VI Class - CBSE Mathematics - Part - II

2 MENSURATION
INTRODUCTION :
With each plane figure, we think of their regions and their boundaries. For expression of two plane
figures, some measures are needed. For example Perimeter, Area etc.
Ø Perimeter : The concept of perimeter is widely used in our daily life . For example,
Þ in fencing a field.
Þ in preparing a track to conduct sports
Þ in building a compound wall etc.
“PERIMETER” is the distance covered along the boundary forming a closed figure when you go
round the figure once.
Ø Perimeter of a rectangle = 2 × (l + b) . Where l, b are the length and breadth
1
Þ Length of a rectangle = × ( Perimeter) – breadth
2
1
Þ Breadth of rectangle = × (Perimeter) – length
2
Ø Perimeter of a square = 4 × side of square
1
Þ side of a square = × perimeter
4
Ø Perimeter of a scalene triangle is the sum of all the three sides of it.
P = a + b + c. Where a, b, c are the sides.
Perimeter of an equilateral triangle with side “a” is 3a. Perimeter of any polygon is equal to the sum
of all its sides.
The figures having all sides of equal length and all angles of equal measure are known as “regular
figures”. Example : square, equilateral triangle
Regular figures perimeter = number of sides × length of one side

SOLVED EXAMPLES
1. Find the perimeter of each of the following figures:
a) perimeter = the sum of the lengths of the sides = 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm
+ 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm+ 2 cm + 3 cm + 4 cm + 1 cm + 3 cm +
2 cm + 3 cm = 52 cm

4 cm
1 cm
3 cm
3 cm
4 cm

3 cm
2 cm

3 cm
2 cm
3 cm
2 cm

2 cm
4 cm
3 cm

3 cm

3 cm
1 cm
4 cm 1 cm

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Mathematics - Part - II VI Class - CBSE
b) perimeter = 5 × the length of one side
= 5 × 4 cm
= 20 cm

4
cm

cm
4

4 cm
4 cm
4 cm

2. A table-top measures 2m 25 cm by 1m 50 cm. What is the perimeter of the table top?

Sol: Length of table top = 2m 25 cm. Breadth of table top = 1m 50 cm
perimeter of table top = 2 × (length + breadth)
= 2 × (2m 25 cm + 1m 50 cm)
= 2 × (3 m 75 cm)
= 2 × 3.75 m
= 7.50 m
3. A flower bed is in the shape of a square with a side 3.5 m. Each side is to be fenced with 4 rows
of ropes. What is the length of the wire needed?
Sol: Side of square = 3.5 m
Perimeter of a square = 4 × 3.5 m
= 14 m
Rope required to fence with 1 row = 14 m
Rope required to fence with 4 rows = 4 × 14 m
= 56 m
Hence, the length of the wire needed = 56 m
4. Find the perimeter of each of the following shapes:
i) A triangle of sides 5 cm, 7 cm and 8 cm
ii) An equilateral triangle of side 12 cm
iii) An isosceles triangle with equal sides 10 cm each and third side of 9 cm
Sol: i) perimeter = the sum of the sides
= 5 cm + 7 cm + 8 cm
= 20 cm
ii) perimeter = 3 × length of one side
= 3 × 12 cm
= 36 cm
iii) perimeter = the sum of lengths of sides
= 10 cm + 10 cm + 9 cm
= 29 cm

