Question

A rectangular park is 40 m long and 30 m wide. A path of 5 m runs round the inside of the park. Find the area of the path​

Answer 1

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

Let ABCD be a rectangular park with dimensions

• Length, AB = 40 meter

and

• Breadth, BC = 30 meter.

So,

$\bf \: Area_{(rectangle)} = \sf \: length \times breadth$

$\boxed{\bf \: Area_{(ABCD)} = \sf \: 40 \times 30 = 1200 \: {m}^{2} }$

Now,

According to statement,

• A path 5 meter runs around inside the park.

Let PQRS be inner rectangular park except the path whose dimensions are

• Length, PQ = 40 - 10 = 30 meter.

and

• Breadth, PQ = 30 - 10 = 20 meter.

So,

$\boxed{ \bf \: Area_{(PQRS)} = \sf \: 30 \times 20 = 600 \: {m}^{2} }$

Hence,

$\bf \: Area_{(path)} = Area_{(ABCD)} - Area_{(PQRS)}$

$\boxed{\bf \: Area_{(path)} = \: \sf \: 1200 - 600 = 600 \: {m}^{2} }$

Additional Information :-

$\boxed{\bf \: Area_{(square)} = {(side)}^{2} }$

$\boxed{ \bf{Area_{(circle)} = \pi \: {r}^{2} }}$

$\boxed{ \bf{Area_{(parallelogram)} = base \times height}}$

$\boxed{ \bf{Area_{(triangle)} \: = \: \dfrac{1}{2} \times base \times height}}$

Answer 2

✫Question:-

A rectangular park is 40 m long and 30 m wide. A path of 5 m runs round the inside of the park. Find the area of the path.

ㅤㅤㅤㅤ᯽︎Given:-

Length of rectangle =40m

Breadth of rectangle = 30m

ㅤㅤㅤㅤ✻To Find:-

Area of the path

ㅤㅤㅤㅤㅤ✵Solution

$\boxed{ \frak{Area \: of \: rectangle =length ×breadth }}$

$\bf{ \pink{Area \: of \: ABCD = 40×30=1200m²}}$

A.T.Q

• A path of 5 meter runs inside the park

Let EFGH be inner rectangular park excluding the path

$\sf \: |Length \: EF = 40-10=30 meters. |$

$\sf \: | Breadth \: EF=30-10=20 meters |$

$\underline{ \boxed{ \sf{Area \: of \: PQRS = 30×20=600m²}}}$

Hence,

• Area of path = Area of ABCD -Area of EFGH

$\boxed{ \underbrace{ \sf \: Area= 1200- 600m²}}$

Therefore the area of path is 600 m²

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$\: \: \: \: \: \: \: ⠀\large {\boxed{\sf{\mid{\overline {\underline{ \color{maroon}{ {\star More\:To\:know\::}}}\mid}}}}}$

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