1. **State the problem:** We need to find the area of triangle $\triangle DEF$ where sides $d = 990$ cm, $e = 990$ cm, and the included angle $\angle F = 141^\circ$. 2. **Formula used:** The area of a triangle given two sides and the included angle is $$\text{Area} = \frac{1}{2} \times d \times e \times \sin(\angle F)$$ 3. **Apply the values:** $$\text{Area} = \frac{1}{2} \times 990 \times 990 \times \sin(141^\circ)$$ 4. **Calculate $\sin(141^\circ)$:** Since $141^\circ = 180^\circ - 39^\circ$, $$\sin(141^\circ) = \sin(39^\circ) \approx 0.6293$$ 5. **Substitute and simplify:** $$\text{Area} = \frac{1}{2} \times 990 \times 990 \times 0.6293$$ 6. **Calculate intermediate multiplication:** $$\frac{1}{2} \times 990 = 495$$ 7. **Final multiplication:** $$495 \times 990 \times 0.6293 \approx 495 \times 623.007 = 308,488.5$$ 8. **Round to nearest square centimeter:** $$\boxed{308489 \text{ cm}^2}$$ Thus, the area of $\triangle DEF$ is approximately 308,489 square centimeters.