Question

A path 3m wide is built outside and along the boundary of a square field of side100m.Find the area of path .

Answer 1

Given :

• Side of a square field = 100 m
• Breadth of a path built outside the square field = 3 m

To find :

• Area of the path

Knowledge required :-

• Formula of area of square :-

⠀⠀⠀⠀Area of square = side × side

• Unit of area = m² or cm²

~Understanding the concept ::

Here, we have to find the area of the path. Firstly, we will calculate the area of the square field. Then we will add (3 + 3)m in the side of the square field. The resultant value will be the side of the square field including the path. Calculate the area of the square field including the path from that value.

Then to find the area of the path subtract the area of the square field from the area of the square field including the path.

Solution :

Area of the square field :-

⠀⠀⠀⇒ Area = 100 × 100

⠀⠀⠀⇒ Area 10,000

Area of the square field = 10,000 m²

Side of the square field + path = 100 + 3 + 3 = 106 m

Area of the square field + path :-

⠀⠀⠀⇒ Area = 106 × 106

⠀⠀⠀⇒ Area = 11,236

Area of the square field + path = 11,236 m²

Area of the path = Area of the square field + path - Area of the square field

⠀⠀⠀⇒ Area of path = 11,236 - 10,000

⠀⠀⠀⇒ Area of path = 1,236

★ Area of the path = 1,236 m²

Answer 2

Given :-

• Side of Inner square field = 100m
• A path 3m wide is built outside and along the boundary of a square field.

To Find :-

• Area of the Path.

Solution :-

Side of Outer Field :

⟼ Side of inner field + width of path

⟼ 100 + width of path + width of path

⟼ 100 + 3 + 3

⟼ 100 + 6

⟼ Side of Outer Field = 106m

________________

➞ Area of inner field = (side)²

➞ Area of inner field = side × side

➞ Area of inner field = 100 × 100

➞ Area of inner field = 10000 m²

________________

⟾ Area of outer field = (side)²

⟾ Area of outer field = side × side

⟾ Area of outer field = 106 × 106

⟾ Area of outer field = 11236m²

________________

➟ Area of Path = Outer area - inner area

➟ Area of Path = 11236 - 10000

➟ Area of Path = 1236m²

Thus Area of path = 1236m²

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