The word "octagon" should be "hexagon". Rotating the triangle $AB_1C$ centered $A$ such that $B_1$ coincides $C_1$. Assume $C$ moves to $C'$. Then, we can see that the triangle $C'C_1B$ is congruent to $CA_1B$. Therefore, $ABC$ and $ABC'$ is congruent implies $ABC$ is half the area of hexagon.