NCERT Solutions Class 6 Mathematics Chapter 10 Mensuration have been provided below and is also available in Pdf for free download. The NCERT solutions for Class 6 Mathematics have been prepared as per the latest syllabus, NCERT books and examination pattern suggested in Class 6 by CBSE, NCERT and KVS. Questions given in NCERT book for Class 6 Mathematics are an important part of exams for Class 6 Mathematics and if answered properly can help you to get higher marks. Refer to more Chapter-wise answers for NCERT Class 6 Mathematics and also download more latest study material for all subjects. Chapter 10 Mensuration is an important topic in Class 6, please refer to answers provided below to help you score better in exams
Chapter 10 Mensuration Class 6 Mathematics NCERT Solutions
Class 6 Mathematics students should refer to the following NCERT questions with answers for Chapter 10 Mensuration in Class 6. These NCERT Solutions with answers for Class 6 Mathematics will come in exams and help you to score good marks
Chapter 10 Mensuration NCERT Solutions Class 6 Mathematics
Mensuration
Exercise: 10.1
Q.1) Find the perimeter of each of the following figures:
Sol.1) Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once.
Perimeter is the sum of the sides of the polygon
a) Perimeter = 4 + 2 + 1 + 5 = 12 cm
b) Perimeter = 35 + 23 + 35 + 40 = 133 cm
c) Perimeter = 15 + 15 + 15 + 15 = 60 cm
d) Perimeter = 4 + 4+ 4 + 4 + 4 = 20 cm
e) Perimeter = 1 + 4 + 0.5 + 2.5 + 2.5 + 0.5 + 4 = 15 cm
f) Perimeter = 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 = 52 cm
Q.2) The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?
Sol.2) As the lid of the box is sealed around with a tape, we need to find the perimeter of the rectangular box.
Length of the rectangular box = 40 ππ
Width of the box = 10 ππ
Perimeter of a rectangle = 2 (length + width)
So, length of tape required = perimeter of the rectangular box = 2 (40 + 10) = 2(50) = 100cm
Q.3) A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?
Sol.3) Length of the table-top = 2 π 25 ππ = 2 π + 0.25 π = 2.25 π
Width of the table-top = 1 π 50 ππ = 1 π + 0.50 π = 1.50 π
We know that, Perimeter = 2(length + width)
= 2(2.25 + 1.50) = 2(3.75) = 7.50π
Q.4) What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?
Sol.4) A frame is put around the photograph and hence to find the length of the wooden strip to frame we find the perimeter of the photograph.
Length of the photograph = 32 ππ
Width of the photograph = 21 ππ
Perimeter = 2(length + width)
= 2(32 + 21) = 2(53) = 106 ππ
Q.5) A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?
Sol.5) Length of the rectangular land = 0.7 ππ
Width of the land = 0.5 ππ
The rectangular land is to be fenced all around with wire. Hence, perimeter of the
rectangular land = length of the wire.
Perimeter = 2(length + width)
= 2(0.7 + 0.5) = 2(1.2) = 2.4 ππ
Each side is to be fenced with 4 rows of wires. Therefore, total length of the wire needed is 4 times the perimeter.
Total length of wire needed = 4(2.4) = 9.6 ππ
Q.6) Find the perimeter of each of the following shapes:
(a) A triangle of sides 3 cm, 4 cm and 5 cm.
(b) An equilateral triangle of side 9 cm.
(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.
Sol.6) a) Perimeter = 3 ππ + 4 ππ + 5 ππ = 12 ππ
b) An equilateral triangle is a triangle whose sides are equal.
Given, side of an equilateral triangle = 9 ππ
Perimeter = 9 ππ + 9 ππ + 9 ππ OR 3 Γ 9 = 27 ππ
c) An isosceles triangle is a triangle with two equal sides.
Given, equal sides = 8 cm and third side = 6 ππ
Perimeter = 8 ππ + 8 ππ + 6 ππ OR (2 Γ 8) + 6 ππ = 22 ππ
Q.7) Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
Sol.7) Perimeter of a triangle = 10 ππ + 14 ππ + 15 ππ
= 39 ππ
Q.8) Find the perimeter of a regular hexagon with each side measuring 8 m.
Sol.8) A regular hexagon has six sides which are equal.
Given the measure of a side of a hexagon = 8 π
Therefore, Perimeter of the hexagon = 6 Γ 8 = 48π
Q.9) Find the side of the square whose perimeter is 20 m.