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VI Class - CBSE Mathematics - Part - II
5. A piece of wire is 60 cm long. What will be the length of the each side if the string is used to
form:
i) An equilateral triangle ii) A square iii) A regular hexagon iv) A regular pentagon
Sol: Equilateral triangle : Equilateral triangle has all three sides equal.
60 cm
Each side should be = = 20 cm
3
Verification : perimeter = 3 × length of one side
= 3 × 20 cm
= 60 cm
Square : Square has all four sides equal.
60 cm
Each side of square = = 15 cm
4
Regular Hexagon : Regular Hexagon has all six sides equal.
60 cm
The length of each side = = 12 cm
5
6. Find the cost of fencing a rectangular park of length 55 m and breadth 24 m at the rate of
Rs. 15 per metre.
Sol: Length of rectangular park = 55 m
Breadth of rectangular park = 24 m
perimeter of the park = 2 × (length + breadth)
= 2 × (55 m + 24 m)
= 2 × 79 m
= 158 m
cost of 1 metre wire = Rs. 15
cost of 158 m wire = Rs. 15 × 158
= Rs. 2370
Hence, the cost of fencing rectangular park is 2,370.
7. Two sides of a triangle are 15 cm, 17 cm. The perimeter of the triangle is 52 cm. What is its
third side?
Sol: Given, two sides of triangle are 15 cm, 17 cm
Let the third side of it be ‘x’ cm
perimeter of a triangle = sum of all its sides
= 15 cm + 17 cm + x cm
= 32 cm + x cm
But, according to problem,
the perimeter of triangle = 52 cm
so, 32cm + x cm = 52 cm
x = 52 cm – 32 cm
x = 20 cm
\ The third side of a triangle = 20 cm

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Mathematics - Part - II VI Class - CBSE

8. Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with
length 60m and breadth 45 m. Who covers less distance?
Sol: The distance each girl covers in one round is the same as the perimeter of respective field.
\ The distance that Sweety covers in one round
= 4 × side [square field]
= 4 × 75 m [since side = 75 m]
= 300 m.
The distance that Bulbul covers in one round
= 2 × (length + breadth) [rectangular field]
= 2 × (60m + 45 m) [since l = 60m; b = 45 m]
= 2 × 105 m
= 210 m.
Hence,
Sweety covers 300m.
Bulbul covers 210 m.
So, this shows that Bulbul covers less distance than Sweety.
9. Find the perimeter of regular octagon with each side measuring 9cm.
Sol: Regular octagon has all 8 sides equal.
so, number of sides = 8
length of each side = 9 cm.
Perimeter = 8 × length of each side
= 8 × 9 cm
= 72 cm

10. The length of a rectangle is twice of its breadth. If its perimeter is 48cm find the dimensions of
the rectangle?
Sol: Let the breadth of a rectangle be “ x” cm
Then the length = twice of the breadth
= 2 x cm.
Perimeter of a rectangle = 2 × (length + breadth)
= 2 × (2x + x) cm
= 2 × 3x cm
= 6x cm.
But according to problem, the perimeter is 48 cm.
So, 6x cm = 48 cm.
8
48
x= cm
61
x = 8 cm.
i.e, Breadth = 8 cm
Length = 2x.
= 2 × 8 cm
= 16 cm.
\ The dimensions of a rectangle are 16cm, 8 cm.

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VI Class - CBSE Mathematics - Part - II

EXERCISE
1. Find the perimeter of the given shape.
F D
m
6c

3c
4
cm

m
C

5 cm
E

4c
m
A 8 cm B

2. Find the perimeter of each of the following.

a) A triangle of sides 25cm, 30cm, 40cm,
b) An equilateral triangle of side 18m.
c) An isosceles triangle with equal sides 13 cm each and third side 15 cm.
3. Find the length of the tape required to seal all round the lid of a rectangular box of sides 35cm and
23 cm.
4. A piece of wire is 120cm long. What will be the length of each side if the wire is used to form:
a) A square b) An equilateral triangle c) A regular pentagon.
5. A rectangular park measures 40m and 10m. Each side is to be fenced with 5 rows of wires. What
length of the wire is required?
6. Find the cost of fencing a square park of side 150 m at the rate of 15 per metre.
7. Find the perimeter of a regular nonagon of side 14 cm.
8. Bunty and Bubly go for jogging every morning. Bunty goes around a square park of side 80m. Bubly
goes arround a rectangular park with length 90m and breadth 60m. If they both take 3 rounds, who
covers greater distance?

