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**Brilliant’s Composite Mathematics Class 6 Solutions Chapter 17 Area**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Brilliant’s Composite Mathematics Class 6 Math Book, Chapter 17, Area. Here students can easily find step y step solutions of all the problems for Area, Exercise 17.1 and 17.2 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.

**Area Exercise 17.1 Solution**

**Question no – (1)**

**Solution :**

**(i)** Given, length = 36 cm

breadth 25 cm

= (30 × 25) = 900 cm^{2}

**(ii)** Given, length = 37.6 cm

breadth 14.5 cm

= (3.6 × 145) 545.2 cm^{2}

**(iii)** Given, length 14.5

breadth 7.9 m

= (14.5 × 7) = 114.55 m^{2}

**(iv)** Given, length = 15.7

breadth = 85 m.

= (15.7 × 85) = 1334.5 m^{2}

**Question no – (2) **

**Solution :**

= area of a square is – (side)^{2}

**(i) Side = 17 cm**

= (17)^{2} = 289 cm^{2}

**(ii) Side 2.3 cm**

= (2.3)^{2} = 5.29 cm^{2}

**(iii) Side = 1 m 20 cm**

= (1.2)^{2} = 1.44 m^{2}

**(iv) Diagonal 18 cm**

= side = diagonal/1√2 = 18/√2

Area = (18/12)

= 18 × 18/2 × 2

= 162 cm^{2}

**Question no – (3)**

**Solution :**

= 7 dm = 7 × 10 cm = 70 cm

Area = (70 × 39) cm^{2}

= 2730 cm^{2}

**Question no – (4)**

**Solution :**

= 135 cm 1.35 m

Area – (9 × 1.35)m^{2}

= 12.15 m^{2}

**Question no – (5)**

**Solution :**

= 12m 20 cm = 12.2 m

Area = (12.2 × 12.2)m^{2 }

= 148.84 m^{2}

**Question no – (6)**

**Solution :**

= 7.5 dam = 7.5 × 10 = 75m

Area = (75 × 16.5)m^{2}

= 1237.5 m^{2}

**Question no – (7)**

**Solution :**

= 12.4 dam = 124/10 × 10 m = 124 m

**∴** Area = (124)^{2}

= 15376 m^{2}

**Question no – (8)**

**Solution :**

= 1225 are = 1225 × 100m^{2}

= 122500 m^{2}

**∴** Side = √122500

= √35 × 35 × 100

= 350 m

**Question no – (9)**

**Solution :**

= 62 m 5 dm = 62 m 50 cm = 62.5 m

**∴** Area = (62.5)^{2} m^{2} = 3906.25

Need of square metres,

= (10000 – 39065)m^{2}

= 6093.75

**Question no – (10)**

**Solution :**

= Area of the room = (16.5 × 5.5) = 9075 m^{2}

**∴** Cost of carpeting,

= (2 × 90.75)

= 181.5 rupees

**Question no – (11)**

**Solution :**

= Area of the floor = (10×6) = 6 m^{2}

= Wide of carpet = 7.5 cm = 75/100 m

**∴** Carpet need = 60/75/100

= 60 × 100/75

= 80 m

**Question no – (12)**

**Solution :**

= Area = 5.3824 hectares = 53824 m^{2}

= Side = √53824

= √232 × 232

= 232

= Perimeter = 4 × 232 = 928

**∴** Cost = 928 × 1.50 = 139^{2}

**Question no – (13)**

**Solution :**

Area of the floor = 5.25/100 × 4.5/10

= 225/8 = m^{2}

**∴** Carpet need,

= 189/8 × 100/125

= 189/10

= 1.89 m

**Question no – (14)**

**Solution :**

Area of carpet – 32 m 75 cm × 80 cm

= 32.75 m × 0.8 cm

= 26.2 m^{2}

Cost = (12 × 26.2)

