SChand Composite Mathematics Class 7 Chapter 14 Perimeter and Area Exercise 14A

 Exercise 14 A

Question 1 

Copy and complete the following table: 

$\begin{array}{c|c|c|c|}\hline \text { Length } & \text { Breadth } & \text { Area } & \text { Perimeter } \\\hline \text { (P) } 5 \mathrm{~m} & (3 \mathrm{~m}) & 15 \mathrm{~m}^{2} & 116 \mathrm{~m})\\\text { (ii) } 5 \mathrm{~cm} & (7 \mathrm{~m}) & \left(35 \mathrm{~m}^{2}\right) & 24\mathrm{~cm} \\\text { (iii) }(15 \mathrm{~cm}) & 9.5 \mathrm{~cm} & 142.5 \mathrm{~cm}^{2} & 49\mathrm{~cm} \\\text { (iv) }(16 \mathrm{~cm}) & 30 \mathrm{~cm} & 480 \mathrm{~cm}^{2} & (92\mathrm{~cm}) \\\hline\end{array}$

Question 2

Find (a) the area (b) the perimeter of the square PQRS if. 

 (i) $P Q=Q R=20 \mathrm{~cm} \quad$ Area $=P Q \times Q R=20 \times 20=400 \mathrm{~cm}^{2}$

Perimeter $=4 \times$ side $=4 \times 20=80 \mathrm{~cm}$

(ii) $P Q=Q R=1.2 \mathrm{~m} \quad$ Area $=P Q \times Q R=1.2 \times 1.2=1.14 \mathrm{~m}^{2}$

Perimeter $=4 \times$ side $=4 \times 1.2=4.8 \mathrm{~m}$

Question 3

Find the perimeter of the following squares: 

(i) Area = $=64 \mathrm{~cm}^{2}$

Sol:

$\begin{aligned} S^{2} &=64 \\ \text { Side } &=8 \mathrm{~cm} \end{aligned}$

Perimeter $=4 \times$ side

$=4 \times 8$

$=32 \mathrm{~cm}$

(ii) area $=196 \mathrm{~cm}^{2}$

Sol: $s^{2}=196$

Taking square root 

Side = 14 cm

Perimeter = $4 \times$ side

$=4 \times 14$

$=56 \text { Cm}$

(iii) Area = $2.25 \mathrm{m}^{2}$

Sol: $s^{2}=$ 2.25 

Taking square root side = 1.5m

P= $4 \times 1.5$

=6m

Question 4

(i) The perimeter of the square is 20cm . find its area . 

Sol: Side of square = $\frac{1}{4} \times$ perimeter of square

$=\frac{1}{4} \times 20=5 \mathrm{~cm}$

Area of square = Side $\times$ side 

$=5 \times 5=25$ $\operatorname{cm}^{2}$

(ii) The perimeter of a square field in 3km. Find its area in hectares. 

Sol: Side = $\frac{1}{4} \times$ perimeter

$=\frac{1}{4} \times 8=2 \mathrm{~km}$ or 2000m

Area of square = $side \times side$

$=2,000 \times 2000=40,00,000 \mathrm{~m}^{2}$

1 hectare = 10000 $m^{2}$

$1 m^{2}=\frac{1}{10000}$ Hectare 

$\frac{4000000}{10000}$= 400 hectare