AREA
w The amount of surface enclosed by a closed figure is called its “Area”.
w The area of a closed figure can be found by using a graph paper (or) a squared paper.
w While measuring the area on squared paper the following conventions to be adopted.
i) The area of one full square is to be taken as 1 square unit.
1
ii) If the area occupied exactly half a square, it is to be taken as square unit.
2
iii) If the area occupied more than half of a square, it is to be taken 1 square unit.
iv) If the area occupied less than half of a square, we can ignore the portion of that area.
w The units of perimeter is same as the units of the length of the object.
w The units of area is square centimetres if the dimensions of the figure is given centimetres. The units
of area is square metres if the dimensions of the figure is given in metres.
w Areas of smaller figures are measured in sq. cm (or) sq. m
w Areas of larger figures are measured in sq. km (or) hectares (or) ares
w The area of a rectangle = length × breadth
The area of a square = side × side
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Mathematics - Part - II VI Class - CBSE

w 1 are = 100 sq. m

1 hectare = 10,000sq.m = 100 ares.
1 sq. km = 100 Hectares.
Area A
w Length of a rectangle = =
breadth b
Area A
Breadth of a rectangle = =
Length l
Side of a square = area .
w If the length and breadth of a rectangle are doubled, its area increases by 4 times
w If the length and breadth of a rectangle are doubled and tripled respectively, its area increases by 6 times.
w If the side of a square is doubled, its area increases by 4 times.
1
w If the side of a square is halved, its area decreases by 4 times . [Becomes of actual area]
4

SOLVED EXAMPLES
1. Find the area of the rectangles with the given measurements :
a) 50 cm and 16 cm b) 25 cm and 20 cm
Sol: a) Length of a rectangle = 50 cm
Breadth of a rectangle = 16 cm
Area of a rectangle = length × breadth
= 50 cm × 16 cm
= 800 sq.cm
b) Length of a rectangle = 25 cm
Breadth of a rectangle = 20 cm
Area of a rectangle = length × breadth
= 25 × 20
= 500 sq. cm

2. Find the areas of squares whose sides are :

a) 17 cm b) 26 m
Sol: a) Side of the square = 17 cm
Area of the square = side × side
= 17 cm × 17 cm
= 289 sq. cm
b) Side of the square = 26 m
Area of the square = side × side
= 26 m × 26 m
= 676 sq.m
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VI Class - CBSE Mathematics - Part - II
3. The area of a rectangular frame is 1,125sq. cm. If its breadth (width) is 25 cm, What is its
length?
Sol: Let the length be ‘l’ cm
breadth (b) = 25 cm
Area of rectangle = l × b
= l × 25 cm
But, according to the problem, the area of
rectangle = 1,125 sq. cm
∴ l × 25 cm = 1,125 sq. cm
1,125
l=
25 cm
l = 45 cm.

∴ length of the rectangle = 45 cm

4. The length of a rectangular field is 58 m and the breadth is half of its length. Find the area of
the field.
Sol: Length of a rectangular field = 58 m
breadth = half of the length
1
= × 58 m = 27 m
2
∴ length (l) = 58 m
breadth (b) = 27 m
Area of rectangle = l × b
= 58 m × 27 m
= 1,566 sq. m
5. The length of a rectangular floor is 20m, more than its breadth. If the perimeter of the floor is
280m, what is its length? Find its area?
Sol: Let the breadth be ‘x’
∴ length = 20 metre more than its breadth.
= 20 + x
Given, the perimeter of the floor = 280 m.
2 × (length + breadth) = 280 m [ 3 perimeter = 2 × (l + b)]
⇒ 2 × (20 + x + x) = 280 m [ 3 l = 20 + x; b = x]
⇒ 2 × (20 + 2x) = 280 m
280
⇒ 20 + 2x = m
2
⇒ 20 + 2x = 140 m
⇒ 2x = 140m – 20 m
⇒ 2x = 120 m

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Mathematics - Part - II VI Class - CBSE

