Question

A rectangle playing ground is 25 m long and 15 m broad A path of 3 metres width is all around inside it along the border. Find the area of path

Answer 1

Given :

• Length of rectangle = 25 m
• Breadth of rectangle = 15 m
• Length of path = 3 m

To find :

• Area of the path

According to the question,

➞ Area of rectangle = l × b

Where,

• l = Length
• b = Breadth

➞ Area of rectangle = 25 m × 15 m

➞ Area of rectangle = 375 m²

• So,the area of rectangle is 375 m².

Now,

• Including path

So,

➞ Length = 25 m + 3 m + 3 m = 31 m

➞ Breadth = 15 + 3 m + 3 m = 21 m

★ Area of rectangle including path,

➞ Area of rectangle = l × b

➞ Area of rectangle = 31 m × 21 m

➞ Area of rectangle = 651 m²

• So, the area of rectangle including path is 651 m².

Now,

➞ Area of path = Area of rectangle including path - Area of rectangle

➞ Area of path = 651 m² - 375 m²

➞ Area of path = 276 m²

• So,the area of path is 276 m².

Answer 2

${\large{\bold{\sf{\underline{Understanding \; the \; question}}}}}$

➨ This question says that the rectangular playground has length as 25 metres and 15 metres as breadth. A path of 3 metres width ( breadth ) is all around inside it along the border. We have to find the area of that path.

${\large{\bold{\sf{\underline{Given \; that}}}}}$

➨ Length of rectangular playground = 25 metres.

➨ Breadth of rectangular playground = 15 metres.

➨ Path of 3 metres in breadth is all around inside it along the border.

${\large{\bold{\sf{\underline{To \; find}}}}}$

➨ Area of path.

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

➨ Area of path = 276 m²

${\large{\bold{\sf{\underline{Using \; concepts}}}}}$

➨ Area of rectangle formula.

${\large{\bold{\sf{\underline{Using \; formulas}}}}}$

➨ Area of rectangle = Length × Breadth

${\large{\bold{\sf{\underline{We \; also \; write \; these \; as}}}}}$

➨ Length as L

➨ Breadth as B

➨ Area as A

${\large{\bold{\sf{\underline{Full \; Solution}}}}}$

~ Let us find area of that rectangular playground firstly'

➸ Area of rectangular playground = Length × Breadth

➸ Area of rectangular playground = (25 × 15) metres

➸ Area of rectangular playground = 375 m²

~ Now let's find area of that playground including border and inside area

➸ Length = ( 25 + 3 + 3 ) m = 31 m

➸ Breadth = ( 15 + 3 + 3 ) m = 21 m

➸ Area = Length × Breadth

➸ Area of = ( 31 × 21 ) metres

➸ Area = 651 m²

~ Now at last let us find area of path

➸ Area of path = Area of playground including border and inside area - rectangular playground area

➸ Area of path = ( 651 - 375 ) m²

➸ Area of path = 276 m²

( Diagram of this question is in attachment )

${\large{\bold{\sf{\underline{Knowledge}}}}}$

Rectangle diagram -

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large x cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large y cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Rectangle with Diagonal -

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large x cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large y cm}\end{picture}$

Perimeter of rectangle formula = 2(length + breadth)

Area of rectangle formula = Length × Breadth.