SOLUTION: A circle is inscribed inside an equilateral triangle. If the circumference of the circle is 6 cm, then what is the area of the triangle in cm²?

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Question 1147336: A circle is inscribed inside an equilateral triangle. If the circumference of the circle is 6 cm, then what is the area of the triangle in cm²?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Draw this. The triangle can be broken up into 6 30-60-90 triangles, with the short side the radius r. The long side on the triangle is r *sqrt(3).
Here, the circle has C=6=2 pi r
so r=3/pi
The area of one of the six triangles is A=1/2 * (3/pi) sqrt(3)* (3/pi)
There are 6 of them, so A=3*9 sqrt (3)/ pi ^2
This is 4.738 cm^2
Alternative approach.
The base of the triangle is (6/pi) sqrt(3)
The height is (9/pi) since the intersection is 2/3 of the way from the vertex to the opposite side.
The area is (1/2)(6/pi)sqrt(3)(9/pi)=27 sqrt(3)/pi^2=4.738 cm^2