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?

Triangle PQR has area of X

Triangle STU has area of X/4 because joining midpoints of all 3 sides splits PQR into 4 equal triangles

Triangle A "Hole" also splits STU into 4 equal parts, A has area of X/16

Donut is Triangle PQR-"Hole"

Donut's area is 15X/16

Posted by Josiah Lumpkin on 2006-01-03 14:45:58