Question 139977
A regular dodecagon has 12 equal sides.
The radius of the dodecagon is equal to the radius of the circumscribed circle.
Using the formula for the area of a regular polygon of n sides and having a radius R:
{{{A = (1/2)nR^2Sin(360/n)}}} Substitute n = 12 and simplify.
{{{A = (1/2)(12)R^2Sin(360/12)}}}
{{{A = 6R^2Sin(30)}}}
{{{A = 6R^2(0.5)}}}
{{{A = 3R^2}}}...and since the value of R is not provided, this is as far as we can go!