Let each side of the equilateral triangle be \(a\) units. ∴ Height of the equilateral triangle = \(\frac{\sqrt{3}a}{2}\) cm ∴ Radius of the circumcircle = \(\frac{\sqrt{3}a}{2} \times \frac{2}{3} = \frac{a}{\sqrt{3}}\) cm ∴ Ratio of the area of the equilateral triangle to the area of its circumcircle = \(\frac{\sqrt{3}a^2}{4} : \pi \left(\frac{a}{\sqrt{3}}\right)^2\) = \(\frac{\sqrt{3}a^2}{4} : \frac{\pi a^2}{3}\) = \(3\sqrt{3} : 4\pi\)