**Mensuratio****n Class 6 Ex. 10.3**

**Mensuration, Ncert Class 6, Chapter 10, Exercise 10.2 Math Free Solution.**

**Exercise 10.3**

**Question 1:- Find the areas; of the rectangle 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 1: –**

(a) Length of the rectangle = 3cm

Breadth of the rectangle = 4cm

Since, the area of the rectangle = length x breadth

= 3 cm x 4 cm

= 12 square cm.

(b) Length of the rectangle = 12m

Breadth of the rectangle = 21m

Since, the area of the rectangle = length x breadth

= 12 m x 21 m

= 252 square m.

(c) Length of the rectangle = 2km

Breadth of the rectangle = 3km

Since, the area of the rectangle = length x breadth

= 2 km x 3 km

= 6 square km

(d) Length of the rectangle = 2m

Breadth of the rectangle = 70cm = 0.70m

Since, the area of the rectangle = length x breadth

= 2 m x 0.70 m

= 1.4 square m

**Question 2:- Find the areas; of the square whose sides are :-**

**(a) 10 cm**

**(b) 14 cm**

**(c) 5 m**

**Solution 2:- **

(a) The side of the square = 10 cm;

Since, the area of the square = Side x Side; [By the formula of area of square]

= 10 cm x 10 cm

= 100 square cm.

(b) The side of the square = 14 cm;

Since, the area of the square = Side x Side;

= 14 cm x 14 cm

= 196 square cm.

(c) The side of the square = 5 cm;

Since, the area of the square = Side x Side;

= 5 m x 5 m

= 25 square m.

**Question 3 :- The length and breadth of three-rectangle 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 area?**

**Solution 3:-**

(a) Length of the rectangle = 9m

Breadth of the rectangle = 6m

Since, the area of the rectangle = length x breadth

= 9 m x 6 m

= 54 square m.

(b) Length of the rectangle = 17m

Breadth of the rectangle = 3m

Since, the area of the rectangle = length x breadth

= 17 m x 3 m

= 51 square m.

(c) Length of the rectangle = 4m

Breadth of the rectangle = 14m

Since, the area of the rectangle = length x breadth

= 4 m x 14 m

= 56 square m

The rectangle (c) has the largest area, i.e., 56 square meter and rectangle (b) has the smallest area, i.e., 51 square meter.

**Question 4 :- ****The area; of a rectangular-garden 50m long is 300 square m. Find the width; of the garden.**

**Solution 4:-**

Length of the rectangle garden = 50m

Breadth of the rectangle = 300 square meter

Since, the area of the rectangle = length x breadth

300 = 50 m x breadth

Breadth = 300/50 m = 6 m.

Hence, the breadth of the garden is 6m.

**Question 5 :- What is the cost of tiling a rectangular-plot of land 500m long and 200m wide at the rate of ₹8 per hundred square m?**

**Solution 5:- **

Length of the rectangle plot = 500m

Breadth of the rectangle plot = 200m

Since, the area of the rectangle = length x breadth

= 500 m x 200 m

= 1,00,000 square m

Now rate of tiling the plot = ₹8 per 100 square meter

Cost of tiling 100 square meter land = ₹8

Cost of tiling 1,00,000 square meter land = ₹(8/100) x 1,00,000 = ₹8000

Hence the required cost = ₹8000.

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

**Solution 6:-**

the length of the table-top = 2 m

the breadth of the table-top = 1m 50cm or 1.50 m

Since, the area of the table-top = length x breadth

= 2 m x 1.50 m

= 3 square meter

Hence, the area of table-top = 3 square metre.

**Question 7 :- A room is 4m-long and 3m 50cm wide. How many square-metres of carpet is needed to cover the floor of the room?**

**Solution 7:-**

The length of the room is = 4 m

The breadth of the room = 3m 50cm = 3.5 m

Since, the area of the room = length x breadth

= 4 m x 3.5 m = 14 square meter

Hence, the area of the carpet needed = 14 square meter.

