Question

Which expression gives the apothem for a regular dodecagon with side length 8?

Answer 1

The answer is B. A = 4 / tan 15.

It's a bit difficult to explain with simply words but, since the figure is a do-decagon, it has 12 sides. When solving these, I divide the number of sides by 360 to find the central angle. Then, since we split that into two to make a right triangle, I divide the central angle by 2.

So..
360 / 12 = 30
30 is the central angle. 30/2 = 15.

Then, you have to use the tangent of the known angle to find the apothem, which would be A = 4 / tan 15.

Hope this helps! :)