1. **State the problem:** We are given triangle $ABC$ with points $D$, $E$, and $F$ as midpoints of sides $AB$, $BC$, and $CA$ respectively. We need to find the ratio of the area of triangle $DEF$ to triangle $ABC$. 2. **Interpret the given information:** Since $D$, $E$, and $F$ are midpoints, we have: - $BD = \frac{1}{2} AB$ means $D$ is the midpoint of $AB$. - $CE = \frac{1}{2} BC$ means $E$ is the midpoint of $BC$. - $AF = \frac{1}{2} CA$ means $F$ is the midpoint of $CA$. 3. **Use midpoint theorem:** Triangle $DEF$ formed by joining midpoints of sides of $ABC$ is called the medial triangle. 4. **Property of medial triangle:** The area of the medial triangle is exactly $\frac{1}{4}$ the area of the original triangle. 5. **Conclusion:** Therefore, the ratio of the area of $\triangle DEF$ to $\triangle ABC$ is $$\frac{\text{Area of } \triangle DEF}{\text{Area of } \triangle ABC} = \frac{1}{4}.$$ Thus, the ratio is $\boxed{\frac{1}{4}}$.