Question

In the figure above, ABCDEFGHIJKL is a regualr dodecagon (a regualr 12-sided polygon). The curved path is made up of 12 semicircles, each of whose diameters is a side of the dodecagon. If the perimeter of the dodecagon is 24, find the area of the shaded region.

Answer 1

if the perimeter of dodecagon is 24 then length of each side = 24/12 = 2
so the diemeter of each semiscircle is 2 and radius is 1.
area of each semicircle is 0.5 * pi * 1^2 and there are 12 of them
so total area is 12 * 0.5 *pi
= 6 pi square units

Answer 2

thank you :)

Answer 3

yw