All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 DoDeCaGon (Posted on 2013-10-18)
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.

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: No Subject | Comment 3 of 4 |

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

 Search: Search body:
Forums (45)
Random Problem
Site Statistics
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox: