Find the inradius of triangle ABC.
Inradius = area /semi-perimeter
Area = (1/2)a^2 * sqrt (3) / 2 = (sqrt (3) / 4) a^2
Seimi-perimeter = (3/2)a
Inradius = [ sqrt (3) / 2 ] a^2 / [ (3/2)a] = a / sqrt 3