regular polygon .

Question

Answer 1

The angle at the top of the triangle is 30 degrees (360/12). So we have a 30-60-90 right triangle.

Side opposite 30 degree angle is 1/2 of the hypotenuse of 4 = 2, so whole side is 4 and perimeter is thru 6*4 = 24.

Side opposite 60 degree angle is the apothem and is 2 sqrt(3).

Area = 1/2 * apothem * perimeter = 1/2 * 2sqrt(3) * 24 = 24 sqrt(3).