Question

Find the area of a circle circumscribed about an equilateral triangle whose side is 18 inches long

Answer 1

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.

$\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies A=\pi (2\sqrt{3})^2\implies A=\pi (2^2)(\sqrt{3})^2\implies A=12\pi$