1. **State the problem:** Calculate the area of a triangle with base 10 cm and height 6 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:** $$\text{Area} = \frac{1}{2} \times 10 \times 6$$ 4. **Calculate the product:** $$\text{Area} = \frac{1}{2} \times 60$$ 5. **Simplify the fraction:** $$\text{Area} = \cancel{\frac{1}{2}} \times \cancel{60} = 30$$ 6. **Final answer:** The area of the triangle is **30 cm\textsuperscript{2}**.