A circular ground whose radius is equal to the side of an equilateral triangle. The area of the equilateral triangle is 400√3 m2. The circular ground has 2 meters broad garden around it. Then, what is the area of the garden (in sq. meters)?

Question

A circular ground whose radius is equal to the side of an equilateral triangle. The area of the equilateral triangle is 400√3 m2. The circular ground has 2 meters broad garden around it. Then, what is the area of the garden (in sq. meters)?

154π
160π
164π
172π
None of these

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 3 : 164π

Given:

Radius of ground = Side of equilateral triangle

Area of equilateral triangle = 400√3 m²

Garden width = 2 meters

Formula Used:

Area of equilateral triangle = √3/4 × (side)²

Area of garden = π (Radius₁² – Radius₂²)

Calculation:

Area of equilateral triangle = √3/4 × (Side)²

⇒ 400√3 = √3/4 × (Side)²

⇒ 1600 = (Side)²

⇒ Side = √(1600)

⇒ Side = 40 m

The radius of the circular ground = 40 m

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The area of the garden = π(42² – 40²)

⇒ π(1764 – 1600)

⇒ 164π sq. m