60
120
⇒ x= 1
2
∴ x = 60 m
Hence, breadth (b) = 60m
length (l) = 20 + x
= 20 + 60 m
= 80 m
Now l = 80 m, b = 60 m
Area of rectangle = l × b
= 80 m × 60 m
= 4800 sq.m

6. What is the cost of tiling a rectangular piece of land 250 m long and 150m wide at the rate of
< 9 per hundred sq. m
Sol: Length of rectangular piece = 250 m
Breadth of rectangular piece = 150 m
Area of rectangular piece = l × b
= 250 m × 150 m
= 37, 500 sq.m
Cost of tiling 100 sq.m = 9
9
∴ cost of tiling 1 sq.m =
100
9
cost of tiling 37,500 sq.m = × 37,500
100
= 3375
7. Five square flower beds each of sides 1m are dug on a piece of land 5m long and 4m wide.
What is the area of the remaining part of the land?
Sol: Length of land = 5m
Breadth of land = 4m
Area of land = l × b = 5 × 4 1m 1m
= 20 sq. m 4m
Side of a square flower bed = 1m 1m 1m 1m
Area of a square flower bed = 1m× 1m = 1 sq.m
Area of 5 square flower beds = 5 × 1 sq. m = 5 sq.m 5m
Hence, area of remaining part of land
= 20 sq. m – 5 sq. m
= 15 sq.m

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VI Class - CBSE Mathematics - Part - II
8. A room is 4m 20 cm long and 3m 65cm wide. How many square metres of carpet is needed to
cover the floor of the room?
Sol: Length of the room = 4m 20 cm = 4. 20 m
Breadth of the room = 3m 65 cm = 3. 65 m
Area of the room = length × breadth
= 4. 20 m × 3.65 m
= 15.33 sq.m
Hence, 15.33 sq.m of carpet is needed to cover the floor of the room.
9. A floor is 8 m long and 5m wide. A square carpet of sides 2.5 m is laid on the floor. Find the
area of the floor that is not carpeted.
Sol: Length of floor (l) = 8 m
Breadth of floor (b) = 5m
Area of floor = l × b
= 8 m × 5 m = 40 sq.m
side of square carpet = 2.5 m
Area of square carpet = 2.5 m × 2.5 m
= 6.25 sq.m
Area of floor = 40 sq .m
Area of carpet = 6.25 sq.m
Hence, area of floor that is not carpeted
= 40 sq m – 6.25 sq.m
= 33.75 sq.m

10. How many tiles with dimensions 8 cm and 15 cm will be needed to fit a region whose length
and breadth are respectively: 200 cm and 120 cm.
Sol: Length of region = 200cm
breadth of region = 120 cm
area of region = l × b
= 200 cm × 120 cm
= 24000 sq.cm
Length of tile = 15 cm
breadth of tile = 8 cm
area of tile = l × b = 15 cm × 8 cm = 120 sq.cm
Number of tiles required
Area of region
=
Area of one tile
2400 sq.cm
= = 200
120 sq.cm
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Mathematics - Part - II VI Class - CBSE

11. Split the following shapes into rectangles and find the area of each in square centimetres.
7
3 1
5 7 7
1 1 7 7 2
2 2 2 4
7 7
a) b) c) 4
4 4 7 7 4 3
1 7 7 3
7
Sol: a) Area of the shape = [(5 × 1) + (4 × 1)] sq. cm 5
1 1 1
= 5 + 4 sq. cm 2 2

4 4
= 9 sqcm 1
b) Area of the shape = [ (7 × 7) + (7 × 7) + (7 × 7) + (7 × 7) + (7 × 7) ] sq. cm
7
= 49 + 49 + 49 + 49 + 49 sq. cm
7 7
7 7 7
= 5 × 49 sq. cm
7 7 7 7
7
= 245 sq.cm 7 7
c) Let the figure may be divided into rectangles marked as A, B, C and D. 7 7
7
Area of rectangle (A) = (3 × 3) sq . cm
= 9 sq. cm (7-5) = 2
Area of rectangle (B) = (1 × 2) sq .cm 3 1 D
= 2 sq. cm 2 4
Area of rectangle (C) = (3 × 3) sq. cm 2 C 3
= 9 sq. cm 1 B 11 2 2
3 4
Area of rectangle (D) = (4 × 2) sq. cm 4 3 A 3
= 8 sq. cm 3
∴ The total area of the figure,
= ( 9 + 2 + 9 + 8) sq. cm
= 28 sq. cm

