Question

Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch radius A = sq. in.

Answer 1

If the radius is the radius of the inscribed circle then the side of the triangle = radius * 6 / (sq root(3))side = 20.785tan 60 = height / half-sideheight = tan 60 * half-sideheight = 1.732 * 10.3925 height = 17.99981 triangle area = .5*side*heighttriangle area = 10.3925 * 17.99981triangle area = 187.06 
If the radius is the radius of the circumscribed circle then the side of the triangle = radius *3 / (sq root(3))side of the triangle = 6 * 3 / sq root(3)side of the triangle = 10.3923048454 half-side = 5.1961524227 height = tan 60 * half-sideheight = 1.732 * 5.196height = 8.9997
triangle area = .5*side*heighttriangle area = 5.196 * 8.9997triangle area = 46.764   
Hope this helps!

Answer 2

The answer is 18 inches