Question

a rectangular park54m×40m has two2m wide roads in the centre running parallel to the breadth.find the area of road​

Answer 1

AnswEr :

$\bold{Given} \begin{cases}\sf{Length\:of \: Park \: ( l ) = 54 m} \\ \sf{Breadth \: of \: Park \: ( b ) = 40 m}\\ \sf{Width \: of \: the \: Road \:( w ) = 2 m} \\ \sf{Area \:of \:Road = ?}\end{cases}$

• According to the Question Now :

$\implies \tt Area \:of \:Road = (Area \: of \:Park) - (Area \: of \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt Parts \:Excluding \: the \: Road)$

$\implies \tt Area \:of \:Road = ( l b ) - [(l - 2)(b - 2)]$

$\implies \tt Area \: of \: Road = (54 \times 40) - [(54 - 2) \times(40 - 2)]$

$\implies \tt Area \: of \:Road = 2160 - ( 52 \times 38)$

$\implies \tt Area \:of \: Road = 2160 - 1976$

$\implies \boxed{\red{\tt Area \:of \:Road = 184 \: {m}^{2}}}$

⠀

∴ Therefore, Area of the Road is 184 m²

_________________________________

• Shortcut Trick :

$\longrightarrow \tt Area \:of \:Road = [(Length + Breadth) - Width] \times Width$

$\longrightarrow \tt Area \:of \:Road = [(54 + 40) - 2] \times 2$

$\longrightarrow \tt Area \:of \:Road = [94 - 2] \times 2$

$\longrightarrow \tt Area \:of \:Road = 92 \times 2$

$\longrightarrow \boxed{\red{\tt Area \:of \:Road = 184 \: {m}^{2}}}$

⠀

∴ Therefore, Area of the Road is 184 m².

Answer 2

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

Given:

A rectangular park 54m × 40m has 2m wide roads in the centre running parallel to the breadth.

$\bf{\Large{\underline{\rm{\red{To\:find\::}}}}}$

The area of road.

$\bf{\Large{\underline{\sf{\pink{Explanation\::}}}}}$

We have,

$\begin{cases}\{Length\:of\:rectangular\:park,[l]=54m}\\{Breadth\:of\:rectangular\:park,[b]=40m}\\{Width\:of\:the\:road,[w]=2m}\end{cases}$

We know that area of rectangle: (Length × Breadth)   [sq.units]

• Area of rectangular park;

→ Area= (54 × 40)m²

→ Area= 2160m²

&

• Area of path excluding the roads;

A rectangular park has two 2m wide roads in the center running parallel to the breadth.

$\begin{cases}\sf{New\:length=(54-2)m=52m}\\sf{New\:breadth=(40-2)m=38m}\end{cases}$

→ Area= (52 × 38)m²

→ Area= 1976m²

Now,

Area of road=(Area of rectangular park)-(Area of path excluding road)

⇒ Area of road = (2160)m² - (1976)m²

⇒ Area of road = 184m².

Thus,

The area of the road is 184m².