Let radius of incircle = $$r$$, => Radius of circumcircle = $$2r$$ Difference in area = $$pi [(2r)^2 - (r)^2] = 2156$$ => $$3 imes frac{22}{7} imes r^2 = 2156$$ => $$r^2 = frac{2156 imes 7}{66}$$ => $$r = sqrt{frac{686}{3}}$$ Now, height of equilateral triangle = $$3 r = frac{sqrt{3}}{2} a$$    (where $$a$$ is side of triangle) => $$3 imes sqrt{frac{686}{3}} = frac{sqrt{3}}{2} a$$ => $$a = 2 sqrt{686}$$ $$ herefore$$ Area of triangle = $$frac{sqrt{3}}{4} a^2$$ = $$frac{sqrt{3}}{4} imes 4 imes 686 = 686 sqrt{3} cm^2$$