1962 AHSME Problems/Problem 18
Problem
A regular dodecagon ( sides) is inscribed in a circle with radius
inches. The area of the dodecagon, in square inches, is:
Solution
The formula for the area of a regular dodecagon is . The answer is
.
(If you don't know this formula, it's pretty easy to figure out that the area of a square inscribed in a circle is
, and all the choices except
are less than
. Remember, the more sides a regular polygon has, the closer its area gets to
.)