aime26-09

Proposed solution

To find the area of hexagon $AA'CC'BB'$, we first need to determine the lengths of the sides of the triangle formed by the intersection of lines $B'CC', AAB, AB'C$. Then, we can use Heron's formula to find the area of each of the triangles formed by the intersection of lines $B'CC', AAB, AB'C$. Then, we can use the area of each of the triangles formed by the intersection of lines $B'CC', AAB, AB'C$ as a function of the side lengths of the triangle formed by the intersection of lines $B'CC', AAB, AB'C$.

Then, we can use Heron's formula to find the area of each of the triangles formed by the intersection of lines $B'CC', AAB, AB'C$ as a function of the side lengths of the triangle formed by the intersection of lines $B'CC', AAB, AB'C$.

Then, we can use Heron's formula to find the area of each of the triangles formed by the intersection of lines $B'CC', AAB, AB'C$ as a function of the side lengths of the triangle formed by the intersection of lines $B'CC', AAB, AB'C$.

Then, we can use Heron's formula to find the area of each of the triangles formed