Step 1: Recall the formulas of the radius of the circumscribed circle and the radius the inscribed circle.
NOTE: If R is the radius of the circumscribed circle and r the radius the
inscribed circle to an equilateral triangle of side a,
FORMULAS: r = a *\frac{\sqrt{3}}{6}
R = a *\frac{\sqrt{3}}{3}
Step 2: Find the ratio of the area of the circumscribed circle to the area of the inscribed circle.
NOTE: \frac{Area\ of\ the\ circumscribed\ circle}{Area\ ofthe\ inscribed\ circle.}
= \frac{\pi * R^2}{\pi* r^2}
= \frac{R^2}{r^2}
Step 3: Write the formulas for R and r and simplify
NOTE: = (\frac{a*\frac{\sqrt{3}}{3}}{\frac{\sqrt{3}}{6}})^2
= (\frac{6}{3})^2
= 4
