Problem 25 (1999 AMC 8)

Points $B$, $D$, and $J$ are midpoints of the sides of right triangle $ACG$. Points $K$, $E$, $I$ are midpoints of the sides of triangle $JDG$, etc. If the dividing and shading process is done $100$ times (the first three are shown) and $AC=CG=6$, then the total area of the shaded triangles is nearest [See figure in original PDF]