1. **State the problem:** Find the area of triangle PQR with sides $QR=8.7$ cm, $RP=8$ cm, and base $QP=6$ cm. 2. **Formula used:** We use Heron's formula for the area of a triangle given all three sides: $$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$ where $s$ is the semi-perimeter: $$s = \frac{a+b+c}{2}$$ 3. **Calculate the semi-perimeter:** $$s = \frac{8.7 + 8 + 6}{2} = \frac{22.7}{2} = 11.35$$ 4. **Apply Heron's formula:** $$\text{Area} = \sqrt{11.35(11.35 - 8.7)(11.35 - 8)(11.35 - 6)}$$ 5. **Calculate each term inside the square root:** $$11.35 - 8.7 = 2.65$$ $$11.35 - 8 = 3.35$$ $$11.35 - 6 = 5.35$$ 6. **Multiply the terms:** $$11.35 \times 2.65 \times 3.35 \times 5.35$$ 7. **Calculate the product:** $$11.35 \times 2.65 = 30.0775$$ $$30.0775 \times 3.35 = 100.760125$$ $$100.760125 \times 5.35 = 539.06666875$$ 8. **Find the square root:** $$\sqrt{539.06666875} \approx 23.22$$ 9. **Final answer:** The area of triangle PQR is approximately **23.2 cm²** to the nearest tenth. Note: The previously crossed out value 23.8 was close, but recalculation with precise $s$ gives 23.2.