
In this class, you will learn about perimeters and areas of a few more plane figures.
11.2  SQUARES AND RECTANGLES
A yush and Deeksha made pictures. A yush made his picture on a rectangular sheet of length
60 cm and breadth 20 cm while Deeksha made hers on a rectangular sheet of length 40 cm
and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for framing, if the cost of framing is ` 3.00 per cm?
If the cost of lamination is ` 2.00 per cm
2
, who has to pay more for lamination?
For finding the cost of framing, we need to find perimeter and then multiply it by the rate
for framing. For finding the cost of lamination, we need to find area and then multiply it by the
rate for lamination.
What would you need to find, area or perimeter, to answer the following?
1. How much space does a blackboard occupy?
2. What is the length of a wire required to fence a rectangular flower bed?
3. What distance would you cover by taking two rounds of a triangular park?
4. How much plastic sheet do you need to cover a rectangular swimming pool?
Do you remember,
Perimeter of a regular polygon = number of sides × length of one side
Perimeter of a square = 4 × side
Chapter  11
Perimeter and
Area
TRY THESE
MATHEMATICS 206 206 206 206 206
Perimeter of a rectangle = 2 × (l + b)
Area of a rectangle = l × b, Area of a square = side × side
Tanya needed a square of side 4 cm for completing a collage. She had a
rectangular sheet of length 28 cm and breadth 21 cm (Fig 11. 1). She cuts off
a square of side 4 cm from the rectangular sheet. Her friend saw the remaining
sheet (Fig 11.2) and asked T anya, “Has the perimeter of the sheet  increased
or decreased now?”
Has the total length of side AD increased after cutting off the square?
Has the area increased or decreased?
Tanya cuts off one more square from the opposite side (Fig 11.3).
Will the perimeter of the remaining sheet increase further?
Will the area increase or decrease further?
So, what can we infer from this?
It is clear that the increase of perimeter need not lead to increase in area.
1. Experiment with several such shapes and cut-outs. Y ou might find it useful to draw
these shapes on squared sheets and compute their areas and perimeters.
Y ou have seen that increase in perimeter does not mean that area will also increase.
2. Give two examples where the area increases as the perimeter increases.
3. Give two examples where the area does not increase when perimeter increases.
EXAMPLE 1 A door-frame of dimensions 3 m × 2 m is fixed on the wall of dimension
10 m × 10 m. Find the total labour charges for painting the wall if the
labour charges for painting 1 m
2 
of the wall is ` 2.50.
SOLUTION Painting of the wall has to be done excluding the area of the door.
Area of the door = l × b
=3 × 2 m
2
  = 6 m
2
Area of wall including door = side × side = 10 m × 10 m = 100 m
2
Area of wall excluding door = (100 - 6) m
2
 = 94 m
2
Total labour charges for painting the wall = ` 2.50 × 94 = ` 235
EXAMPLE 2 The area of a rectangular sheet is 500 cm
2
. If the length of the sheet is
25 cm, what is its width? Also find the perimeter of the rectangular sheet.
SOLUTION Area of the rectangular sheet = 500 cm
2
Length (l) = 25 cm
Fig 11.2
B
A D
C
Fig 11.3
A
D
B C
Fig 11.1
TRY THESE
Fig 11. 4
PERIMETER AND AREA 207 207 207 207 207
Area of the rectangle = l × b  (where  b = width of the sheet)
Therefore, width b =
Area
l
 = 
500
25
 = 20 cm
Perimeter of sheet = 2 × (l + b) = 2 × (25 + 20) cm = 90 cm
So, the width of the rectangular sheet is 20 cm and its perimeter is 90 cm.
EXAMPLE 3 Anu wants to fence the garden in front of her
house (Fig 11.5), on three sides with lengths
20 m, 12 m and 12 m. Find the cost of fencing
at the rate of ` 150 per metre.
SOLUTION The length of the fence required is the perimeter
of the garden (excluding one side) which is
equal to 20 m + 12 m + 12 m, i.e.,  44 m.
Cost of fencing = ` 150 × 44 = ` 6,600.
EXAMPLE 4 A wire is in the shape of a square of side 10 cm. If the wire is
rebent into a rectangle of length 12 cm, find its breadth. Which encloses
more area, the square or the rectangle?
SOLUTION Side of the square = 10 cm
Length of the wire = Perimeter of the square = 4 × side = 4 × 10 cm
= 40 cm
Length of the rectangle, l = 12 cm. Let b be the breadth of the rectangle.
Perimeter of rectangle = Length of wire = 40 cm
Perimeter of the rectangle = 2 (l + b)
Thus, 40 = 2 (12 + b)
or
40
2
 = 12 + b
Therefore, b =20 - 12 = 8 cm
The breadth of the rectangle is 8 cm.
