Krishna
0

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