Trigonometry

Geometry Level 2

In an equilateral triangle, 3 coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle.

The area of the triangle is :

6 + 4 3 6 + 4\sqrt 3 12 + 7 3 12 + 7\sqrt 3 3 + 4 3 3 + 4\sqrt 3 4 + 2 3 4 + 2\sqrt 3

Hardik Siloiya by Hardik Siloiya , 19, India

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1 solution

Hardik Siloiya
Jan 27, 2016

The line joining the vertex of the triangle and the centre of the coin makes angle π/6 with the sides of the triangle. The length of each of the sides of the equilateral triangle is 2 + 2 cot π/6 =2(1 + √ .3 ). 

       Hence its area is  √ .3/4(1+√ .3 )^2  = 6+ 4√ .3
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