1. **State the problem:** We need to find the area of a right triangle with a base of 8 cm and a height of 3 cm. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Substitute the given values:** $$\text{Area} = \frac{1}{2} \times 8 \times 3$$ 4. **Calculate the multiplication:** $$\text{Area} = \frac{1}{2} \times 24$$ 5. **Simplify the fraction:** $$\text{Area} = \cancel{\frac{1}{2}} \times \cancel{24}$$ $$\text{Area} = 12$$ 6. **Final answer:** The area of the triangle is 12 square centimeters.