The area of a regular 12-gone with radius r is 3r2.
(whereas the area of the circle with radius r is πr2)
Proof: The area of the dotted triangle is 1/2 of the area of the rectangle with sides
of length r and r/2.
Remark: The assertion is just a special case of the general formula
for the area A of a regular n-gone with radius r:
A = n/2 × sin(360o/n) × r2,
since sin(360o/12) = sin(30o) = 1/2.
(See Renato Pandi and Hans
Walser, Basel, in Puzzle Aktivitäten im Zwölfeck,
MNU 65.02 (2012).)