Sol.9) Perimeter of a square = 4 Γ side of a square
Given Perimeter = 20 π
So, 20 π = 4 Γ π πππ
Side of the square = 20/4 = 5π
Q.10) The perimeter of a regular pentagon is 100 cm. How long is its each side?
Sol.10) A regular pentagon has five sides which are equal.
So, perimeter of a regular hexagon = 5 Γ side.
Given the perimeter of a regular hexagon = 100 ππ
So, 100 ππ = 5 Γ side
Side = 100/5 = 20 ππ
Q.11) A piece of string is 30 cm long. What will be the length of each side if the string is used to form :
(a) a square? (b) an equilateral triangle? (c) a regular hexagon?
Sol.11) a) The string is used to form a square and hence the length of the string is the perimeter of the shape formed.
So perimeter of the square formed = 30 ππ = The length of the string.
Perimeter of a square is 4 Γ side
So, 4 Γ side = 30 ππ
Side = 30/4 = 7.5 ππ
b) The string is used to form an equilateral triangle and hence the length of the string is the perimeter of the shape formed.
So perimeter of the equilateral triangle formed = 30 ππ Perimeter of an equilateral triangle is 3 Γ side. [An equilateral triangle has three equal sides]
So, 3 Γ side = 30 ππ
Side = 30/3 = 10 ππ
c) The string is used to form a regular hexagon and hence the length of the string is the perimeter of the shape formed.
So perimeter of the regular hexagon formed = 30 ππ
Perimeter of a regular hexagon is 6 Γ side. [A regular hexagon has six equal sides]
So, 6 Γ side = 30 ππ
Side = 30/6 = 5ππ
Q.12) Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm.
What is its third side?
Sol.12) Perimeter of the triangle = 36 ππ
Sides of the triangle = 12 ππ and 14 ππ
We know that the perimeter of a triangle = sum of all the sides.
That is, 36 ππ = 12 ππ + 14 ππ + third side
36 = 26 + third side
Third side = 36 β 26 = 10 ππ
Hence, the measure of the third side of the triangle is 10 ππ
Q.13) Find the cost of fencing a square park of side 250 π at the rate of π
π . 20 πππ πππ‘ππ
Sol.13) Side of the square = 250π
The square park is to be fenced all around and hence we need to find the perimeter of the park, i.e. length of fencing required = perimeter of the square.
Perimeter of a square = 4 Γ side
= 4 Γ 250 = 1000 π
So, Length of fencing required = 1000 π
Now, cost of fencing per meter = π
π . 20
So, cost of fencing 1000 π = 1000 Γ 20 = π
π . 20,000
Q.14) Find the cost of fencing a rectangular park of length 175 π and breadth 125 π at the rate of π
π . 12 πππ πππ‘ππ.
Sol.14) Length of the rectangular park is 175 π
Width of the rectangular park is 125 π
Perimeter of the park = 2(length + width)
= 2(175 + 125)
= 2(300) = 600 π
Cost of fencing per meter = π
π . 12
Cost of fencing the park is = 600 Γ 12 = π
π . 7200
Q.15) Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance?
Sol.15) Sweety and Bulbul run around the park and hence the distance covered by them is the perimeter of the park.
Sweety runs around a square park of side = 75π
Perimeter of the park = 4 Γ side
= 4 Γ 75 = 300 π
Bulbul runs around a rectangular park of length = 60 π and width 45 π
Perimeter of the rectangular park = 2(length + width) = 2(60 + 45) = 2(105) = 210 π
So, Distance covered by Sweety is 300 π and by Bulbul is 210 π.
Therefore, Bulbul covers lesser distance.
Q.16) What is the perimeter of each of the following figures? What do you infer from the answers?
Sol.16) a) Perimeter = 25 + 25 + 25 + 25 = 4 Γ 25 = 100 ππ
b) Perimeter = 20 + 30 + 20 + 30 = 2(20 + 30) = 2(50) = 100 ππ
c) Perimeter = 10 + 40 + 10 + 40 = 2(10 + 40) = 2(50) = 100 ππ
d) Perimeter = 30 + 30 + 40 = 100 ππ
Inference: The perimeters of the shapes are all equal.
Q.17) Avneet buys 9 square paving slabs, each with a side of Β½ m. He lays them in the form of a square.
(a) What is the perimeter of his arrangement (i)?
(b) Shari does not like his arrangement. She gets him to lay them out like a cross.
