In triangle ABC, let D, E and F be the midpoints of BC, CA and AB. What is the ratio of the area of triangle DEF to the area of triangle ABC?

**Principle.** The triangle formed by joining the midpoints of the sides of any triangle (called the *medial triangle*) is similar to the original with a side ratio of $1 : 2$. Areas scale as the square of the side ratio. **Ratio.** $\left(\dfrac{1}{2}\right)^2 = \dfrac{1}{4}$. **Why option A ($\tfrac{1}{2}$) is tempting.** It would be the ratio if you halved one dimension only — but in 2D, halving every side halves *both* base and height, so the area drops to a quarter.