Question 279226
Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 
6-inch radius 

from http://www.mathopenref.com/polygonregulararea.html: 
If you know the radius (distance from the center to a vertex): 
{{{ area = (R^2Nsin(2pi/N))/2 }}} 
where
R  is the radius (circumradius)
N  is the number of sides
{{{ pi }}}  is PI, approximately 3.142
SIN  is the sine function calculated in radians

{{{ sin(0) = 0 }}}

{{{ sin(pi/3) =  sqrt(3)/2 }}}

{{{ sin(pi/2) = 1 }}}

{{{ sin(2*pi/3) = sqrt(3)/2 }}}

{{{ sin(pi) = 0 }}}

{{{ area = (6^2 * 3 * sin(2/3 * pi))/2 }}}
{{{ area = (36 * 3 * sqrt(3)/2)/2 }}}
{{{ area = 18 * 3 * sqrt(3) * 1/2 }}}
{{{ area = 9 * 3 * sqrt(3) }}}
{{{ area = 27 * sqrt(3) }}}
{{{ area = approximately 46.7654 square inches  }}}