What is the perimeter of her arrangement [(ii)]?
(c) Which has greater perimeter?
(d) Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)
Sol.17) a) The side of each square is Β½ m and hence the length of the side of the square formed is 1/2 + 1/2 + 1/2 = 3/2 π
So, Perimeter of the square formed is 4(3/2) = 1/2 ππ
b) Shari arranges into cross form
So, the Perimeter of this shape = 1/2 + 1 + 1 + 1/2 + 1 + 1 + 1/2 + 1 + 1 + 1/2 + 1 + 1 = 10 π
c) It is apparent that Shariβs arrangement has a greater perimeter.
d) No, it cannot be arranged such that the perimeter of the image is greater than 10 ππ.'
Exercise: 10.2
Q.1) Find the areas of the following figures by counting square:
Sol.1) The area of one full square is taken as 1 π π. π’πππ‘.
If it is a centimetre square sheet, then area of one full square will be 1 π π. ππ.
Ignore portions of the area that are less than half a square.
If more than half of a square is in a region, just count it as one square.
If exactly half the square is counted, take its area as 1/2 π π. πππ‘ππ.
a) There are 9 full squares. So, Area of the shape = 9 π π. π’πππ‘π
b) There are 5 full squares and so the area of the shape is 5 π π. π’πππ‘π .
c) There are 2 full squares and 4 exactly half squares. So, Area of the shape
= 2 + 4 Γ 1/2 = 2 + 2 = 4 π π. π’πππ‘π .
d) There are 8 full squares and hence the area of the shape is 8 π π. π’πππ‘π .
e) There are 10 full squares and hence the area of the shape is 10 π π. π’πππ‘π .
f) There are 2 full squares and 4 exactly half squares. So, Area of the shape
= 2 + 4 Γ 1/2 = 2 + 2 = 4 π π. π’πππ‘π .
g) There are 4 full squares and 4 exactly half squares. So, Area of the shape
= 4 + 4 Γ 1/2 = 4 + 2 = 6 π π. π’πππ‘π .
h) There are 5 full squares and hence the area of the shape is 5 π π. π’πππ‘π .
i) There are 9 full squares and hence the area of the shape is 9 π π. π’πππ‘π .
j) There are 2 full squares and 4 exactly half squares. So, Area of the shape
= 2 + 4 Γ 1/2 = 2 + 2 = 4 π π. π’πππ‘π .
k) There are 4 full squares and 2 exactly half squares. So, Area of the shape
= 4 + 2 Γ 1/2
= 4 + 1 = 5 π π. π’πππ‘π .
l) Less than half filled squaresβ 4; Area estimate = 0
More than half filled squares β 3; Area estimate = 3 π π. π’πππ‘π
Half-filled squares β 2; Area estimate = 2 Γ 1/2 = 1 π π. π’πππ‘
Full squares β 2; area estimate = 2 π π. π’πππ‘π .
Area of the shape = 0 + 3 + 1 + 2 = 6 π π. π’πππ‘π
m) Less than half filled squares β 5; Area estimate = 0
More than half filled squares β 9; Area estimate = 9 π π. π’πππ‘π
Half-filled squares β 0; Area estimate = 0
Full squares β 5; area estimate = 5 π π. π’πππ‘π .
Total area of the shape is 9 + 5 = 14 π π. π’πππ‘π .
n) Less than half filled squares β 6; Area estimate = 0
More than half filled squares β 10; Area estimate = 10 π π. π’πππ‘π
Half-filled squares β 0; Area estimate = 0
Full squares β 8; area estimate = 8 π π. π’πππ‘π .
Total area of the shape is 10 + 8 = 18 sq. units.
Exercise: 10.3
Q.1) Find the areas of the rectangles whose sides are:
(a) 3 cm and 4 cm (b) 12 m and 21 m (c) 2 km and 3 km
(d) 2 m and 70 cm
Sol.1) Area of a rectangle = length Γ breadth
a) Length = 3 ππ; breadth = 4 ππ
Area = 3 Γ 4 = 12 π π. ππ
b) Length = 12 π; breadth = 21 π
Area = 12 Γ 21 = 252 π π. π
c) Length = 2 ππ; breadth = 3 ππ
Area = 2 Γ 3 = 6 π π. ππ
d) Length = 2 π; breadth = 70 ππ = 0.7 π
Area = 2 Γ 0.7 = 1.4 π π. π
Q.2) Find the areas of the squares whose sides are:
(a) 10 cm (b) 14 cm (c) 5 m
Sol.2) Area of a square = side Γ side
a) Side = 10 ππ
Area = 10 Γ 10 = 100 π π. ππ
b) Side = 14 ππ
Area = 14 Γ 14 = 196 π π. ππ
c) Side = 5 π
Area = 5 Γ 5 = 25 π π. π
Q.3) The length and breadth of three rectangles are as given below:
(a) 9 m and 6 m (b) 17 m and 3 m (c) 4 m and 14 m
Which one has the largest area and which one has the smallest?
