Question

A path 2 m wide is built along the border and inside a square garden of side 32m. Find the area of the path.

Answer 1

Answer:

Area of the square garden=s×s

side =30m

area =30m ×30m

=900m^2

area of the inner square garden=

one side=30m-4m(after building the path)

side =26m

area=26m×26m

=676m^2

area of the path=

(area of outer square garden)-(area of inner square garden)

=900-676

=224m^2

therefore, area of path =224m^2

Step-by-step explanation:

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Answer 2

To Find :

The Area of the Path.

Given :

• Length of the Square garden = 32 m

• Width of the Path = 2 m

We Know :

Area of a Square :

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blue{\sf{\underline{\boxed{A = (Side)^{2}}}}}$

Concept :

Since the path was build along the length of the square garden it formed a new Square .

Length of New Square = length of the original square - 4

==> (32 - 4) m

==> 28 m

Hence the length of the new Square is 28 m

Now , according to the information :

Area of Path = Area of Square garden - Area of Square garden with the path

By solving it we will get the area of the path.

Solution :

Area of the Square garden :

• Side of the Square garden = 32 m

Using the formula for Area of a Square and by Substituting the value in it , we get :

$\implies \sf{A = (Side)^{2}} \\ \\ \\ \implies \sf{A = 32^{2}} \\ \\ \\ \implies \sf{A = 1024 m^{2}} \\ \\ \\ \therefore \purple{\sf{Area = 1024 m^{2}}}$

Hence ,the area of the Square garden is 1024 m².

Area of the New Square garden :

• Side of the new Square = 28 m

Using the formula for Area of a Square and by Substituting the value in it , we get :

$\implies \sf{A = (Side)^{2}} \\ \\ \\ \implies \sf{A = 28^{2}} \\ \\ \\ \implies \sf{A = 784 m^{2}} \\ \\ \\ \therefore \purple{\sf{Area = 784 m^{2}}}$

Hence, the area of the Square garden is 784 m².

Area of the Path :

Area of Path = Area of Square garden - Area of Square garden with the path

By substituting the values in it , we get :

»» Area of Path = (1024 - 784) m²

»» Area of Path = 240 m²

Hence , the Area of the path is 240 m².