= 314.40

**Question no – (15)**

**Solution :**

Length – 52 m 60 cm = 52.6 m

Breadth – 30 40 cm = 30..4 m

Perimeter = 2 × (52.6 + 30.4) = 2 × 83.0= 166 m

Cost = 166 × 75 = 1245

**Question no – (16)**

**Solution :**

Area of the rood = (9.68 × 6.2) m^{2} – 60.016 m^{2}

Area of granite tiles,

= (22 × 10) = 220 cm^{2}

= 220/100 × 100 m^{2}

= 0.022 m^{2}

**∴** Number of tiles

= 60.016/0.022

= 2728 tiles

Now the Cost,

= 2728 × 3.50 = 9548

**Question no – (17)**

**Solution :**

Area = 6607.5 = 88 m^{2}

Breadth = 8 m

**∴** Length = 88/8 = 11 m

**Question no – (18)**

**Solution :**

Area of carpet,

= 3 m × 2 m

= 6m^{2}

Area of hall,

= 30 × 12

= 360 m^{2}

Number of carpets,

= 360/6

= 60 carpets

**Question no – (19)**

**Solution :**

= Let, length – 3x, breadth – 4x

**∴** 3x × 4x = 432

= 12×^{2} = 432

= x^{2} = 342/12

= x √36

= 6

**∴** Length – 18 m and breadth – 24 m

**∴** Perimeter,

= 2 × (18 + 24)

= 2 × 42

= 84 m

**Question no – (20)**

**Solution :**

Breadth = 45/9 = 5 m

**∴** Perimeter,

= 2 (9 + 5)

= 2 × 14

= 28 m

**Question no – (21)**

**Solution :**

Let, the side of the given square be x cm

**∴** Side of the new square = y = x/2

**∴** x^{2} = 36

= x = 6 m

= y = x/2 = 6/2

= 3 m

Thus, the area of the square 3 m.

**Question no – (22)**

**Solution :**

**(a) **side – √40000 = 200 m

Perimeter – 4 × 200 = 800 m

Time taken in one round,

= 800/6000 × 60

= 8 min

For 3 round time taken,

= 3 × 8

= 24 min

**(b) **Cost of fencing,

= 800 × 2.80

= 224 Rs

**Question no – (23)**

**Solution :**

Let, the breadth of hall = x m

Length = x + 12 m

**∴** Perimeter of hall,

= 2 (x + x + 12) = 128

= 2x + 12 = 64

= 2x = 64 – 12

= x 52/2 = 26 m

**∴** Area of hall,

= x × (x + 12)

= 26 × 38

= 988 m^{2}

**Area Exercise 17.2 Solution **

**Question no – (1)**

**Solution : **

**Length of without path,**

= 100 – (2 × 8)

= 100 – 16

= 48 m

**Wide of path,**

= 80 – (2 × 8)

= 80 – 16

= 64 m

**Area of count y,**

= 100 × 80

= 8000 m^{2}

**Area of without path,**

= 84 × 64

= 5376

= 2624 m^{2}

**Question no – (2)**

**Solution :**

**Area of rectangular plot,**

= 40 × 25

= 1000 m^{2}

**Length of without gravel walk**

= 40 + (2 × 1.5)

= 40 + 3 = 43 m^{2}

**Wide of without gravel walk,**

= 28 × 43

= 1204 m^{2}

**Area of the walk,**

= 1204 – 1000

= 204 m^{2}

**Question no – (3)**

**Solution :**

**Area of rectangular plot,**

= (120 × 50)

= 6000 m^{2}

**Length without path,**

= 120 – (2 × 10)

= 120 – 20

= 100 m

**Wide without path**

= 50 – (20 × 10)

= 50 – 20

= 30 m

**Area without path,**

= 100 × 30

= 3000 m^{2}

**Area of path,**

= 6000 – 3000

= 3000 m^{2}

**Cost,**

= 300 × 067

= 2010 Rs

**Question no – (4)**

**Solution :**

**Area of the rectangular garden,**

= (450 × 300)