Area of the square = (side)
2
= 10 cm × 10 cm = 100 cm
2
Area of the rectangle = l × b
= 12 cm × 8 cm = 96 cm
2
So, the square encloses more area even though its perimeter is the same as that of the rectangle.
EXAMPLE 5 The area of a square and a rectangle are equal. If the side of the square is
40 cm and the breadth of the rectangle is 25 cm, find the length of the
rectangle. Also, find the perimeter of the rectangle.
SOLUTION Area of square = (side)
2
= 40 cm × 40 cm = 1600 cm
2
Fig 11.5
MATHEMATICS 208 208 208 208 208
It is given that,
The area of the rectangle = The area of the square
Area of the rectangle = 1600 cm
2
, breadth of the rectangle = 25 cm.
Area of the rectangle = l × b
or 1600 = l × 25
or
1600
25
 = l or l = 64 cm
So, the length of rectangle is 64 cm.
Perimeter of the rectangle = 2 (l + b) = 2 (64 + 25) cm
= 2 × 89 cm = 178 cm
So, the perimeter of the rectangle is 178 cm even though its area is the same as that of
the square.
EXERCISE 11.1
1. The length and the breadth of a rectangular piece of land are 500 m and 300 m
respectively . Find
(i) its area (ii) the cost of the land, if 1 m
2
 of the land costs ` 10,000.
2. Find the area of a square park whose perimeter is 320 m.
3. Find the breadth of a rectangular plot of land, if its area is 440 m
2
 and the length is
22 m. Also find its perimeter.
4. The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth.
Also find the area.
5. The area of a square park is the same as of a rectangular park. If the side of the
square park is 60 m and the length of the rectangular park is 90 m, find the breadth of
the rectangular park.
6. A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the
same wire is rebent in the shape of a square, what will be the measure of each side.
Also find which shape encloses more area?
7. The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is
30 cm, find its length. Also find the area of the rectangle.
8. A door of length 2 m and breadth  1m is fitted in a wall. The length of the
wall is 4.5 m and the breadth is 3.6 m (Fig11.6). Find the cost of white
washing the wall, if the rate of white washing the wall is ` 20 per m
2
.
Fig 11.6
PERIMETER AND AREA 209 209 209 209 209
11.2.1  Triangles as Parts of Rectangles
Take a rectangle of sides 8 cm and 5 cm. Cut the rectangle along its diagonal to get two
triangles (Fig 11.7).
Superpose one triangle on the other.
Are they exactly the same in size?
Can you say that both the triangles are equal in area?
Are the triangles congruent also?
What is the area of each of these triangles?
Y ou will find that sum of the areas of the two triangles is the same as the area of the
rectangle. Both the triangles are equal in area.
The area of each triangle =
1
2
(Area of the rectangle)
=
1
2
×× () lb
 = 
1
2
85 () ×
 =
40
2
20
2
= cm
Take a square of side 5 cm and divide it into 4 triangles as shown (Fig 11.8).
Are the four triangles equal in area?
Are they congruent to each other? (Superpose the triangles to check).
What is the area of each triangle?
The area of each triangle =
1
4
Area of the square ()
=
1
4
1
4
5
2
(() side) cm
22
=
 = 6.25 cm
2
11.2.2  Generalising for other Congruent Parts of Rectangles
A rectangle of length 6 cm and breadth 4 cm is divided into two
parts as shown in the Fig 11.9. Trace the rectangle on another paper
and cut off the rectangle along EF to divide it into two parts.
Superpose one part on the other, see if they match. (Y ou may
have to rotate them).
Are they congurent? The two parts are congruent to each other. So,
the area of one part is equal to the area of the other part.
Therefore, the area of each congruent part = 
1
2
(The area of the rectangle)
= 
1
2
64 ×× ()cm
2
 = 12 cm
2
Fig 11.7
Fig 11.8
Fig 11.9
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Viva Questions

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NCERT Textbook - Perimeter and Area Class 7 Notes | EduRev

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Objective type Questions

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shortcuts and tricks

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ppt

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mock tests for examination

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NCERT Textbook - Perimeter and Area Class 7 Notes | EduRev

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Extra Questions

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Summary

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