PRACTICE EXERCISE
1. Find the area of the rectangle whose length and breadth are 2m and 70 cm.
2. The area of a rectangular garden is 260 sq.m and its width is 13 m find its length.
3. Find the area of a square plot whose side is 19 cm.
4. Which of the following has a larger area and by how much? (a) A rectangle of length 21 cm and
width 11 cm, or (b) A square of side 18 cm
5. A tile measures 32 cm by 25 cm. How many tiles will be required to cover a floor of size 4m by 3 m.

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VI Class - CBSE Mathematics - Part - II
6. The floor of a square hall is made up of square blocks. The side of the hall is equal to 15m and the
side of each block is 1.5 m. Find the number of blocks which cover the floor of the square hall.
7. The area of a rectangle is 650 cm2 and one of its sides is 13 cm. Find the perimeter of the rectangle.
8. Find the cost of fencing a rectangular field 34 m long and 18m wide at < 2.25 per metre. What is the
cost of cultivating the field at < 4.50 per square metre?
9. The total cost of flooring a room at < 8.50 per square metre is < 510. If the length of the room is 8
metres, find its breadth.
10. A table is 150 cm long and 90 cm wide. Find its area. What will be its painting cost if the rate of
painting is < 3 per 100 sq. cm?
11. In a square park of side 20 m flower beds of square shape in each corner of the park are made. If each
side of flower beds are 2.5m, find the area of the flower beds and the remaining part of the park.
12. Split the following shape into rectangles and find the area of each in square centimetres.
1 4
1
13
10 9 6 1
1
6 1
4

OBJECTIVE TYPE QUESTIONS

I. Multiple Choice questions :
1. Perimeter of a rectangle = [ ]
a) Length × Breadth b) Length + Breadth
c) 2 × (Length + Breadth) d) 2 × [Length × Breadth]
2. Perimeter of a square = [ ]
a) 4 × length of a side b) 2 × length of a side
c) 3 × length of a side d) 6 × length of a side
3. Perimeter of an equilateral triangle = [ ]
a) 2 × length of a side b) 3 × length of a side
c) 4 × length of a side d) 6 × length of a side
4. Perimeter of a regular hexagon = [ ]
a) 3 × length of a side b) 4 × length of a side
c) 5 × length of a side d) 6 × length of a side
5. Aparna went to a park 20m long and 10 m wide. She took one complete round of it. The distance
covered by her is [ ]
a) 12 m b) 14 m c) 24 m d) 60 m
6. Perimeter of a regular pentagon = [ ]
a) 4 × length of a side b) 3 × length of a side c) 6 × length of a side d) 5 × length of a side

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Mathematics - Part - II VI Class - CBSE

2m
7. The perimeter of the figure is 2 m 2m [ ]
2m
a) 8 m b) 16 m c) 4 m d) None of these

4m
8. 3m 3 m The perimeter of the figure is [ ]
4m
a) 12 m b) 14 m c) 24 m d) 7 m
9. Area of a rectangle = [ ]
a) length × breadth b) length + breadth
c) 2 × (length + breadth) d) 2 × (length × breadth)
10. Area of a square = [ ]
a) side × side b) 4 × length of a side c) 2 × length of a side d) 6 × length of a side
11. If a page is 25 cm long and 20 cm wide, then the perimeter of this page is [ ]
a) 90 cm b) 45 cm c) 500 cm d) 5 cm

4 cm
m
3c

2 cm 6 cm . The perimeter of the figure =

12. [ ]
2
cm

3 cm
a) 20 cm b) 10 cm c) 24 cm d) 15 cm
13. The cost of fencing a rectangular park of length 10 m and breadth 5m at the rate of 10 per metre

a) 300 b) 600 c) 150 d) 1200 [ ]

