Five lines parallel to the base of a triangle divide the other sides of the triangle each into six equal segments and the area into six distinct parts. If the area of the largest of these parts is 66 cm^2, then the area, in cm^2 of the original triangle is
Let the base of the triangle have length $b$. Then each of the segments has length $b/6$. One of the smaller triangles adjacent to the base has area $66/6=11$. Thus, the area of the triangle with base $b$ and height $h$ is equal to \[
\frac{bh}{2}=11\cdot 6=66.
\] Solving, we find $bh=66\cdot 2$, so the area of the triangle is $\boxed{264}$.