# Brilliant’s Composite Mathematics Class 6 Solutions Chapter 17

## 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

= (30 × 25) = 900 cm2

(ii) Given, length = 37.6 cm

= (3.6 × 145) 545.2 cm2

(iii) Given, length 14.5

= (14.5 × 7) = 114.55 m2

(iv) Given, length = 15.7

= (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)m

= 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

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

= 12×2 = 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

= 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 :

Updated: June 12, 2023 — 7:49 am