14. The perimeter of a regular hexagon of side 5 m is [ ]
a) 5m b) 25 m c) 30 m d) 20 m
15. If the perimeter of a regular pentagon is 10m, then the length of the side is [ ]
a) 1 m b) 2 m c) 5 m d) 10 m
16. The area of a square of side 1 cm is [ ]
a) 1 cm2 b) 4 cm2 c) 9 cm2 d) 16 cm2
17. Two sides of a triangle are 5 cm and 4 cm. The perimeter of the triangle is 12 cm. The length of the
third side is [ ]
a) 1 cm b) 2 cm c) 3 cm d) 6 cm
18. The area of a rectangular sheet of paper is 20 cm2. Its length is 5 cm, then its width, is [ ]
a) 1 cm b) 2 cm c) 3 cm d) 4 cm
19. The distance travelled by Sangeeta, if she takes 5 rounds of a square park of side 10m is [ ]
a) 200 m b) 100 m c) 400 m d) 800 m

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20. If an athlete takes 10 rounds of a rectangular park, 40 m long and 30 m wide, then the total distance
covered by him is [ ]
a) 1400 m b) 700 m c) 70 m d) 2800 m
21. The amount of a surface enclosed by a closed figure is called [ ]
a) Perimeter b) Area c) Breadth d) None
22. 1 hectare in sq.m is [ ]
a) 100 b) 1000 c) 10,000 d) 10
23. 1 sq. km in hectares is [ ]
a) 10 b) 100 c) 1000 d) 10,000
24. If the side of a square increased by 4 times then its area increases by [ ]
a) 4 times b) 8 times c) 12 times d) 16 times
25. The breadth of rectangle, whose area is 600 sq.m and length 30m, is [ ]
a) 20 m b) 6 m c) 15 m d) 30m

II. Fill in the Blanks.

1. The perimeter of rectangle having length 20 cm and breadth 15 cm is ___________.
2. The perimeter of a triangle having sides 20 cm, 15 cm and 10 cm is ___________.
3. The perimeter of a regular heptagon whose side is 20 cm is ___________.
4. Perimeter of regular polygon having ‘n’ sides = ___________.
5. The length of a rectangle whose perimeter is 90cm and sides are in the ratio of 5 : 4 is ___________.
6. Perimeter of rhombus = ___________.
7. The units for area of 2D figure is ___________.
8. 1.7 km = ___________ m.
9. 1 m2 = ___________ cm2.
10. 1 cm2 = ___________ mm2.

III. Very short answer questions :

1. Define perimeter.
2. Find the perimeter of the following shape.
3 cm
E D
6 cm
4 cm
F C
2 cm
5 cm
A B
7 cm

3. Find the side of a square whose perimeter is 124 cm.

4. Find the third side of a triangle having perimeter as 90 cm and the lengths of two sides as 9 cm and
40 cm.
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Mathematics - Part - II VI Class - CBSE

3
5. The length of the rectangle is 80 m and the breadth is of its length. Find the area of rectangle.
4
6. Find the length of a rectangle whose breadth is 48 cm and the area is 1728 sq.cm.
7. Find the perimeter of equilateral triangle with side of length 5 cm.
8. Find the perimeter of an isosceles triangle with equal sides 4 cm each and third side 6 cm.
9. A piece of string is 120 cm long. What will be the length of each side if the string is bent in the form
of a regular hexagon?
10. A square piece of ground is 75 m long. Find the cost of erecting a fence round it at <4 per metre.
KEY
I. Multiple Choice Questions :
1) c 2) a 3) b 4) d 5) d 6) d 7) a 8) b
9) a 10) a 11) a 12) a 13) a 14) c 15) b 16) a
17) c 18) d 19) a 20) a 21) b 22) c 23) b 24) d
25) a

