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?

The Donut is (15/16)*X  The smaller triangle(the hole) is 1/4 of STU and STU is 1/4 of PQR, therefore The smaller triangle(the hole) is 1/16 of PQR.  Leaving the rest(the donut) to be 15/16 of PQR.  SO the answer is that the donut is 15/16ths of X.

Posted by Scott on 2006-01-01 20:26:42