**Question 8 :- A floor is 5m long and 4m wide. A square-carpet of sides 3m is laid on the floor. Find the area of the floor that is not carpeted ?**

**Solution 8:- **

The length of the floor = 5m

The breadth of the floor = 4 m

Since, the area of the floor = length x breadth

= 5m x 4m = 20 square meter;

Side of the square-carpet = 3m

Since, the area of the square-carpet = side x side

= 3m x 3m = 9 square meter

So, the area of the floor which is not carpeted = 20 sq m – 9 sq m = 11 square meter.

**Question 9 :- Five-square; flower beds each of side 1m are dug on a piece of land 5m long and 4m wide. What is the area; of the remaining part of the land?**

**Solution 9:- **

The side of the one square flower-bed = 1 m.

Since, the area of 1 square flower bed = 1m x 1m = 1 square meter.

So, the area of 5 square flower beds = 1 sq m x 5 = 5 square meter.

Now, the length of a piece of land = 5m;

the breadth of the land = 4 m

Since, the area of the land = length x breadth

=5m x 4m = 20 square meter

So, the area of the remaining part of the land = 20 sq m – 5 sq m = 15 square meter.

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

**Solution 10:-**

(a) Splitting the given figure into 4 parts

Since, the area of the rectangle = length x breadth;

The area of HKLM = 3 x 3 = 9 square cm

The area of HIJG = 1 x 2 = 2 square cm

The area of GFED = 3 x 3 = 9 square cm

The are of ABCD = 2 x 4 = 8 square cm

So, the total area of the whole figure :-

= 12 sq cm + 6 sq cm + 4 sq cm + 6 sq cm = 28 square cm.

(b) Splitting the given figure into 4 parts, we get

The area of ABCD = 3 x 1 = 3 square cm

The area of BFED = 3 x 1 = 3 square cm

The area of FGHL = 3 x 1 = 3 square cm

So, the total area of the given figure :-

= 3 sq cm + 3 sq cm + 3 sq cm = 9 square cm.

**Question 11 :- Split the following shape into rectangle and find their area (The measures are given in centimetres).**

**Solution 11:- **

(a) Splitting the given figure into 2 parts , we get

Since, the area of the rectangle = length x breadth

The area of ABCD = 10 x 2 = 20 square cm

The are of DGFE = 10 x 2 = 20 square cm

So, the total area of the whole given figure = 20 sq cm + 20 sq cm = 40 square cm.

(b) Splitting the given figure :-

Since, the Area of square = side x side

= 7 cm x 7 cm = 49 square cm

Since, the given figure has 5 identical square of side 7 cm

So, the total area of the whole figure

= 49 sq cm + 49 sq cm + 49 sq cm + 49 sq cm + 49 sq cm = 245 sq cm.

(c) Splitting the given figure into 2 parts , we get

Since, the area of the rectangle = length x breadth

The area of ABCD = 5 x 1 = 5 square cm

The are of EGHF = 4 x 1 = 4 square cm

So, the total area of the whole figure = 5 sq cm + 4 sq cm = 9 square cm.

**Question 12 :- How many tiles; whose length and breadth are 12cm and 5cm respectively will be needed to fit in a rectangular-region whose length and breadth are respectively : –**

**(a) 100cm and 144cm;**

**(b) 70cm and 36cm;**

**Solution 12:- **

Length of the one tile = 12 cm

Breadth of the one tile = 5 cm

Since, the area of the rectangle = length x breadth

= 12 cm x 5 cm = 60 square cm

(a) The length of the rectangular region = 144 cm

The breadth of the rectangular region = 100 cm

Since, the area of the rectangular region = length x breadth

= 144 cm x 100 cm

= 14,400 square cm

So, the number of tiles needed to cover the whole rectangular region

= 14400 square cm ÷ 60 square cm

= 240 tiles.

(b) The length of the rectangular region = 70 cm

The breadth of the rectangular region = 36 cm

Since, the area of the rectangular region = length x breadth

= 70 cm x 36 cm

= 2,520 square cm

So, the number of tiles needed to cover the whole rectangular region

= 2,520 sq cm ÷ 60 sq cm

= 42 tiles.

**Chapter 10 Mensuration Class 6 Exercise. 10.3 for Free**

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