The document NCERT Solutions(Part - 2) - Mensuration Class 6 Notes | EduRev is a part of the Class 6 Course Mathematics (Maths) Class 6.

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**Exercise 10.2**

**Question 1**

Find the areas of the following figures by counting square:

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

**Answer 1:**

**(a)** Number of filled square = 9

∴ Area covered by squares = 9 x 1 = 9 sq. units

**(b)** Number of filled squares = 5

∴ Area covered by filled squares = 5 x 1 = 5 sq. units

**(c)** Number of full filled squares = 2

Number of half-filled squares = 4

∴ Area covered by full filled squares = 2 x 1 = 2 sq. units

And Area covered by half-filled squares =

∴ Total area = 2 + 2 = 4 sq. units

**(d)** Number of filled squares = 8

∴ Area covered by filled squares = 8 x 1 = 8 sq. units

**(e)** Number of filled squares = 10

∴ Area covered by filled squares = 10 x 1 = 10 sq. units

**(f) **Number of full filled squares = 2

Number of half-filled squares = 4

∴ Area covered by full filled squares = 2 x 1 = 2 sq. units

And Area covered by half-filled squares =

∴ Total area = 2 + 2 = 4 sq. units

**(g)** Number of full filled squares = 4

Number of half-filled squares = 4

∴ Area covered by full filled squares = 4 x 1 = 4 sq. units

And Area covered by half-filled squares =

∴ Total area = 4 + 2 = 6 sq. units

**(h) **Number of filled squares = 5

∴ Area covered by filled squares = 5 x 1 = 5 sq. units

**(i)** Number of filled squares = 9

∴ Area covered by filled squares = 9 x 1 = 9 sq. units

**(j)** Number of full filled squares = 2

Number of half-filled squares = 4

∴ Area covered by full filled squares = 2 x 1 = 2 sq. units

And Area covered by half-filled squares =

∴ Total area = 2 + 2 = 4 sq. units

**(k) **Number of full filled squares = 4

Number of half-filled squares = 2

∴ Area covered by full filled squares = 4 x 1 = 4 sq. units

And Area covered by half-filled squares

∴ Total area = 4 + 1 = 5 sq. units

**(l) **Number of full filled squares = 3

Number of half-filled squares = 10

∴ Area covered by full filled squares = 3 x 1 = 3 sq. units

And Area covered by half-filled squares

∴ Total area = 3 + 5 = 8 sq. units

**(m)** Number of full filled squares = 7

Number of half-filled squares = 14

∴ Area covered by full filled squares = 7 x 1 = 7 sq. units

And Area covered by half-filled squares

∴ Total area = 7 + 7 = 14 sq. units

**(n) **Number of full filled squares = 10

Number of half-filled squares = 16

∴ Area covered by full filled squares = 10 x 1 = 10 sq. units

And Area covered by half-filled squares

∴ Total area = 10 + 8 = 18 sq. units

**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 1:**

**(a)** Area of rectangle = length x breadth

= 3 cm x 4 cm = 12 cm^{2 }

**(b)** Area of rectangle = length x breadth

= 12 m x 21 m = 252 m^{2 }

**(c)** Area of rectangle = length x breadth

= 2 km x 3 km = 6 km^{2 }

**(d)** Area of rectangle = length x breadth

= 2 m x 70 cm

= 2 m x 0.7 m = 1.4 m^{2 }

**Question 2**

**Find the areas of the squares whose sides are:**

**(a) 10 cm**

**(b) 14 cm**

**(c) 5 m**

**Answer 2:** (a) Area of square = side x side = 10 cm x 10 cm = 100 cm^{2}

(b) Area of square = side x side = 14 cm x 14 cm = 196 cm^{2}

(c) Area of square = side x side = 5 m x 5 m = 25 m^{2}

**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 3:** **(a)** Area of rectangle = length x breadth = 9 m x 6 m = 54 m^{2 }

**(b)** Area of rectangle = length x breadth= 3 m x 17 m = 51 m^{2 }

**(c)** Area of rectangle = length x breadth= 4 m x 14 m = 56 m^{2 }

Thus, the rectangle (c) has largest area, and rectangle (b) has smallest area.

**Question 4**

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

**Answer 4:**

Length of rectangle = 50 m and Area of rectangle = 300 m^{2}

Since, Area of rectangle = length x breadth

Therefore,

Thus, the breadth of the garden is 6 m.

**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 5: **Length of land = 500 m and Breadth of land = 200 m

Area of land = length x breadth = 500 m x 200 m = 1,00,000 m^{2}

Cost of tilling 100 sq. m of land = 8

∴ Cost of tilling 1,00,000 sq. m of land = = 8000

**Question 6**

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

**Answer 6:** Length of table = 2 m

Breadth of table = 1 m 50 cm = 1.50 m

Area of table = length x breadth

= 2 m x 1.50 m = 3 m^{2}

**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 7:** Length of room = 4 m

Breadth of room = 3 m 50 cm = 3.50 m

Area of carpet = length x breadth

= 4 x 3.50 = 14m^{2}

**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 8:** Length of floor = 5 m and breadth of floor = 4 m

Area of floor = length x breadth

= 5 m x 4 m = 20 m^{2} Now, Side of square carpet = 3 m

Area of square carpet = side x side = 3 x 3 = 9 m^{2}

Area of floor that is not carpeted = 20 m^{2} – 9 m^{2} = 11 m^{2}

**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 9:** Side of square bed = 1 m

Area of square bed = side x side = 1 m x 1 m = 1 m^{2}

∴ Area of 5 square beds = 1 x 5 = 5 m^{2}

Now, Length of land = 5 m

Breadth of land = 4 m

∴ Area of land = length x breadth = 5 m x 4 m = 20 m^{2}

Area of remaining part = Area of land – Area of 5 flower beds

= 20 m^{2} – 5 m^{2} = 15 m^{2}

**Question 10**

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

**Answer 10:**

**(a)**

Area of HKLM = 3 x 3 = 9 cm^{2}

Area of IJGH = 1 x 2 = 2 cm^{2}

Area of FEDG = 3 x 3 = 9 cm^{2 }

Area of ABCD = 2 x 4 = 8 cm^{2}

Total area of the figure = 9 + 2 + 9 + 8 = 28 cm^{2 }

**(b)**

Area of ABCD = 3 x 1 = 3 cm^{2}

Area of BDEF = 3 x 1 = 3 cm^{2}

Area of FGHI = 3 x 1 = 3 cm^{2}

Total area of the figure = 3 + 3 + 3 = 9 cm^{2}

**Question 11**

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

**Answer 11: **

**(a) **

Area of rectangle ABCD = 2 x 10 = 20 cm^{2}

Area of rectangle DEFG = 10 x 2 = 20 cm^{2}

Total area of the figure = 20 + 20 = 40 cm^{2}

**(b) **

There are 5 squares each of side 7 cm.

Area of one square = 7 x 7 = 49 cm^{2 }

Area of 5 squares = 49 x 5 = 245 cm^{2 }

**(c) **

Area of rectangle ABCD = 5 x 1 = 5 cm^{2 }

Area of rectangle EFGH = 4 x 1 = 4 cm^{2 }

Total area of the figure = 5 + 4 cm^{2 }

**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 12:**

**(a) **Area of region = 100 cm x 144 cm = 14400 cm^{2}

Area of one tile = 5 cm x 12 cm = 60 cm^{2}

Thus, 240 tiles are required.

**(b) **Area of region = 70 cm x 36 cm = 2520 cm^{2}

Area of one tile = 5 cm x 12 cm = 60 cm^{2}

Thus, 42 tiles are required.

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