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Mathematics Class 6 Chapter 25 Perimeter and Area of Plane Figures
Exercise 25 (A)
1. What do you
understand by a plane closed figure?
Solution:
Any geometrical
plane figure which is bounded by straight or curved lines in a plane is called
a plane closed figure
Following figures
is a plane closed figure
2. The interior of
a figure is called region of the figure. Is this statement true?
Solution:
The interior of the
figure along with its boundary is called region of the figure. Hence, the given
statement is true.
3. Find the
perimeter of each of the following closed figures:
Solution:
The perimeter of
the closed figures can be calculated as follows
Perimeter = Sum of
all the sides
Perimeter = AB + AC
+ CD + DG + GH + FH + EF + BE
= 15 + 5 + 10 + 25
+ 15 + 5 + 10 + 25
= 110 cm
Therefore, the
perimeter of the closed figure = 110 cm
(ii) The perimeter
of the closed figures can be calculated as follows
Perimeter = Sum of
all the sides
Perimeter = AB + AC
+ CD + DG + BF + EF + EH + GH
= 20 + 4 + 8 + 20 +
4 + 8 + 20 + 4
= 88 cm
Therefore, the
perimeter of the closed figure = 88 cm
4. Find the
perimeter of a rectangle whose:
(i) length = 40 cm
and breadth = 35 cm
(ii) length = 10 m
and breadth = 8 m
(iii) length = 8 m
and breadth = 80 cm
(iv) length = 3.6 m
and breadth = 2.4 m
Solution:
(i) Given
Length of the
rectangle = 40 cm
Breadth of the
rectangle = 35 cm
Hence, the
perimeter of the rectangle is calculated as follows
Perimeter = 2
(Length + Breadth)
Perimeter = 2 (40 cm
+ 35 cm)
= 2 × 75 cm
= 150 cm
= 150 / 100 m
We get,
= 1.5 m
Hence, the
perimeter of the rectangle = 1.5 m
(ii) Given
Length of the
rectangle = 10 m
Breadth of the
rectangle = 8 m
Hence, the
perimeter of the rectangle is calculated as follows:
Perimeter = 2
(Length + Breadth)
Perimeter = 2 (10 m
+ 8 m)
= 2 × 18 m
We get,
= 36 m
Hence, the
perimeter of the rectangle = 36 m
(iii) Given
Length of the
rectangle = 8 m
Breadth of the
rectangle = 80 cm
We know that,
100 cm = 1 metre
Hence, the breadth
can be converted into metre from centimetre as below
Breadth = 80 cm
= 80 / 100 m
We get,
= 0.8 m
Hence, the
perimeter of the rectangle is calculated as follows:
Perimeter = 2
(Length + Breadth)
Perimeter = 2 (8 m
+ 0.8 m)
= 2 × 8.8 m
We get,
= 17.6 m
Hence, the
perimeter of the rectangle = 17.6 m
(iv) Given
Length of the
rectangle = 3.6 m
Breadth of the
rectangle = 2.4 m
Hence, the
perimeter of the rectangle is calculated as follows:
Perimeter = 2
(Length + Breadth)
Perimeter = 2 (3.6
m + 2.4 m)
= 2 × 6 m
We get,
= 12 m
Hence, the
perimeter of the rectangle = 12 m
5. If P denotes
perimeter of a rectangle, l denotes its length and b denotes its breadth, find:
(i) l, if P = 38 cm
and b = 7 cm
(ii) b, if P = 3.2
m and l = 100 cm
(iii) P, if l = 2 m
and b = 75 cm
Solution:
(i) Given
P = 38 cm and b = 7
cm
Length of the
rectangle (l) can be calculated as below
Length (l) = P / 2
– b
= 38 / 2 – 7 cm
We get,
= 19 cm – 7 cm
= 12 cm
Hence, the length
of the rectangle = 12 cm
(ii) Given
P = 3.2 m and l =
100 cm
The breadth of the
rectangle (b) can be calculated as follows
Here, the length is
in centimetre. Hence, it can be converted into metre from centimetre as below
Length = 100 cm
= 100 / 100 m
Breadth (b) = P / 2
– 1
= 3.2 / 2 – 1 m
= 1.6 m – 1 m
We get,
= 0.6 m
Hence, the breadth
(b) of the rectangle = 0.6 m
(iii) Given
L = 2 m and b = 75
cm
The perimeter of
the rectangle can be calculated as below:
We know that,
100 cm = 1 m
Here, the breadth
is in centimetre. Hence, it can be converted into metre from centimetre as
below
Breadth = 75 cm
= 75 / 100 m
We get,
= 0.75 m
Perimeter = 2
(Length + Breadth)
Perimeter = 2 (2 m
+ 0.75 m)
= 2 × 2.75 m
We get,
= 5.5 m
Hence, the
perimeter of the rectangle = 5.5 m
6. Find the
perimeter of a square whose each side is 1.6 m.
