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 The solution by akash)

Connecting the mid-points results in 4 equal trianglea, therefor STU = 1/4 x.   Then area A = 1/4 STU or 1/16x.  THe area of the donut = x-1/16x or 15/16x.

nuff-said

Posted by Pete on 2006-01-02 00:08:57