## Chapter 10 Mensuration Exercise 10.3

Question 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

Answer:

a)

Area of rectangle = l × b

= 3 cm × 4 cm

= 12 cm²

b)

Area of rectangle = l × b

= 12 m × 21 m

= 252 m²

c)

Area of rectangle = l × b

= 2 km × 3 km

= 6 km²

d)

Area of rectangle = l × b

= 200 cm × 70 cm

= 14000 m²

Question 2: Find the areas of the squares whose sides are:

a) 10 cm

b) 14 cm

c) 5 m

Answer:

a)

Area of square = s × s

= 10 cm × 10 cm

= 100 cm²

b)

Area of square = s × s

= 14 cm × 14 cm

= 196 cm²

c)

Area of square = s × s

= 5 m × 5 m

= 25 m²

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?

Answer:

a)

Area of rectangle = l × b

= 9 m × 6 m

= 54 m²

b)

Area of rectangle = l × b

= 17 m × 3 m

= 51 m²

c)

Area of rectangle = l × b

= 4 m × 14 m

= 56 m²

Therefore, the rectangle which has the length 4 m and breadth 14 m has the largest area.

Question 4: The area of a rectangular garden 50 m long is 300 sq m. Find the width of the garden.

Answer:

Given

Length of rectangular garden = 50 metre

Area of rectangular garden = 300 metre²

To find: Width of the garden

Let the breadth of the rectangular garden be x.

= 50 × x = 300

= x = 300/50

= x = 6

Therefore, the width of the rectangular garden is 6 metre.

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.?

Answer:

Given

Length of the rectangular plot of land = 500 m

Breadth of the rectangular plot of land = 200 m

Cost of tiling rectangular plot at 100 m² = ₹8

To find: Cost of tiling the entire rectangular plot

Area of rectangle = l × b

= 500 m × 200 m

= 100000 m²

Therefore, the area of the rectangular plot is 100000 m².

Cost of tiling rectangular plot at 100 m² = ₹8

Cost of tiling 100000 m² = ?

= 100000/100

= 1000 × 8

= ₹8000

Therefore, the cost of tiling the rectangular plot of land is ₹8000.

Question 6: A table-top measures 2 m by 1 m 50 cm. What is its area in square metres?

Answer:

Given

Length of table-top = 2 m

Breadth of table-top = 1 m 50 cm = 1.5 m

To find: Area of table top in m²

Area of rectangle = l × b

= 2 × 1.5

= 3 m²

Therefore, the area of the table-top is 3 m².

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?

Answer:

Given

Length of the room = 4 m

Breadth of the room = 3 m 50 cm = 3.5 m

To find: Carpet required to floor the room in m²

Area of rectangle = l × b

= 4 × 3.5

= 14 m²

Therefore, 14 m² of carpet is needed to cover the floor of the room.

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.

Answer:

Given

Length of the floor = 5 m

Breadth of the floor = 4 m

Length of the side of the carpet = 3 m

To find: Area of the floor than is not carpeted

Area of rectangle = l × b

= 5 m × 4 m

= 20 m²

Area of square = s × s

= 3 m × 3 m

= 9 m²

Area not carpeted = Area of floor - Area of square carpet

= 20 m² - 9 m²

= 11 m²

Therefore, 11 m² of the area of floor is not carpeted.

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?

Answer:

Given

Length of the side of flower beds = 1 m

Number of flower beds = 5

Length of the land = 5 m

Breadth of the land = 4 m

To find: The area of the remaining part of the land

Area of land = ?

Area of rectangle = l × b

= 5 m × 4 m = 20 m²

Area of one flower bed = ?

Area of square = s × s

= 1 m × 1 m = 1 m²

Area of five flower beds = 1 × 5 = 5 m²

Area of the remaining part of the land = Area of land - Area of five flower beds

= 20 m² - 5 m² = 15 m²

Therefore, the area of the remaining part of land is 15 m².

Question 10: By splitting the following figures into rectangles, find their areas (The measures are given in centimetres).

Answer:

a)

b)

Question 11: Split the following shapes into rectangles and find their areas. (The measures are given in centimetres)

Answer:

a)

b)

c)

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

Answer:

a)

Given

Tiles length = 12 cm

Tiles breadth = 5 cm

Length of rectangular region = 100 cm

Length of rectangular region = 144 cm

To find: Tiles required to fit in a rectangular region

Tile area = ?

Area of rectangle = l × b

= 12 cm × 5 cm

= 60 cm²

Rectangular region area = ?

Area of rectangle = l × b

= 144 cm × 100 cm

= 14400 cm²

Tiles required = Area of rectangular region/Area of tile

= 14400/60

= 240 tiles

Therefore, 240 tiles are required to fit in a rectangular region of length 144 cm and breadth 100 cm.

b)

Given

Tiles length = 12 cm

Tiles breadth = 5 cm

Length of rectangular region = 70 cm

Length of rectangular region = 36 cm

To find: Tiles required to fit in a rectangular region

Tile area = ?

Area of rectangle = l × b

= 12 cm × 5 cm

= 60 cm²

Rectangular region area = ?

Area of rectangle = l × b

= 70 cm × 36 cm

= 2520 cm²

Tiles required = Area of rectangular region/Area of tile

= 2520/60

= 42 tiles

Therefore, 42 tiles are required to fit in a rectangular region of length 70 cm and breadth 36 cm.

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