Euclidean geometry, triangle area problem.

Question

Consider the triangle $ABC$. Let $D$ and $E$ be the trisection points of $BC$. Let $F$ be the point in $AC$ that satisfy $CF=3(AF)$. If the area of the triangle $CEF$ is $40 cm^2$, find the area of the triangle $ABC$.

Answer 1

Hint: triangles $\triangle ECF$ and $\triangle ECA$ have a shared altitude, while triangles $\triangle ECA$ and $\triangle BCA$ have a common base. In each case, there is a straightforward way to derive the area of the larger triangle from the area of the smaller one.