Geometry: Equilateral Triangle Circles

For an equilateral triangle of side $a$, circumradius $R = \frac{a}{\sqrt{3}}$ and inradius $r = \frac{a}{2\sqrt{3}}$. Difference in area = $\pi R^2 - \pi r^2 = \pi \left(\frac{a^2}{3} - \frac{a^2}{12}\right) = \frac{\pi a^2}{4} = 2156$. $\frac{22}{7} \cdot \frac{a^2}{4} = 2156 \implies a^2 = \frac{2156 \cdot 28}{22} = 2744$ Area of equilateral triangle = $\frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} (2744) = 686\sqrt{3} \text{ sq. cm.}$$$$$