= 13500 m^{2}

**∴**** length without path**

= 450 – (2 × 5)

= 458 – 10

= 440 m

**∴**** Wide without path,**

= 300 – (2 × 5)

= 300 – 10

= 290

**∴**** Area without part,**

= (44 × 290)

= 127600 m^{2}

**∴**** Area of path,**

= 135000 – 12600

= 7400 m^{2}

**∴**** Cost,**

= 7400 × 1.40

= 10360 Rs

**Question no – (5)**

**Solution :**

**Area of the path to length,**

= 90 × 3

= 270 m^{2}

**Area of path to breadth,**

= 60 × 3

= 180 m^{2}

**Area of common place,**

= 3 × 3

= 9m^{2}

**∴**** Area of path,**

= 270 + 180 – 9

= 441m^{2}

**Question no – (6)**

**Solution :**

**Let, the side of square = x m**

**Then the area of path,**

= (x + 6)^{2} – x^{2} = 14520

= (x + 6 + x) (x + 6 – x) = 14520

= (2x + 6) 6 = 14520

= 2x + 6 = 14520

= 2x = 2420 – 6

= x = 2414/2 = 1207

**∴**** Area,**

= x^{2} = 1207 × 1207

= 1256849 m^{2}

**Question no – (7)**

**Solution : **

**Area of the saree,**

= 15 × 1.25/10 25/4

= 6.25 m^{2}

= 6.25/100 × 100 × 100 m^{2}

= 62500 cm^{2}

**Area of without border,**

= [(500 – 50) × (125 – 50)]

= 450 × 75

= 33750 cm^{2}

**Area of order,**

= 2500 – 33750

= 28750

**Cost of printing the border,**

= 28750/100 × 1.50

= 431.25 Rs

**Question no – (8)**

**Solution :**

**Area of path parallel length,**

= 40 × 1.5

= 60 m^{2}

**∴**** Area of path parallel to length wide,**

= 30 × 2

= 60 m^{2}

**∴**** Area of common path,**

= 1.5 × 2

= 3 m^{2}

**∴**** Area of path,**

= 60 + 60 – 3

= 117 m^{2}

**∴**** Cost of gravelling the paths,**

= 117 × 3.50

= 409.50 Rs

**Question no – (9)**

**Solution :**

**Area of plot,**

= 60 × 40

= 2400 m^{2}

**∴**** Area without path,**

= [60 – 8) × (40 – 8)]

= 52 × 32

= 1664 m^{2}

**∴**** Area of path,**

= 2400 – 1664

= 736 m^{2}

**∴**** Cost of constructing path,**

= 736 × 8

= 5888 Rs

**∴**** Cost of grass portion,**

= 1664/100 × 350

= 5824 Rs

**Question no – (10)**

**Solution :**

**Area let rectangular field,**

= (36 × 30)

= 1080 m^{2}

**Area without path,**

= 1080 – 360

= 720

**Let, width path – x m**

= (36 – 2x) × (30 – 2x) = 720

= (18 – x) × (15 –x) = 180

= 270 – 15x – 18x + x^{2} = 180

= x^{2} – 33x + 270 – 180 = 0

= x^{2} – 33x + 90 = 0

= x^{2} – 30x – 3x + 90 = 0

= x (x – 30) – 3 (x – 30) = 0

= x – 3 = 0

= x = 3

Or, x – 30 = 0

= x = 30 [Not possible]

**Question no – (11)**

**Solution :**

Let, the side of the square field – x

**∴** Side with path,

= x + 2 × 3

= x + 6

**∴** (x + 6)^{2} – x^{2} = 29040

= (x + 6 – x) (x + 6 + x) = 29040

= 2x + 6 = 29040/6

= 2x =- 4840 – 6 = 4834

= x = 4834/2 = 2417

**∴** Area of field,

= (24 17)^{2}

= 5841889

**Next Chapter Solution : **

👉 Chapter 18 👈