Question

1. Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 750 m and breadth 350 m are parallel to its sides. Find the area of the roads. Also, find the area of the park excluding cross roads. Convert the area in hectares. [1 hectare = 10000 m²]

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Answer 1

$\large\underline{\sf{Solution-}}$

Given that, Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 750 m and breadth 350 m are parallel to its sides.

Let assume that ABCD be a rectangular park such that AB = 750 m and BC = 350 m

So,

$\rm \: Area_{(ABCD)} = Length \times Breadth$

$\rm \: Area_{(ABCD)} = AB \times BC$

$\rm \: Area_{(ABCD)} = 750 \times 350$

$\rm\implies \:Area_{(ABCD)} = 262500 \: {m}^{2}$

Now, Let further assume that EFGH and PQRS be the two cross roads of width 10 m, running parallel to AB and BC.

Dimensions of EFGH

• Length, EF = 750 m

• Breadth, FG = 10 m

So,

$\rm \: Area_{(EFGH)} = Length \times Breadth$

$\rm \: Area_{(EFGH)} = EF \times FG$

$\rm \: Area_{(EFGH)} = 750 \times 10$

$\rm\implies \:\rm \: Area_{(EFGH)} = 7500 \: {m}^{2}$

Dimensions of PQRS

• Length, PQ = 350 m

• Breadth, QR = 10 m

So,

$\rm \: Area_{(PQRS)} = Length \times Breadth$

$\rm \: Area_{(PQRS)} = PQ \times QR$

$\rm \: Area_{(PQRS)} = 350 \times 10$

$\rm\implies \:\rm \: Area_{(PQRS)} = 3500 \: {m}^{2}$

Now,

$\rm \: Area_{(cross\:roads)}$

$\rm \: = \: Area_{(EFGH)} + Area_{(PQRS)} - Area_{(square \: KLMN)}$

$\rm \: = \: 7500 + 3500 - 10 \times 10$

$\rm \: = \: 11000 - 100$

$\rm \: = \: 10900 \: {m}^{2}$

$\rm \: = \: \dfrac{10900}{10000} \: hectares$

$\rm \: = \: 1.09 \: hectares$

So,

$\color{green}\rm\implies \:\boxed{ \rm{ \:Area_{(cross\:roads)} \: = \: 1.09 \: hectares \: \: }}$

Now,

$\rm \: Area_{(park \: without \: cross \: roads)}$

$\rm \: = \: Area_{(ABCD)} - Area_{(cross\:roads)}$

$\rm \: = \: 262500 - 10900$

$\rm \: = \: 251600 \: {m}^{2}$

$\rm \: = \: \dfrac{251600}{10000} \: hectares$

$\rm \: = \: 25.16 \: hectares$

Hence,

$\color{green}\rm\implies \:\boxed{ \rm{ \: Area_{(park \: without \: cross \: roads)} = 25.16 \: hectares \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$