1. **State the problem:** We need to find the area of a right-angled triangle with a base of 9 meters and a height of 8 meters. 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:** Here, base $= 9$ m and height $= 8$ m, so: $$A = \frac{1}{2} \times 9 \times 8$$ 4. **Calculate the product:** $$A = \frac{1}{2} \times 72$$ 5. **Simplify the expression:** $$A = \cancel{\frac{1}{2}} \times \cancel{72} = 36$$ 6. **Final answer:** The area of the triangle is $36$ square meters.