Area and its Perimeter
Q. What is area?
Ans:
Area
is the amount of space occupied by a figure or thing on a plane surface.
Q. What
is the unit used to measure area?
Ans:
Area
is measured by using the units like
Square
centimeter ( sq. cm ) , square meter ( sq. m ), Square Kilometer ( sq. km ),
square feet ( sq. ft ) etc.
Q. What
is perimeter?
Ans:
Perimeter
is the total length of the boundary of a figure.
Q. What
is the unit used to measure perimeter?
Ans:
Perimeter
is measured by using the units like cm, meter , kilometer etc.
Cover
with Stamps
This
stamp has an area of 4 square cm. Guess how many such stamps will cover this
big rectangle.
Solution:
Area
of the stamp is 4 sq. cm
Side
of the stamp is 2 cm
Check
your guess.
A ) Measure
the yellow rectangle. It is ………… cm long.
Ans:
14 cm
B ) How
many stamps can be placed along its length?
Ans:
14 ÷ 2 = 7 stamps
C ) How
wide is the rectangle? ……….. cm
Ans:
The rectangle is 8 cm wide.
D ) How
many stamps can be placed along its width?
Ans: 8
÷ 2 = 4 stamps
E ) How
many stamps are needed to cover the rectangle?
Ans:
Total stamps needed to cover the rectangle
= 7 X 4 = 28 stamps
G ) What
is the area of the rectangle? ……….. sq. cm
Ans:
Each
stamp has area = 4 sq. cm
The rectangle
contains 28 such stamps.
So
area of 28 stamps = 4 X 28 = 112 sq. cm
H ) What
is the perimeter of the rectangle? …….. cm
The
perimeter of the rectangle
= 14 + 14 + 8 + 8
= 44 cm
Practice
time
a ) Arbaz
plans to tile his kitchen floor with green square tiles. Each side of the tile
is 10 cm. His kitchen is 220 cm in length and 180 cm wide. How many tiles will
he need?
Solution:
|
Kitchen Floor |
Length
= 220 cm
Width
= 180 cm
Area
of the kitchen = Length X width
= 220 X 180
= 39600 sq.cm
|
Tile |
Length
of the tile = 10 cm
Area
of the tile = Side X side
= 10 X 10 = 100
sq.cm
Total
tiles required = 39600 ÷ 100
100 | 39600 | 396
300
_____________________
960
900
_____________________
600
600
_____________________
0
He
will need 396 tiles.
b ) The fencing of a square garden is 20 m in
length. How long is one side of the garden?
Solution:
|
Garden |
The fencing of a square garden = 20 m
Which means perimeter of the square garden = 20 m
Length of the side of the garden = 20 ÷
4 = 5 m
c) A
thin wire 20 cm long is formed into a rectangle. If the width of this rectangle
is 4 cm, what is its length?
Solution:
|
Thin wire formed into a rectangle |
Length of the thin wire = 20 cm
A thin wire formed into a rectangle. It means the
perimeter of the rectangle = 20 cm
Width of the rectangle = 4 cm
We know,
Length + Length + Breadth + Breadth = Perimeter of
a rectangle
= 2 X length + 2 X breadth = perimeter
When we do
Perimeter – 2 X breadth
We get , 2 X length
So 2 X length = 20- 2 X 4 = 20 – 8 = 12 cm
Then length = 12 ÷
2 = 6 cm
Hence
the length of the rectangle is 6 cm.
d ) A
square carrom board has a perimeter of 320 cm. How much is its area?
Solution:
Perimeter
of the square carrom board = 320 cm
Side
of the board = 320 ÷ 4 = 80 cm
Area
of the board = 80 X 80 = 6400 sq. cm
Hence
the area of the square carrom board is
6400 sq. cm.
e ) How
many tiles like the triangle given here will fit in the white design?
Area
of the design = …………… sq. cm
Solution:
In the
center there is a square.
This
square is the combination of two triangles.
There
are four triangles at the four corners.
Hence
total triangles = 4 + 2 = 6
Area of each triangle is half square cm.
As there are 6 triangles
So the area of the design = 3 square cm.
f ) Sanya , Aarushi, Manav and Kabir made greeting cards.
Complete the table for their cards.
|
Whose card |
Length |
Width |
Perimeter |
Area |
|
Sanya |
10 cm |
8 cm |
|
|
|
Manav |
11 cm |
|
44 cm |
|
|
Aarushi |
|
8 cm |
|
80 sq. cm |
|
Kabir |
|
|
40 cm |
100 sq. cm |
Solution
|
Whose card |
Length |
Width |
Perimeter |
Area |
|
Sanya |
10 cm |
8 cm |
2 X
10 + 2 X 8 = 20 + 16 = 36
cm |
10 X
8 = 80
sq. cm |
|
Manav |
11 cm |
44 –
22 = 22 Then
22÷2 = 11 cm |
44 cm |
11 X 11 = 121 sq. cm |
|
Aarushi |
80 ÷ 8 = 10 cm |
8 cm |
10 +
10 + 8 + 8 = 36 cm |
80 sq. cm |
|
Kabir |
40 ÷ 4 = 10 cm |
100 ÷ 10 = 10 cm |
40 cm |
100 sq. cm |
Practice Time
A ) Look at the table. If you were to write the area of each
of these which column would you choose? Make a (√
)
|
|
Square cm |
Square metre |
Square km |
|
Handkerchief |
|
|
|
|
Sari |
|
|
|
|
Page of your book |
|
|
|
|
School land |
|
|
|
|
Total land of a city |
|
|
|
|
Door of your classroom |
|
|
|
|
Chair seat |
|
|
|
|
Blackboard |
|
|
|
|
Indian flag |
|
|
|
|
Land over which a river flows |
|
|
|
Answer:
|
|
Square cm |
Square metre |
Square km |
|
Handkerchief |
√ |
|
|
|
Sari |
|
√ |
|
|
Page of your book |
√ |
|
|
|
School land |
|
√ |
|
|
Total land of a city |
|
|
√ |
|
Door of your classroom |
|
√ |
|
|
Chair seat |
√ |
|
|
|
Blackboard |
|
√ |
|
|
Indian flag |
|
√ |
|
|
Land over which a river flows |
|
|
√ |
B ) Draw a
square of 9 square cm. Write A on it. Write another square with double the
side. Write B on it.
|
B |
|
A 9 sq. cm |
Answer:
1. The
perimeter of square A is …………………. Cm
Ans:
Area of square A = 9 sq. cm
Side
of square A = 3 cm
Perimeter
of square A = 3 X 4 = 12 cm
2. The
side of square B is ………………….. cm.
Ans:
Side of square A = 3 cm
Side
of square B is double the side of square A
Side
of square B = 3 X 2 = 6 cm
3. The area
of square B is …………………. Sq. cm.
Ans:
Side of square B = 6 cm
Area of
square B = 6 X 6 = 36 sq. cm.
4. The
area of square B is …………… times the area of square A.
Ans:
Area
of square B = 36 sq. cm
Area
of square A = 9 sq. cm
No. of
times the area of square B than square A
= 36 ÷ 9 = 4 times.
5. The
perimeter of square B is ……………….. cm.
Ans:
Side of square B = 6 cm
Perimeter
of square B = 6 X 4 = 24 cm
6. The
perimeter of square B is ……………. times the perimeter of square A.
Ans:
Perimeter
of square A = 12 cm
Perimeter
of square B = 24 cm
No. of
times the perimeter of square B than square A
= 24 ÷ 12 = 2 times.
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