1. **State the problem:** We have an isosceles triangle with two equal sides of length 8.5 cm and a base of length 8 cm. We need to find the area of this triangle. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Find the height:** Since the triangle is isosceles, the height splits the base into two equal segments of length $\frac{8}{2} = 4$ cm. 4. Use the Pythagorean theorem to find the height $h$: $$h = \sqrt{8.5^2 - 4^2}$$ $$= \sqrt{72.25 - 16}$$ $$= \sqrt{56.25}$$ $$= 7.5 \text{ cm}$$ 5. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 8 \times 7.5$$ $$= 4 \times 7.5$$ $$= 30 \text{ cm}^2$$ **Final answer:** The area of the triangle is $30$ cm².