Area of an equilateral triangle inscribed in a circle with a radius of 6 centimeters

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If you draw the radius to the vertex of the triangle and then draw a perpendicular line from the center to the side of the triangle you create z 30-60-90 triangle. The short side of this little triangle is 3 and the other side is 3√3.  Double this to get the length of the original triangle as 6√3. The area of an equilateral triangle is √3s^2/4 √3(6√3)^2/4 = 27√3