Solution:
Given
Each side of a
square = 1.6 m
Hence, the
perimeter of a square can be calculated as follow:
Perimeter = 4 ×
side
= 4 × 1.6 m
We get,
= 6.4 m
Hence, the
perimeter of a square = 6.4 m
7. Find the side of
the square whose perimeter is 5 m.
Solution:
Given
The perimeter of
the square = 5 m
Hence, the side of
the square can be calculated as below
side = Perimeter /
4
= (5 / 4) m
We get,
= 1.25 m
Hence, the side of
the square = 1.25 m
8. A square field
has each side 70 m whereas a rectangular field has length = 50 m and breadth =
40 m. Which of the two fields has greater perimeter and by how much?
Solution:
Given
The side of square
field = 70 m
Length of a
rectangular field = 50 m
Breadth of a
rectangular field = 40 m
So,
The Perimeter of
the square field = 4 × side
= 4 × 70 m
We get,
= 280 m
The Perimeter of
the rectangular field = 2 (length + breadth)
= 2 (50 m + 40 m)
= 2 × 90 m
We get,
= 180 m
Therefore, the
perimeter of the square field is greater than the perimeter of rectangular
field by 280 m – 180 m = 100 m
9. A rectangular
field has length = 160 m and breadth = 120 m. Find:
(i) the perimeter
of the field
(ii) the length of
fence required to enclose the field
(iii) the cost of
fencing the field at the rate of 80 per metre
Solution:
(i) Given
Length of the
rectangular field = 160 m
Breadth of the
rectangular field = 120 m
Hence, the
perimeter of the rectangular field can be calculated as below:
Perimeter = 2
(Length + Breadth)
Perimeter = = 2
(160 m + 120 m)
= 2 × 280 m
We get,
= 560 m
Therefore, the
perimeter of the field = 560 m
(ii) The length of
fence required to enclose the field is equal to the perimeter of the
rectangular field. Therefore, the length of the fence is 560 m
(iii) Given
The cost of fencing
the field per metre = Rs 80
Hence, total cost
of fencing the field can be calculated as follows:
Total Cost = Length
of fence × Rate of fence
= 560 m × Rs 80 per
metre
We get,
= Rs 44, 800
Therefore, total
cost of fencing the field = Rs 44,800
10. Each side of a
square plot of land is 55 m. Find the cost of fencing the plot at the rate of
Rs 32 per metre.
Solution:
Given
Each side of a
square field = 55 m
Hence, the
perimeter of square field can be calculated as follows:
Perimeter = 4 ×
side
= 4 × 55 m
We get,
= 220 m
We know that, the
length of fence required to enclose the field is the perimeter of the square
field.
Therefore, the
length of fence = 220 m
Given
Cost of fence per
metre = Rs 32
Hence, total cost
of fencing the field can be calculated as follows:
Total cost of
fencing the field = Length of fence × Rate of fence
= 220 m × 32
We get,
= Rs 7040
Therefore, total
cost of fencing the field = Rs 7040
