A regular dodecagon is inscribed in a square of area 24 as shown, where four vertices of the dodecagon are at the midpoints of the sides of the square. Find the area of the dodecagon.

(In reply to No Subject by Ady TZIDON)

In case the previous calculations don't make it clear:

The dodecagon is divided into 12 congruent isosceles triangles from the center.  Each has two sides of length 12 meeting at an angle of 30 degrees.  The SAS area formula is .5*a*b*sin(C)
Since sin(30)=.5 and a=b we have
12*.5*a^2*.5
=3a^2
Where a^2 would be a quarter of the big square, so a^2=6

3*6=18

Posted by Jer on 2013-10-18 10:56:29