## 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 cm^{2}

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

Area = length x breadth = 12 × 21

= 252 m^{2}

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

Area = length x breadth = 2 × 3

= 6 km^{2}

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

Area = length x breadth = 2 × 0.70

= 1.40 m^{2}

**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 = side^{2}

= 10^{2}

= 100 cm^{2}

(b) Area of square = side^{2}

= 14^{2}

= 196 cm^{2}

(c) Area of square = side^{2}

= 5^{2}

=25 cm^{2}

**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 m^{2}

(b) Area of rectangle = l × b

= 17 × 3

= 51 m^{2}

(c) Area of rectangle = l × b

= 4 × 14

= 56 m^{2}

Area of rectangle 56 m^{2} i.e (c) is the largest area and area of rectangle 51 m^{2} 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 m^{2}

∴ 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 m^{2}

## 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 m^{2}

## 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 m^{2}

Area of square carpet = 3 × 3

= 9 m^{2}

Area of floor that is not carpeted = 20 – 9

= 11 m^{2}

∴ Area of the floor that is not carpeted is 11 m^{2}

## 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 m^{2}

Area of 5 square bed = 1 × 5

= 5 m^{2}

Area of land = 5 × 4

= 20 m^{2}

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

= 20 – 5

= 15 m^{2}

∴ Remaining part of the land is 15 m^{2}

## 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 cm^{2}

(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 cm^{2}

Area of b rectangle = 2 × 1

= 2 cm^{2}

Area of c rectangle = 5 × 1

= 5 cm^{2}

Total area = 2 + 2 + 5

= 9 cm^{2}

## 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 cm^{2}

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 cm^{2}

Area of one tile = 5 × 12

= 60 cm^{2}

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

= 2520 / 60

= 42

Hence, 42 tiles are needed.