S.chand publication New Learning Composite mathematics solution of class 7 Chapter 14 Perimeter and Area Exercise 14B

 Exercise 14B

Question 1

Find area of  a rectangle which has the following dimensions

(a) (18×10) cm²

=180

(b) (25×12) cm²

=300

(c) (1.2×0.8) m²

=0.96 m²

Question 2

Find the area of a square whose side length equals

(a) 7² cm²

=49

(b) 18² cm²

=324

(c) (1.5)² cm²

=2.25

(d) x² cm²

Question 3

Find in hectares the area of a

(a) Rectangular farm measuring 400m by 275m

=400×275 m²

=110000 m²

=11 ha

(b) Square farm having one side 650 m

=(650)² m²

=422500 m²

=42.25 ha

Question 4

Find the length of a rectangle whose 

(a) Area=360 cm² and breadth=15 m

Length$=\frac{360}{15}$ cm

=24 cm

(b) Area=4.5 m² and breadth=1.8 m

Length $=\frac{4.8}{1.8}$ m

=2.5 m

Question 5

Find the perimeter of a square whose area is 

(a) 49 cm²

Side length of the square =√49 cm

=7 cm

Perimeter=(4×7)cm

=28 cm

Question 6

(a) Find the area of a square whose perimeter is 84

Side length of the square$=\frac{84}{4}$ cm

=21

Area of the square=(21)² cm²

=441 

(b) The perimeter of  a square field is 6 km. Find it area in hectares

6 km= 60 ha

Side length of the square field $=\frac{60}{4}$ =15 ha

∴Area of the square field =(15)² ha

=225

Question 7

Area of the plot = (80 x 40) m²

= 3200 m²

Cost of the plot = Rs (3200 x 50000)

= Rs. 160000000

Question 8

Area of the tile = (25 x 20) cm²

= 500 cm²

Area of the floor = (12 x 9) cm²

= (1200 x 900) cm²

= 1080000 cm²

No of tiles required = 1080000/500

= 2160

Question 9

Area of the square handkerchief = (35)² cm²

= 1225 cm²

3.5 m = 350 Cm

Total area of rectangular material = (70 x 350) cm²

= 24500 cm²

No of handkerchiefs = 24500/1225

=20

Question 10

Area of the floor = (6×9) m²

= 54 m²

Area of the rug = (4×7) m²

= 28 m²

Area of the floor not covered = (54-28) m²

= 26 m²

Question 11

Area of the small square = (13)² cm²

= 169 cm²

Area of the larger square = (169+56) cm²

= 225 cm²

Therefore, Side length of the larger sq = √(225 ) m

= 15 m

Question 12

Find the areas of the following figures in which all the corners are right angled and the dimensions are shown in centimeters

(a)

Figure to be added

▭ABCG, AG=BC=(18-6)=12 unit
AB=GC=(5+5)=10 unit

∴Area of ▭ABCG=(12×10)=120 sq unit

▭CDEF, EF=CD=6 unit 

FC=DE= 5

∴Area of ▭CDEF=(6×5)=30 sq unit

∴Area of figure ABDEFG=(120+30)=150 sq unit 

(b)

Figure to be added

▭ABCJ, AJ=BC=5 unit

AB=CJ=12 unit

∴Area of ▭ABCJ=(5×12)=60 sq unit

▭CDHI, CD=IH=20-(5+5)=10 unit

CI=DH=(12-9)=3 unit

∴Area of ▭CDHI=(10×3)=30 sq unit

▭ DEFG, dE=FG=5 unit

DG=EF=12 unit

∴Area of ▭DEFG=(5×12)=60 sq unit

∴Area of figure ABEFGIJ=(60+30+60) sq unit

=150

(c)

Figure to be added

▭ABCJ, AB=CJ=20 unit

AJ=BC=12 unit

∴Area of ▭ABCJ=(20×12)=240 sq unit

▭CDHI, CD=IH=(18-12)=6 unit

CI=DH=(20-6)=14 unit

∴Area of ▭CDHI=(6×14)=84 sq unit

▭EFGH, EF=GH=20 unit

EH=FG=20 unit

∴Area of ▭EFGH=(20×20)=400 sq unit

∴Area of figure ABCDEFGHIJ=(240+84+400) sq unit

=724

Question 13

A builder charges 400 per square meter to construct paths. Find the cost of laying this path. (All measurement are in metres)

Figure to be added

▭ABCD, AD=BC=1.5 m

AB=CD=5.5 m

Area of ▭ABCD=(1.5×5.5)m²

=8.25 m²

▭DEFJ, DJ=EF=(9-15) m=7.5 m

DE=JF=(5.5-4)=1.5 m

Area of ▭DEFJ

=(7.5×1.5)=11.25 m²

▭FGHI, IH=FG=1.5 m

FI=GH=4 m

Area of ▭FGHI=(1.5×4)=6 m²

Total area of the path=(8.25+11.25+6)=25.5 m²

∴Cost of lying=(25.5×400)=10200

Question 14

A wire is in the shape if a rectangular. Its length is 40 cm and breadth is 22 cm. If thee same wire is no bent in the shape of a square, what will be the measure of each side? Also, find which shape encloses more area ?

Length of rectangle=40 cm

Breadth of rectangle=22 cm

Let, the side of a square = a cm

If the same wire is rebent in the shape of a square then perimeter of a square = perimeter of rectangle

4a=2(l+b)

4a=2(40+22)

4a=2×62

4a=124

$a=\frac{124}{4}=31$

∴Side of a square=31 cm

∴Area of the rectangle=(40×22)=880 cm²

∴Area of the square=(31)² cm²

=961

∴Area of the square is more

Question 15

Figure to be added

Area of the table cover=(3.5×2.5)=8.75 m²

25 cm=0.25 m

Length of table top cover

=3.5-(0.25+0.25)m

=(3.5-0.5) m

=3 m

Breadth of the table top cover={2.5-(1.25+0.25)}m

={2.5-0.5}=2 m

∴Area of the table top cover=(3×2)m²

=6

∴Cost of polishing=(6×20)=120 

Question 16

The dimensions of  a plot are 200 m×150 m. A builder builds 3 roads which are 3m wide along the length on either side and one in the middle. On either side of the middle road he builds houses to sell. How much of the area did he use for building the houses ?

Figure to be added

Area of the plot=(200×150)=30000 m²

Area of one road=(200×3)=600 m²

Area of three road=(600×3)=1800 m²

∴Area for the houses=(30000-1800) m²

=28200  m²

Question 17

Find the area of the crossroads at right angles to each other through the centre of the field

Figure to be added

∴The required Area=Area of vertical road+Area of horizontal road+Area of center block

=(62×2)+(75×2)-(2×2)

=124+150-4

=270 sq m

Question 18

Find the area of the shaded portion. All corners are right angled

Figure to be added

The required area=2(vertical shaded area)+(middle horizontal shaded area)

=2(19.6×2)+{5.4(15-2+2)}

=2×39.2+(5.4×11)

=78.4+59.4

=137.8 sq m

Question 19

Find the cost of whitewashing the walls if a room 10m long , 6m wide and 4m high allowing 25 sq m for doors, windows etc at 50 per sq m

Length of the room=10 m

Width of the room=6 m

Height of the room=4 m

So, the area of the walls of room (i.e. area of the room except base)

=(2×10×4)+(2×6×4)

=80+48=128 sq m

∴We have to paint the wall after allowing 25 sq m for door, windows etc

So, the area of wall that have to paint

=128-25=103 sq m

∴Total cost of painting=(103×50)=5150