A triangle $A B C$ has an area equal to 944. Let $D$ be the midpoint of $[A B]$, $E$ the midpoint of $[B C]$, and $F$ the midpoint of $[A E]$. What is the area of $D E F$?
Answer: 118. Let $|A B C|$ denote the area of $A B C$. We have $|D E F|=\frac{1}{\text{Answer } 2}|D E A|$ because these two triangles have the same base $[D E]$, but the height of $D E A$ is twice that of $D E F$. Similarly, $|D E A|=\frac{1}{\text{Answer } 2}|B E A|=\frac{1}{\text{Answer4 }}|A B C|$, so $|D E F|=\frac{1}{\text{Answer8 }}|A B C|=118$.