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In an equilateral triangle, 3 coins of radii I unit each are kept so that they touch each other and the sides is the triangle. Find the area of the triangle.

In an equilateral triangle, 3 coins of radii I unit each are kept so that they touch each other and the sides is the triangle. Find the area of the triangle.

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
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From figure, side of the equilateral triangle= 2r
where r is the radius of each coin.

From trignometry, the side AD=2rsin60^{\circ}=\sqrt{3}r
Therefore, area of the triangle=\dfrac{1}{2}\times base\times height=\dfrac{1}{2}\times 2r\times \sqrt{3}r=\sqrt{3}r^2=\sqrt{3}

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