1. **State the problem:** We need to find the area of a right triangle with legs measuring 3 meters and 4 meters. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify base and height:** In a right triangle, the two legs are perpendicular, so one leg can be the base and the other the height. Here, base = 3 meters and height = 4 meters. 4. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 3 \times 4$$ 5. **Simplify the multiplication:** $$\text{Area} = \frac{1}{2} \times 12$$ 6. **Simplify the fraction:** $$\text{Area} = \cancel{\frac{1}{2}} \times \cancel{12} 6$$ 7. **Final answer:** $$\boxed{6 \text{ square meters}}$$ The correct choice is C: 6 square meters.