Mensuration (Exercise 10.3)

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Mensuration


Exercise 10.3


EX 10.3 QUESTION 1.


Find the area 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

Solution:

(Area of rectangle = Length × Breadth)

(a) l = 3 cm and b = 4 cm

Area = length x breadth = 3 × 4

= 12 cm2

(b) l = 12 m and b = 21 m

Area = length x breadth = 12 × 21

= 252 m2

(c) l = 2 km and b = 3 km

Area = length x breadth = 2 × 3

= 6 km2

(d) l = 2 m and b = 70 cm = 0.70 m

Area = length x breadth = 2 × 0.70

= 1.40 m2


EX 10.3 QUESTION 2.


Find the areas of the squares whose sides are:

(a) 10 cm

(b) 14 cm

(c) 5 m

Solution:

(a) Area of square = side2

= 102

= 100 cm2

(b) Area of square = side2

= 142

= 196 cm2

(c) Area of square = side2

= 52

=25 cm2


EX 10.3 QUESTION 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?

Solution:

(a) Area of rectangle = l × b

= 9 × 6

= 54 m2

(b) Area of rectangle = l × b

= 17 × 3

= 51 m2

(c) Area of rectangle = l × b

= 4 × 14

= 56 m2

Area of rectangle 56 m2 i.e (c) is the largest area and area of rectangle 51 m2 i.e (b) is the smallest area.


EX 10.3 QUESTION 4.


The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.

Solution:

Area of rectangle = length × width

300 = 50 × width

width = 300 / 50

width = 6 m

∴ The width of the garden is 6 m


EX 10.3 QUESTION 5.


What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹ 8 per hundred sq m.?

Solution:

Area of land = length × breadth

= 500 × 200

= 1,00,000 m2

∴ Cost of tiling 1,00,000 sq m of land = (8 × 1,00,000) / 100

= ₹ 8000


EX 10.3 QUESTION 6.


A table top measures 2 m by 1 m 50 cm. What is its area in square metres?

Solution:

Given

Length = 2m

Breadth = 1m 50 cm = 1.50 m

Area = length x breadth = 2 × 1.50

= 3 m2


EX 10.3 QUESTION 7.


A room is 4 m long and 3 m 50 cm wide. How many square metres of carpet is needed to cover the floor of the room?

Solution:

Given

Length = 4m

Breadth = 3 m 50 cm = 3.50 m

Area = length x breadth = 4 × 3.50

=14 m2


EX 10.3 QUESTION 8.


A floor is 5 m 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.

Solution:

Area of floor = length x breadth = 5 × 4

= 20 m2

Area of square carpet = 3 × 3

= 9 m2

Area of floor that is not carpeted = 20 – 9

= 11 m2

∴ Area of the floor that is not carpeted is 11 m2


EX 10.3 QUESTION 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?

Solution:

Area of flower square bed = 1 × 1

= 1 m2

Area of 5 square bed = 1 × 5

= 5 m2

Area of land = 5 × 4

= 20 m2

Remaining part of the land = Area of land – Area of 5 square bed

= 20 – 5

= 15 m2

∴ Remaining part of the land is 15 m2


EX 10.3 QUESTION 10.


By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).

Solution:

 

 

Area of the rectangle I = length x breadth
= 4 cm x 3 cm = 12 sq cm

Area of the rectangle II = length x breadth
= 3 cm x 2 cm = 6 sq cm.

Area of the rectangle III = length x breadth
= 4 cm x 1 cm = 4 sq cm

Area of the rectangle IV = length x breadth
= 3 cm x 2 cm = 6 sq cm

∴ Total area of the whole figure
= 12 sq cm + 6 sq cm + 4 sq cm + 6 sq cm
= 28 sq cm.

(b)

 

Area of the rectangle I
= 12 cm x 2 cm = 24 sq cm

Area of the rectangle II
= 8 cm x 2 cm = 16 sq cm

Area of rectangle III
= 3 cm x 1 cm = 3 sq cm

∴ Total area of the given figure = 3 sq cm + 3 sq cm + 3 sq cm = 9 sq cm.


EX 10.3 QUESTION 11.


Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)

 

Solution:

(a)

 

Total area of the figure = 12 × 2 + 8 × 2

= 40 cm2

(b)

Area of the rectangle I
= 7 cm x 7 cm = 49 sq cm

Area of the rectangle II
= 21 cm x 7 cm = 147 sq cm

Area of the rectangle III
= 7 cm x 7 cm = 49 sq cm

∴ Total area of the whole figure
= 49 sq cm + 147 sq cm + 49 sq cm
= 245 sq cm.

(c)

Area of a rectangle = 2 × 1

= 2 cm2

Area of b rectangle = 2 × 1

= 2 cm2

Area of c  rectangle = 5 × 1

= 5 cm2

Total area = 2 + 2 + 5

= 9 cm2


EX 10.3 QUESTION 12.


How many tiles whose length and breadth are 12 cm and 5 cm 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

Solution:

(a) Area of rectangle = 100 × 144

= 14400 cm

Area of one tile = 5 × 12

= 60 cm2

Number of tiles = (Area of rectangle) / (Area of one tile)

= 14400 / 60

= 240

Hence, 240 tiles are needed

(b) Area of rectangle = 70 × 36

= 2520 cm2

Area of one tile = 5 × 12

= 60 cm2

Number of tiles = (Area of rectangle) / (Area of one tile)

= 2520 / 60

= 42

Hence, 42 tiles are needed.