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
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