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

If the radius is the radius of the inscribed circle then the

side of the triangle = radius * 6 / (sq root (3))

side = 20.785

tan 60 = height / half-side

height = tan 60 * half-side

height = 1.732 * 10.3925

height = 17.99981

triangle area =.5*side*height

triangle area = 10.3925 * 17.99981

triangle 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-side

height = 1.732 * 5.196

height = 8.9997

triangle area =.5*side*height

triangle area = 5.196 * 8.9997

triangle area = 46.764