Question

a school has a lawn which is 60m long and 40m wide. a path of width 5m is constructed out side the lawn find the area of the path(draw the figure)
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Answer 1

${\underline{\underline{\bf{Given:}}}}$

• Length of the lawn = 60 m.
• Width of the lawn = 40 m.
• A path is constructed outside the lawn.
• Width of the path = 5 m.

${\underline{\underline{\bf{Need\:to\: find:}}}}$

• The area of the path.

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{(Rectangle)}=lb\:sq.units}}}$

$\:\:\:\:\:\:\sf{Here,}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet{\sf{\:l=length}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet{\sf{\:b=breadth\:(width)}}$

${\underline{\underline{\bf{Solution:}}}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎Look at the figure in the attachment! There, we can observe that the path runs around the lawn, forming a larger rectangle. And the lawn seems to be smaller rectangle. So, the area of the lawn can be found by subtracting the the area of smaller rectangle from the area of larger rectangle.

‎ ‎ ‎ ‎ ‎ ‎We are given with the measures of smaller rectangle and width of path. To obtain the required answer, we need to find the measures of larger rectangle. If we observe at the figure clearly, we will be able to find the measures of length and width easily.

Length of larger rectangle:

$\rightarrow$ Width of path + Length of lawn + Width of path

$\rightarrow{\sf{5 + 60 + 5}}$

$\rightarrow{\sf{65 + 5}}$

$\rightarrow{\underline{\underline{\sf{70\:m}}}}$

Breadth of larger rectangle:

$\rightarrow$ Width of path + Width of lawn + Width of path

$\rightarrow{\sf{5+40+5}}$

$\rightarrow{\sf{45+5}}$

$\rightarrow{\underline{\underline{\sf{50\:m}}}}$

Now, we've obtained the measures of larger rectangle. So, let's find the area of larger rectangle and smaller rectangle.

Area of larger rectangle:

$\:\:\:\:\:\:\implies{\sf{lb\:sq.units}}$

$\:\:\:\:\:\:\implies{\sf{70\times 50}}$

$\:\:\:\:\:\:\implies{\underline{\underline{\sf{3500\:{m}^{2}}}}}$

Area of smaller rectangle (lawn):

$\:\:\:\:\:\:\implies{\sf{lb\:sq.units}}$

$\:\:\:\:\:\:\implies{\sf{60\times 40}}$

$\:\:\:\:\:\:\implies{\underline{\underline{\sf{2400\:{m}^{2}}}}}$

★ Area of path:

$\rightarrow$ Area of larger rectangle - Area of smaller rectangle

$\rightarrow{\sf{3500-2400}}$

$\rightarrow{\underline{\underline{\sf{\red{1,100\:{m}^{2}}}}}}$

${\underline{\underline{\bf{Required\: answer:}}}}$

• Therefore, the area of the path that runs around the lawn is 1,100 m².

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