mathexpress99.in
Class VI / CBSE / Chap 10 / Mensuration.
Chapter Facts :
1. Perimeter of a rectangle = 2 × (length + breadth)
2. Perimeter of a square = 4 × length of its side.
Also side of a square = perimeter  4
3. Perimeter of an equilateral triangle = 3 × length of a side.
Also side of an equilateral triangle = perimeter  3
4. Perimeter of a regular polygon with ‘n’ sides = n × length of a side.
Also side of a regular polygon with ‘n’ sides = perimeter  n
5. Area of a rectangle = length × breadth
Also : length = area  breadth
Also : breadth = area  length
Area of a square = side × side.
area of floor
6. Number of tiles needed to cover a floor =
area of one tile
Formative assessment
A ) Multiple Choice Questions.
In each of the following tick the correct option.
1. Perimeter is always measured in
(a) sq. m
(b) sq. cm
(c) cm
(d) given units
2. Area is always measured in
(a) given units
(b) cm
(c) m
(d) sq. units
3. Area of rectangle is 240 m2. If its length is 16 m, them its breadth is
(a) 15 m
(b) 8 m
(c) 224 m
(d) 14 m
4. If the length and breadth of a rectangle are doubled, then its perimeter is
(a) halved
(b) doubled
(c) tripled
(d) none of these
5. Two squares of side 4 cm each are joined together. The perimeter of the resulting Figure is
(a) 16 m
(b) 32 cm
(c) 24 cm
(d) 64 cm
6. The area of a square is 225 cm2 . The perimeter of square will be
(a) 15 cm
(b) 25 cm
(c) 45 cm
(d) 60 cm
7. The length and breadth of a rectangle are in the ratio 2 : 1.If its breadth is 13 m then its
perimeter is
(a) 39 m
(b) 78 m
(c) 160 m
(d) 120 m
8. Perimeter of a square is 44 m. Its area is
(a) 176 m2
(b) 121 m2
(c) 11 m2
(d) 44 m2
9. The perimeter of a rectangle is 36 m and the length is twice the breadth. Then area of
the rectangle is
(a) 144 m2
(b) 72 m2
(c) 256 m2
(d) 160 m2
10. The perimeter of a square whose side is ‘y’ units is
(a) y units
(b) y2 units
(c) 2y units
(d) 4y units .
B ) Fill in the blanks
1. The standard unit of _________ is metres.
2. The standard unit of _________ is sq. metres.
3. Amount of surface enclosed by a closed figure is called its _________ .
4. The area of a square with side 11 cm is ________ sq. cm.
5. Perimeter of a square with side 15 cm is ________ cm.
6. A rectangle with dimensions 6 cm x 2 cm and a square have the same perimeter.
Copyright with the author.
mathexpress99.in
Then , area of the rectangle is _________ sq. cm ; area of the square is _________sq.
cm .
7. A polygon having all its sides and angles equal is called a _________ polygon.
8. 1.5 m2 = _________ cm2.
9. 1sqcm = _________ cm × 1cm.
10. 1sqm = 1m × _________ m = 100cm × _________ cm. = _________ sq. cm.
C ) True / False
State whether the given statements are true (T) or false (F).
1. The sum of the lengths of a polygon is called its area.
T/F
2. Perimeter of a regular heptagon of side 6cm is 42cm.
T/F
3. 125 cm2 = 1.25 m2.
T/F
4. To find the cost of a frame of a picture, we need to find the perimeter of the picture.
T/F
5. If the side of a square is doubled, its perimeter is also doubled.
6. The area of a square is 225 m2, its side would be 15 m long.
T/F
7. Perimeter of a regular hexagon is 600 cm . Then each of its side is 1m.
8. Area of square is 169 sq. cm. Then its perimeter is 52 cm.
T/F
T/F
9. Perimeter of a regular pentagon = 4 × side.
10. When length of a rectangle is increased by 2 m its area increases by 8 sq. m. Then its
breadth is 4m.
T/F
D ) True false with Justification
Say true or false for each of the following. Justify your answer
1. If length of a rectangle is halved and breadth is doubled then the area of the rectangle
becomes four times.
T/F
________________________________________________________
________________________________________________________
_________________________________________________________
2. Area of a square becomes four times if the side of the square is doubled. T/F
________________________________________________________
________________________________________________________
_________________________________________________________
3. A farmer who wants to fence his field, must find the area of the field.
________________________________________________________
T/F
________________________________________________________
_________________________________________________________
4. An engineer who plans to build a compound wall on all sides of a house must find the
perimeter of the compound. T/F
________________________________________________________
Copyright with the author.
mathexpress99.in
________________________________________________________
_________________________________________________________
5. To find the cost of painting a wall we need to find the area of the wall. T/F
________________________________________________________
________________________________________________________
_________________________________________________________
E ) Matching
Match the following:
Column I
(a) Area of a rectangle
(b) Area of a square
(c) Perimeter of a rectangle
(d) Perimeter of a square
(e) Perimeter of a hexagon
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Column II
2(l + b)
4 × side
6 × side
side2
l×b
8 x side
Summative assessment
1 mark Q’s
1. Find the perimeter of a rectangle with length 16 cm and breadth 12 cm.
2. Base of a tent is a regular hexagon of perimeter 72 m. What is the length of each side
of the base?
3. Length of a chord is 434 cm. What will be the length of each side if this chord is used
to form an regular heptagon ?
