1. The problem is to find the area of a right triangle with legs measuring 8.9 cm and 8.1 cm. 2. The formula for the area of a right triangle is: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. Here, the base is 8.1 cm and the height is 8.9 cm. 4. Substitute the values into the formula: $$\text{Area} = \frac{1}{2} \times 8.1 \times 8.9$$ 5. Calculate the product inside the multiplication: $$8.1 \times 8.9 = 72.09$$ 6. Now multiply by \frac{1}{2}: $$\text{Area} = \frac{1}{2} \times 72.09 = 36.045$$ 7. Therefore, the area of the triangle is: $$\boxed{36.045 \text{ cm}^2}$$