let's recall that an equilateral triangle has all interior angles of 60°.
Check the picture below.
so as you can see, 2√3 = x = r, namely the radius of the circle.
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies A=\pi (2\sqrt{3})^2\implies A=\pi (2^2)(\sqrt{3})^2\implies A=12\pi[/tex]
