Area of Equilateral Triangle with Inradius R

For an equilateral triangle of side $a$, inradius $r = R = \frac{a}{2\sqrt{3}} \Rightarrow a = 2\sqrt{3}R$. Area = $\frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} (2\sqrt{3}R)^2 = \frac{\sqrt{3}}{4} (12R^2) = 3\sqrt{3}R^2$.