SOLUTION: A circle is inscribed in the equilateral triangle and its radius is 6 cm, what is the area of the equilateral triangle?

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Question 1014588: A circle is inscribed in the equilateral triangle and its radius is 6 cm, what is the area of the equilateral triangle?
Answer by ikleyn(52884) About Me  (Show Source):
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A circle is inscribed in the equilateral triangle and its radius is 6 cm, what is the area of the equilateral triangle?
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Since the radius of the inscribed circle is r = 6 cm,
the side of the triangle is 2%2Ar%2Asqrt%283%29 = 20.785 cm.


Then the area of the triangle is the product of its semi-perimeter and the radius of the inscribed circle 

S = %283%2A2%2Ar%5E2%2Asqrt%283%29%29%2F2 = 3%2A20.758%2A6%2F2 = 187.06 cm%5E2.


See the lessons
 
  Formulas for area of a triangle 
  Proof of the formula for the area of a triangle via the radius of the inscribed circle

in this site.