Exercise 10.3 - Chapter 10 Mensuration class 6 ncert solutions Maths - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

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:

It is known that,

Area of rectangle = Length × Breadth

(a) l = 3 cm

b = 4 cm

Area = l × b = 3 × 4 = 12 cm²

(b) l = 12 m

b = 21 m

Area = l × b = 12 × 21 = 252 m²

(c) l = 2 km

b = 3 km

Area = l × b = 2 × 3 = 6 km²

(d) l = 2 m

b = 70 cm = 0.70 m

Area = l × b = 2 × 0.70 = 1.40 m²

Question 2:

Find the areas of the squares whose sides are:

(a) 10 cm (b) 14 cm (c) 5 m

Answer:

It is known that,

Area of square = (Side)²

(a) Side = 10 cm

Area = (10)² =100 cm²

(b) Side = 14 cm

Area = (14)² = 196 cm²

(c) Side = 5 m

Area = (5)² = 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:

It is known that,

Area of rectangle = Length × Breadth

(a) l = 9 m

b = 6 m

Area = l × b = 9 × 6 = 54 m²

(b) l = 17 m

b = 3 m

Area = l × b = 17 × 3 = 51 m²

(c) l = 4 m

b = 14 m

Area = l × b = 4 × 14 = 56 m²

It can be seen that rectangle (c) has the largest area and rectangle (b) has the smallest area.

Question 4:

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

Answer:

Let the breadth of the rectangular garden be b.

l = 50 m

Area = l × b = 300 square m

50 × b = 300

b = 

Question 5:

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

Answer:

Area of rectangular plot = 500 × 200 = 100000 m²

Cost of tiling per 100 m² = Rs 8

Cost of tiling per 100000 m² =  = Rs 8000

Question 6:

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

Answer:

Length (l) = 2 m

Breadth (b) = 1 m 50 cm =

Area = l × b = 2 × 1.5 = 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:

Length (l) = 4 m

Breadth (b) = 3 m 50 cm = 3.5 m

Area = l × b = 4 × 3.5 = 14 m²

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:

Length (l) = 5 m

Breadth (b) = 4 m

Area of floor = l × b = 5 × 4 = 20 m²

Area covered by the carpet = (Side)² = (3)² = 9 m²

Area not covered by the carpet = 20 − 9 = 11 m²

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:

Area of the land = 5 × 4 = 20 m²

Area occupied by 5 flower beds = 5 × (Side)² = 5 × (1)² = 5 m²

∴ Area of the remaining part = 20 − 5 = 15 m²

Question 10:

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

(a) (b)

Answer:

(a) The given figure can be broken into rectangles as follows.

Area of 1^st rectangle = 4 × 2 = 8 cm²

Area of 2^nd rectangle = 6 × 1 = 6 cm²

Area of 3^rd rectangle = 3 × 2 = 6 cm²

Area of 4^th rectangle = 4 × 2 = 8 cm²

Total area of the complete figure = 8 + 6 + 6 + 8 = 28 cm²

(b) The given figure can be broken into rectangles as follows.

Area of 1^st rectangle = 3 × 1 = 3 cm²

Area of 2^nd rectangle = 3 × 1 = 3 cm²

Area of 3^rd rectangle = 3 × 1 = 3 cm²

Total area of the complete figure = 3 + 3 + 3 = 9 cm²

Question 11:

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

Answer:

(a) The given figure can be broken into rectangles as follows.

Area of 1^st rectangle = 12 × 2 = 24 cm²

Area of 2^nd rectangle = 8 × 2 = 16 cm²

Total area of the complete figure = 24 + 16 = 40 cm²

(b) The given figure can be broken into rectangles as follows.

Area of 1^st rectangle = 21 × 7 = 147 cm²

Area of 2^nd square = 7 × 7 = 49 cm²

Area of 3^rd square = 7 × 7 = 49 cm²

Total area of the complete figure = 147 + 49 + 49 = 245 cm²

(c) The given figure can be broken into rectangles as follows.

Area of 1^st rectangle = 5 × 1 = 5 cm²

Area of 2^nd rectangle = 4 × 1 = 4 cm²

Total area of the complete figure = 5 + 4 = 9 cm²

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) Total area of the region = 100 × 144 = 14400 cm²

Area of one tile = 12 × 5 = 60 cm²

Number of tiles required =

Therefore, 240 tiles are required.

(b) Total area of the region = 70 × 36 = 2520 cm²

Area of one tile = 60 cm²

Number of tiles required =

Therefore, 42 tiles are required.