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 20131018 10:56:29 