Sol.3) a) Length = 9 π; breadth = 6 π
Area = 9 Γ 6 = 54 π π. π
b) Length = 17 π; breadth = 3 π
Area = 17 Γ 3 = 51 π π. π
c) Length = 4 π; breadth = 14 π
Area = 4 Γ 14 = 56 π π. π
c) has the largest area and b) has the smallest area
Q.4) The area of a rectangular garden 50 π long is 300 π π. π. find the width of the garden.
Sol.4) Length of the rectangular garden is 50 π
Area = 300 π π. π
Area of a rectangle = length Γ breadth
i.e., 300 = 50 Γ ππππππ‘β
Breadth (300/50)π = 6 π
So, breadth (width) of the garden is 6 π.
Q.5) What is the cost of tiling a rectangular plot of land 500 π long and 200 π wide at the rate of π
π 8 πππ βπ’πππππ π π. π ?
Sol.5) To tile a rectangular plot, we need to find the area of the plot.
Given length of the plot = 500 π
Width of the plot = 200 π
So, area of the plot = 500 Γ 200 = 1,00,000 π π. π
The cost of tiling 100 π π. π = π
π 8.
So, the cost of tiling 1,00,000 π π. π is 8 Γ 1,00,000/100 = π
π . 8,000
Q.6) A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?
Sol.6) Length of the table-top = 2 π
Width of the table-top = 1 π 50 ππ = 1.50 π
So, area of the table-top = length Γ breadth
= 2 Γ 1.50 = 3 π π. π
Q.7) A room is 4 π long and 3 π 50 ππ wide. How many square metres of carpet are needed to cover the floor of the room?
Sol.7) Length of the room is 4 π
Width of the room is 3 π 50 ππ = 3.50 π
To carpet the room, we need to find the area of the floor.
So, Area of the room = length Γ breadth = 4 Γ 3.50 = 14 π π. π
Therefore, 14 π π. πππ‘πππ of carpet is needed to cover the floor of the room.
Q.8) A floor is 5 π long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.
Sol.8) Given Length of the floor = 5 π
Width of the floor = 4 π
A square carpet is laid on the floor as shown below.
We need to find the area of the shaded portion.
Area of the square carpet = 3 Γ 3 = 9 π π. π
So, 9 π π. π of the floor is covered with carpet.
Total area of the floor = 5 Γ 4 = 20 π π. π
So, area of the floor that is not carpeted = 20 β 9 = 11 π π. π
Q.9) Five square flower beds each of sides 1 m are dug on a piece of land 5 m long and 4 m wide. What is the area of the remaining part of the land?
Sol.9) Area of the piece of land = 5 Γ 4 = 20 π π. π
Area of each flower bed = 1 Γ 1 = 1 π π. π
Five square beds are dug on the land.
So, area of five such flower beds = 5 π π. π
So, area of the remaining part of the land is the shaded portion shown above.
Area of the remaining part = Area of the piece of land β area of the 5 flower beds.
= 20 β 5 = 15 π π. π
Q.10) By splitting the following figures into rectangles, find their areas. (The measures are given in centimetres).
Length = 4 ππ, Breadth = 3 ππ;
Area = 4 Γ 3 = 12 π π. ππ
Area of B:
Length = 3 ππ, Breadth2 + 1 = 3 ππ
Area = 3 Γ 3 = 9 π π. ππ
Area of C:
Length = 2 + 1 + 1 = 4 ππ, Breadth = (4 + 1) β 3 = 2 ππ;
Area = 4 Γ 2 = 8 π π. ππ
Area of D:
Length = Breadth = 1 ππ;
Area = 1 π π. ππ
Part D is a portion in both Part A and B.
