Question

A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.

Answer 1

Given

• Dimensions of a rectangular park :-
• Length of a rectangular park = 45 m
• Breadth of a rectangular park = 30 m
• Breadth of a path constructed outside the park = 2.5 m

Knowledge required :-

• Formula to calculate area of rectangle :-

⠀⠀⠀ Area of rectangle = l × b

[Where : l is the length of the rectangle and b is the breadth of the rectangle.]

~Understanding the concept ::

Here, we have to find the area of the path. For that firstly, we will find the area of the rectangular park by using the formula of area of rectangle. Then we will find the dimensions of the park + path and its area. To find the area of path we will subtract the area of the rectangular park from area of the rectangular park including the path.

Solution

Area of the rectangular park :-

⠀⠀⠀⇒ Area = l × b

⠀⠀⠀⇒ Area = 45 × 30

⠀⠀⠀⇒ Area = 1350

Area of the rectangular park = 1350 m²

Dimensions of the park including the path :-

• Length of the park + path = 45 + 2.5 + 2.5 = 50 m
• Breadth of the park + path = 30 + 2.5 + 2.5 = 35 m

Area of the park + path :-

⠀⠀⠀⇒ Area = l × b

⠀⠀⠀⇒ Area = 50 × 35

⠀⠀⠀⇒ Area = 1750

Area of the path + park = 1750 m²

Area of the path = Area of the park + path - Area of the path

⠀⠀⠀⇒ Area of the path = (1750 - 1350)m²

⠀⠀⠀⇒ Area of the path = 400

★ Area of the path = 400 m²

Answer 2

Given :-

• Length of Inner Rectangle = 45m
• Breadth of Inner Rectangle = 30m
• A path 2.5 m wide is constructed outside the park.

To Find :-

• Area of the Path

Solution :-

❏ In this question, Length and Breadth of inner rectangle is given and it is also given that a 2.5m wide path is constructed outside of the park. So, for finding the Area of the Path we have to substract Area of inner Rectangle from Area of outer Rectangle.

Dimensions of Outer Rectangle :

⟼ Length of Inner Rectangle = 45m

⟼ Length of Outer Rectangle = 45 + 2.5 + 2.5

⟼ Length of Outer Rectangle = 45 + 5

⟼ Length of Outer Rectangle = 50m

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⟼ Breadth of Inner Rectangle = 30m

⟼ Breadth of Outer Rectangle = 30 + 2.5 + 2.5

⟼ Breadth of Outer Rectangle = 30 + 5

⟼ Breadth of Outer Rectangle = 35m

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Area of Outer Rectangle :

➞ Area of Outer Rectangle = L × B

➞ Area of Outer Rectangle = 50 × 35

➞ Area of Outer Rectangle = 1750m²

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Area of Inner Rectangle :

➞ Area of Inner Rectangle = L × B

➞ Area of Inner Rectangle = 45 × 30

➞ Area of Inner Rectangle = 1350m²

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Area of Path :

⟾ Area = Area of Outer - Inner Rectangle

⟾ Area = 1750 - 1350

⟾ Area of Path = 400m²

Thus, Area of Path = 400m²

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