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.

The answer is 18.

The 'proof without words' is pretty enough to be worth a link:

http://www.cut-the-knot.org/Curriculum/Geometry/KurschakTile.shtml

Posted by broll on 2013-10-18 09:47:50