Brilliant’s Composite Mathematics Class 6 Solutions Chapter 17

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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 cm²

(ii) Given, length = 37.6 cm

breadth 14.5 cm

= (3.6 × 145) 545.2 cm²

(iii) Given, length 14.5

breadth 7.9 m

= (14.5 × 7) = 114.55 m²

(iv) Given, length = 15.7

breadth = 85 m.

= (15.7 × 85) = 1334.5 m²

Question no – (2) 

Solution :

= area of a square is – (side)²

(i) Side = 17 cm

= (17)² = 289 cm²

(ii) Side 2.3 cm

= (2.3)² = 5.29 cm²

(iii) Side = 1 m 20 cm

= (1.2)² = 1.44 m²

(iv) Diagonal 18 cm

= side = diagonal/1√2 = 18/√2

Area = (18/12)

= 18 × 18/2 × 2

= 162 cm²

Question no – (3)

Solution :

= 7 dm = 7 × 10 cm = 70 cm

Area = (70 × 39) cm²

= 2730 cm²

Question no – (4)

Solution :

= 135 cm  1.35 m

Area – (9 × 1.35)m²

= 12.15 m²

Question no – (5)

Solution :

= 12m 20 cm = 12.2 m

Area = (12.2 × 12.2)m² 

= 148.84 m²

Question no – (6)

Solution :

= 7.5 dam = 7.5 × 10 = 75m

Area = (75 × 16.5)m²

= 1237.5 m²

Question no – (7)

Solution :

= 12.4 dam = 124/10 × 10 m = 124 m

∴ Area = (124)²

= 15376 m²

Question no – (8)

Solution :

= 1225 are = 1225 × 100m²

= 122500 m²

∴ 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 m² = 3906.25

Need of square metres,

= (10000 – 39065)m²

= 6093.75

Question no – (10)

Solution :

= Area of the room = (16.5 × 5.5) = 9075 m²

∴ Cost of carpeting,

= (2 × 90.75)

= 181.5 rupees

Question no – (11)

Solution :

= Area of the floor = (10×6) = 6 m²

= 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 m²

= Side = √53824

= √232 × 232

= 232

= Perimeter = 4 × 232 = 928

∴ Cost = 928 × 1.50 = 139²

Question no – (13)

Solution :

Area of the floor = 5.25/100 × 4.5/10

= 225/8 = m²

∴ 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 m²

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) m² – 60.016 m²

Area of granite tiles,

= (22 × 10) = 220 cm²

= 220/100 × 100 m²

= 0.022 m²

∴ Number of tiles

= 60.016/0.022

= 2728 tiles

Now the Cost,

= 2728 × 3.50 = 9548

Question no – (17)

Solution :

Area = 6607.5 = 88 m²

Breadth = 8 m

∴ Length = 88/8 = 11 m

Question no – (18)

Solution :

Area of carpet,

= 3 m × 2 m

= 6m²

Area of hall,

= 30 × 12

= 360 m²

Number of carpets,

= 360/6

= 60 carpets

Question no – (19)

Solution :

= Let, length – 3x, breadth – 4x

∴ 3x × 4x = 432

= 12ײ = 432

= x² = 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

∴ x² = 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 m²

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 m²

Area of without path,

= 84 × 64

= 5376

= 2624 m²

Question no – (2)

Solution :

Area of rectangular plot,

= 40 × 25

= 1000 m²

Length of without gravel walk

= 40 + (2 × 1.5)

= 40 + 3 = 43 m²

Wide of without gravel walk,

= 28 × 43

= 1204 m²

Area of the walk,

= 1204 – 1000

= 204 m²

Question no – (3)

Solution :

Area of rectangular plot,

= (120 × 50)

= 6000 m²

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 m²

Area of path,

= 6000 – 3000

= 3000 m²

Cost,

= 300 × 067

= 2010 Rs

Question no – (4)

Solution :

Area of the rectangular garden,

= (450 × 300)

= 13500 m²

∴ 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 m²

∴ Area of path,

= 135000 – 12600

= 7400 m²

∴ Cost,

= 7400 × 1.40

= 10360 Rs

Question no – (5)

Solution :

Area of the path to length,

= 90 × 3

= 270 m²

Area of path to breadth,

= 60 × 3

= 180 m²

Area of common place,

= 3 × 3

= 9m²

∴ Area of path,

= 270 + 180 – 9

= 441m²

Question no – (6)

Solution :

Let, the side of square =  x m

Then the area of path,

= (x + 6)² – x² = 14520

= (x + 6 + x) (x + 6 – x) = 14520

= (2x + 6) 6 = 14520

= 2x + 6 = 14520

= 2x = 2420 – 6

= x = 2414/2 = 1207

∴ Area,

= x² = 1207 × 1207

= 1256849 m²

Question no – (7)

Solution : 

Area of the saree,

= 15 × 1.25/10  25/4

= 6.25 m²

= 6.25/100 × 100 × 100 m²

= 62500 cm²

Area of without border,

= [(500 – 50) × (125 – 50)]

= 450 × 75

= 33750 cm²

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 m²

∴ Area of path parallel to length wide,

= 30 × 2

= 60 m²

∴ Area of common path,

= 1.5 × 2

= 3 m²

∴ Area of path,

= 60 + 60 – 3

= 117 m²

∴ Cost of gravelling the paths,

= 117 × 3.50

= 409.50 Rs

Question no – (9)

Solution :

Area of plot,

= 60 × 40

= 2400 m²

∴ Area without path,

= [60 – 8) × (40 – 8)]

= 52 × 32

= 1664 m²

∴ Area of path,

=  2400 – 1664

= 736 m²

∴ 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 m²

Area without path,

=  1080 – 360

= 720

Let, width path – x m

= (36 – 2x) × (30 – 2x)  = 720

= (18 – x) × (15 –x) = 180

= 270 – 15x – 18x + x² = 180

= x² – 33x + 270 – 180 = 0

= x² – 33x + 90 = 0

= x² – 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 – x² = 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 👈