So, Total area of the shape is = 12 + 9 + 8 β 1 = 28 π π. ππ
b) The splitting can be done as shown below:
Area of A:
Length = 3 ππ, Breadth = 1 ππ;
Area = 3 π π. ππ
Area of B:
Length = 3 ππ, Breadth = 1 ππ;
Area = 3 π π. ππ
Area of C:
Length = 3 ππ; Breadth = 1 ππ; Area = 3 π π. ππ
Total area of the shape = 3 + 3 + 3 = 9 π π. ππ
Q.11) Split the following shapes into rectangles and find their areas. (The measures are given incentimetres)
Sol.11) The splitting can be done as follows:
Area of A = 12 Γ 2 = 24 π π. ππ
Area of B = 8 Γ 2 = 16 π π. ππ
Total area = 24 + 16 = 40 π π. ππ
b) Area of A = 7 Γ 7 = 49 π π. ππ
Area of B = 7 Γ 21 = 147 π π. ππ
Area of C = 7 Γ 7 = 49 π π. ππ
Total area of the shape = 49 + 147 + 49 = 245 π π. ππ
c) Area of A = 5 Γ 1 = 5 π π. ππ
Area of B = 4 Γ 1 = 4 π π. ππ
Total area = 5 + 4 = 9 π π. ππ
Q.12) How many tiles whose length and breadth are 12 ππ and 5 ππ respectively will be needed to fit in a rectangular region whose length and breadth are respectively:
(a) 100 cm and 144 cm (b) 70 cm and 36 cm.
Sol.12) Length of the tile = 12 ππ; Breadth of the tile = 5 ππ
Area of one tile = 12 Γ 5 = 60 π π. ππ
a) Length of the rectangular region = 100 ππ
Breadth of the rectangular region = 144 ππ
Area of the rectangular region = 100 Γ 144 = 14400 π π. ππ
β΄ number of tiles needed = 14400/60 = 240 π‘ππππ
b) Length of the rectangular region = 70 ππ
Breadth of the rectangular region = 36 ππ
Area of the rectangular region = 70 Γ 36 = 2520 π π. ππ
Therefore, number of tiles needed = 2520/60 = 42 π‘ππππ
NCERT Solutions Class 6 Mathematics Chapter 1 Knowing our Numbers |
NCERT Solutions Class 6 Mathematics Chapter 2 Whole Numbers |
NCERT Solutions Class 6 Mathematics Chapter 3 Playing with Numbers |
NCERT Solutions Class 6 Mathematics Chapter 4 Basic Geometrical Ideas |
NCERT Solutions Class 6 Mathematics Chapter 5 Understanding Elementary Shapes |
NCERT Solutions Class 6 Mathematics Chapter 6 Integers |
NCERT Solutions Class 6 Mathematics Chapter 7 Fractions |
NCERT Solutions Class 6 Mathematics Chapter 8 Decimals |
NCERT Solutions Class 6 Mathematics Chapter 9 Data Handling |
NCERT Solutions Class 6 Mathematics Chapter 10 Mensuration |
NCERT Solutions Class 6 Mathematics Chapter 11 Algebra |
NCERT Solutions Class 6 Mathematics Chapter 12 Ratio and Proportion |
NCERT Solutions Class 6 Mathematics Chapter 13 Symmetry |
NCERT Solutions Class 6 Mathematics Chapter 14 Practical Geometry |
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NCERT Solutions Class 6 Mathematics Chapter 10 Mensuration
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NCERT Solutions Chapter 10 Mensuration Class 6 Mathematics
Class 6 Mathematics NCERT Solutions Chapter 10 Mensuration is a really good source using which the students can get more marks in exams. The same questions will be coming in your Class 6 Mathematics exam. Learn the Chapter 10 Mensuration questions and answers daily to get a higher score. Chapter 10 Mensuration of your Mathematics textbook has a lot of questions at the end of chapter to test the students understanding of the concepts taught in the chapter. Students have to solve the questions and refer to the step-by-step solutions provided by Mathematics teachers on studiestoday to get better problem-solving skills.
Chapter 10 Mensuration Class 6 NCERT Solution Mathematics
These solutions of Chapter 10 Mensuration NCERT Questions given in your textbook for Class 6 Mathematics have been designed to help students understand the difficult topics of Mathematics in an easy manner. These will also help to build a strong foundation in the Mathematics. There is a combination of theoretical and practical questions relating to all chapters in Mathematics to check the overall learning of the students of Class 6.
Class 6 NCERT Solution Mathematics Chapter 10 Mensuration
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