Question

Question : In the attachment
Class : 7th
Chapter : Perimeter and area


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Answer 1

★ The area of the path is 0.0564 hectare.

Step-by-step explanation

Analysis:-

⠀⠀⠀In the question, it has been stated that there is a rectangular park of length 120 m and breadth 65 m. The outside of the park is surrounded by a path of width 3 m. We've been asked to calculate the area of path (in terms of hectares).

Solution:-

⠀⠀⠀While visualising the diagram, you will notice a structure of concentric rectangles, where the inner rectangle is just the park and the outer rectangle is the park along with the path. So, to find the area of the park, we need to know what does the difference of area of outer rectangle and inner rectangle equals.

⠀⠀⠀⠀Area of the inner rectangle

➧Length (L) × Breadth (B) sq.units

We know that,

• L = 120 m
• B = 65 m

So,

⠀⠀⇢ 120 × 65

⠀⠀⇢ 7,800 m²

⠀⠀⠀⠀Area of the outer rectangle

➧Length (L) × Breadth (B) sq.units

Here,

• L = 123 m (120 + 3)
• B = 68 m (65 + 3)

You may doubt why did we add 3 to the measures of length and breadth of inner rectangle. It was because, the width of the path is 3 m and the path is running around outside of the park. $\:$

⠀⠀⇢ 123 × 68

⠀⠀⇢ 8,364 m²

⠀⠀⠀⠀⠀⠀⠀Area of the path

Finally, let's find the area of the path which is running around the park by subtracting the area of inner rectangle from the area pf outer rectangle.

⠀⠀⇢ 8,364 – 7,800

⠀⠀⇢ 564 m²

We've found the area of the path. But, since we have been asked to find it in terms of hectares, we have to convert the units.

We know that,

➧1 m = 0.0001 hectare

So,

⠀⠀⇢ 564 m = (0.0001 × 564) hectare

⠀⠀⇢ 564 m = 0.0564 hectare

And this is the required answer.

_________________________________________________

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

★ The area of the path is 0.0564 hectare.

Step-by-step explanation

$\sf{\underline{\overline{\pink{Analysis :-}}}}$

⠀⠀⠀In the question, it has been stated that there is a rectangular park of length 120 m and breadth 65 m. The outside of the park is surrounded by a path of width 3 m. We've been asked to calculate the area of path (in terms of hectares).

$\sf{\underline{\overline{\red{Solution :-}}}}$

⠀⠀⠀While visualising the diagram, you will notice a structure of concentric rectangles, where the inner rectangle is just the park and the outer rectangle is the park along with the path. So, to find the area of the park, we need to know what does the difference of area of outer rectangle and inner rectangle equals.

⠀⠀⠀⠀Area of inner reactangle

➧Length (L) × Breadth (B) sq.units

We know that,

L = 120 m

B = 65 m

So,

⠀⠀⇢ 120 × 65

⠀⠀⇢ 7,800 m²

⠀⠀⠀⠀Area of outer reactangle

➧Length (L) × Breadth (B) sq.units

Here,

L = 123 m (120 + 3)

B = 68 m (65 + 3)

You may doubt why did we add 3 to the measures of length and breadth of inner rectangle. It was because, the width of the path is 3 m and the path is running around outside of the park. \:

⠀⠀⇢ 123 × 68

⠀⠀⇢ 8,364 m²

⠀⠀⠀⠀⠀⠀ Area of the path

Finally, let's find the area of the path which is running around the park by subtracting the area of inner rectangle from the area pf outer rectangle.

⠀⠀⇢ 8,364 – 7,800

⠀⠀⇢ 564 m²

We've found the area of the path. But, since we have been asked to find it in terms of hectares, we have to convert the units.

We know that,

➧1 m = 0.0001 hectare

So,

⠀⠀⇢ 564 m = (0.0001 × 564) hectare

⠀⠀⇢ 564 m = 0.0564 hectare

And this is the required answer.

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