1. **State the problem:** Find the area of a triangle with base $10$ cm and height $8$ cm. 2. **Formula:** The area $A$ of a triangle is given by the formula: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Substitute the values:** $$A = \frac{1}{2} \times 10 \times 8$$ 4. **Calculate:** $$A = \frac{1}{2} \times 80$$ 5. **Simplify:** $$A = \cancel{\frac{1}{2}} \times \cancel{80}$$ Actually, to show cancellation properly: $$A = \frac{1}{2} \times 80 = \frac{\cancel{80}}{2} = 40$$ 6. **Final answer:** The area of the triangle is $40$ cm².