If X is the area of any triangle-PQR and you make a hole in the center of this triangle by first joining the midpoints of each side to create smaller triangle-STU and then again joining the midpoints of triangle-STU to create the hole in the center of this triangle, it would create a donut something like this:

          Q 
         / \
        /   \
       /     \
    S /_______\ U
     / \  A  / \
    /   \/_\/   \
   /     \ /     \
P /_______V_______\ R
          T

What is the area of the triangle donut in terms of X?

(In reply to re(2): My interpretation by ajosin)

I think everyone understands what tanx means by "donut", ajosin.  Perhaps he could of said "...it would create the topological equivalent of a 2-D torus with inner and outer "sides" in the form of triangles..." but that wouldn't have made the problem clearer to most of us. 

The first line of the problem statement adequately identifies the "donut" as "...triangle-PQR.." with "...a hole in the center..." followed by instructions for constructing the "hole".

Posted by MindRod on 2006-01-02 12:21:39