II. Fill in the blanks :

1) 70 cm 2) 45 cm 3) 140 cm 4) n × length of a side 5) 25 cm 6) 4 × length of side
7) square units 8) 1700 9) 10,000 10) 100

III. Very Short Answer questions :

1) Perimeter is the distance covered along the boundary of a simple closed figure.
2) 27 cm 3) 31 cm 4) 41 cm 5) 4800 m2 6) 36 cm 7) 15 cm 8) 14 cm 9) 20 cm
10) <1200

COMPETITION CORNER FOR OLYMPIADS

I. Single Answer Type questions :

1. The area of a square with perimeter 28cm is [ ]

a) 7 cm2 b) 49 cm2 c) 784 cm2 d) 196 cm2
2. The side of a square whose perimeter is equal to the perimeter of a rectangle with length 10cm and
breadth 6cm is [ ]
a) 4 cm b) 8 cm c) 16 cm d) 32 cm
3. The area of a rectangle is A one of its sides is ‘x’ then its adjacent side is [ ]
x A X
a) ax b) c) d)
h X A

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VI Class - CBSE Mathematics - Part - II
4. If each side of a square is halved, the area of new square is _______the are of the original square.
a) one - ninth b) double c) one - fourth d) four times [ ]
5. A lawn is rectangular and measures 36m by 30 m. If one bag of fertilizer covers 360m2, then the
number of bags purchased is [ ]
a) 3 b) 4 c) 9 d) 10

II. Multi Answers Type questions :

6. The area of a rectangle is 60m2. One of its side is 10m then [ ]
a) other side is 6m b) perimeter is 32m c) other side is 5 m d) perimeter is 30 m.
7. A rectangular courtyard is 3m 78cm long and 5m 25cm broad. It is desired to pave it with square tiles
of the same size then [ ]
a) largest size of tile used = 21cm b) largest size of tile used = 20cm
c) number of tiles = 400 d) number of tiles = 445

III. Assertion & Reason questions :

8. Assertion (A) : The area of a rectangle will be doubled when the length is doubled and breadth
remaining the same. [ ]
Reason (R) : The perimeter of a square whose area is 2500 m2 is 200m.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true and R is not the correct explanation of A.
c) A is true, R is false
d) A is false, R is true.
9. Assertion (A) : A room is 26m long and 15m wide. A 14m square carpet is laid on the floor. Then
the area not carpeted is 194 m2. [ ]
Reason (R) : A tile measures 10cm × 10cm. Number of tiles required to cover a wall 4m × 2.5 m
is 900.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true and R is not the correct explanation of A.
c) A is true, R is false d) A is false, R is true.

IV. Statement Type questions :

10. Statement A : The length of the side of an equilateral triangle if the perimeter is 18cm is 6 cm.
Statement B : The length of the side of a regular pentagon if the perimeter is 45 cm is 9 cm.
a) Both A and B are true b) Both A and B are false [ ]
c) A is true and B is false d) A is false and B is true
11. Statement A : Mr. Varma has an orchard of length and breath 280m and respectively. He wants
to fence it with 4 rounds of barbed wire. The cost of fencing at Rs 35 permeter is
Rs 1,34,400.
Statement B : The perimeter of an isosceles triangle with equal sides 4cm each and third side
6 cm is 12cm. [ ]
a) Both A and B are true b) Both A and B are false
c) A is true and B is false d) A is false and B is true

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Mathematics - Part - II VI Class - CBSE
V. Match the following :
Column I Column II
12. The breadth of a rectangle of area 8.4 m2 and length 4m is [ ] a) 11 cm
13. The perimeter of a square with side 8 m is [ ] b) 2.1 m
14. The length each of the equal sides of the isosceles triangle if [ ] c) 9 m
perimeter = 30cm, unequal side = 8 cm
15. Length of side of regular pentagon if the perimeter is 45 m is [ ] d) 32 m

KEY
1) b 2) b 3) c 4) c 5) a 6) a 7) b 8) b
9) c 10) a 11) b 12) b 13) d 14) a 15) c

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