1. **Stating the problem:** We are given a right triangle with side lengths 3, 4, and 5. We need to find the area $S$ of this triangle. 2. **Formula used:** The area of a triangle is given by: $$S = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify base and height:** Since the triangle is right-angled, the two sides forming the right angle (3 and 4) can be considered as base and height. 4. **Calculate the area:** $$S = \frac{1}{2} \times 3 \times 4$$ 5. **Simplify:** $$S = \frac{1}{2} \times 12$$ 6. **Final answer:** $$S = 6$$ The area of the right triangle is 6.