4. Length of a string is 117 cm. What will be the length of each side if this string is used
to form an regular nonagon ?
5. The perimeter of a regular pentagon is 1550cm. How long is its each side?
2 mark Q’s
6. The area of a rectangular field is 800sqm. If the length of the field is 80m, find the
perimeter of the field.
7. A wire is bent in the shape of a regular octagon of side 12 cm. It was straightened and
re-bent in shape of a square. What is the side of the square ?
8. Length of a rectangle is three times its breadth. Perimeter of the rectangle is 40cm.
Find its length and width.
9. The perimeter of a isosceles triangle is 28cm. Its base is 10cm. What are the
measurements of the other two sides ?
10. Length of a rectangular field is six times its breadth. If the length of the field is 114 m,
find the breadth and perimeter of the field.
3 mark Q’s
11. The lawn is 12m× 8m, whereas another lawn is 15m×5m. A bamboo fencing is built
around both the lawns. How much fencing is required for both?
12. A magazine charges Rs 40 per sq cm area for advertising. A company decided to order
a half page advertisment. If each page of the magazine is 16cm × 26cm, what amount will
the company has to pay for it?
Copyright with the author.
mathexpress99.in
13. The length of a rectangular field is 10 m and breadth is 4m. If a square field has the
same perimeter as this rectangular field, find which field has the greater area.
14. Perimeter of a square and a rectangle is same. If a side of the square is 15cm and one
side of the rectangle is 18cm, find the area of the rectangle.
15. The length of a rectangular field is twice its breadth. Jamal jogged around it four
times and covered a distance of 6km. What is the length of the field?
4 mark Q’s
16. In an exhibition hall, there are 24 display boards each of length 1m 50cm and breadth
1m. There is a 100m long aluminium strip, which is used to frame these boards. How
many boards will be framed using this strip? Find also the length of the aluminium strip
required for the remaining boards.
17. The perimeter of a square garden is 48 m. A small flower bed covers 18 sqm area
inside this garden. What is the area of the garden that is not covered by the flower bed?
What fractional part of the garden is covered by flower bed? Find the ratio of the area
covered by the flower bed and the remaining area.
18. Length of a rectangular field is 250 m and width is 150 m. Anuradha runs around
this field 3 times. How far did she run? How many times she should run around
the field to cover a distance of 4km?
19. A rectangular path of 60 m length and 3 m width is covered by square tiles of side 25
cm. How many tiles will there be in one row along its width? How many such rows will
be there? Find the number of tiles used to make this path?
20. The area of each square on a chess board is 4 sqcm. Find the area of the board. At the
beginning of game when all the chess men are put on the board, write area of the squares
left unoccupied. Find the area of the squares occupied by chess men.
Value based questions
Q1. A group of villagers decided to plant around a rectangular playground whose area is
12,000 sq. m.
i) If the width of the playground is 80 m, what is its length?
ii) How many plants can be planted around a playground if distance between two
consecutive plants is 1m ?
iii) What is the value depicted here ?
2. Anita who is overweight, was advised by her family doctor to go for a morning walk
in order to reduce her weight. She goes to a park near her house shaped like an equilateral
triangle with side 100 m. She takes four rounds of the park daily.
i) How much distance is covered by Anita daily?
ii) How much more or less than a kilometer does she walk every day ?
iii) What value of Anita is depicted here ?
Answers
Formative assessment
A ) Multiple Choice Questions.
1. (d)
2. (d)
3. (a)
4. (b)
5. (c)
6. (d) 7. (b) 8. (b) 9. (b) 10. (d).
B ) Fill in the blanks
length 2. area 3. area
4. 121
5. 60
6. 12 ;16 .
7. regular 8. 15000 9. 1
10. 1 ; 100 ; 10000
C ) True / False
1. F
2. T
3. F
4. T 5. T
6. T
7. T
8. T
9. F 10. T
Copyright with the author.
mathexpress99.in
D) True /False with Justification.
1. F ; L  ½ L , B  2 B , New area = ½ L x 2 B = LB , Area remains same.
2. T ; x 2x , New area = 2x  2x = 4 x2 = 4 x original area
3. F ; Fencing is to be done along the boundary so he must find the perimeter.
4. T ; Wall is to be built along the boundary so to find the length of the wall we need to know the
perimeter.
5. T ; Cost of paint = area  unit cost.
E) Matching
(a) – (v) ; (b) – ( iv) ; (c) – (i) , (d) – (ii) , (e) – (iii)
Summative assessment
1 mark Q’s
1. 56 cm. 2. 12 m
3. 62 cm 4. 13 cm
5. 310 cm
2 mark Q’s
6. 180 m
7. 24 cm
8. 15 cm, 5 cm
9. 9 cm, 9 cm 10. 19 m, 266 m
3 mark Q’s
11. 80 m
12. Rs 8,320
13. square field
14. 216 sq. cm 15. 500 m
4 mark Q’s
16. 20 ; 20 m
17. 126 sq. m. ; 1/8 ; 1 : 7
18. 2400 m ; 5 times 19. 12 ; 240 ; 2880
20. 256 sq. cm. 128 sq. cm ; 128 sq. cm.
Value Based Questions
Ans. 1. i) 150 m ii) 460 iii) Co-operation.
2. i) 1200 m ii) 200 m more than a km iii) Health consciousness.
Copyright with the author.