The points D, E and F are the mid-points of AB, BC and CA respectively. What is the area of the shaded region?

$\frac{1}{2} \text{ sq. units}$

The correct answer is Option (3) → $\frac{1}{2} \text{ sq. units}$

If points $D, E$ and $F$ are the mid-points of $AB, BC$ and $CA$ respectively, then:

$\text{area of } \Delta DFE = \frac{1}{4} \times \text{area of } \Delta ABC \text{}$

$\text{Required shaded area} = \frac{1}{4} \times \text{area of } ABC \text{}$

$= \frac{1}{4} \times \frac{1}{2} |0(2 - 4) + 2(6 - 0) + 4(0 - 2)| \text{}$

$= \frac{1}{8} |0(2 - 4) + 2(6 - 0) + 4(0 - 2)| \text{}$

$= \frac{1}{8} |4| = \frac{1}{2} \text{ sq. units}$