1. **State the problem:** We have a circle with center $D$, radius $CD = 17$, and a central angle $\angle CDE = 162^\circ$. We need to find the area of sector $CDE$. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by: $$ A = \frac{\theta}{360} \times \pi r^2 $$ 3. **Substitute the known values:** $$ A = \frac{162}{360} \times \pi \times 17^2 $$ 4. **Calculate the radius squared:** $$ 17^2 = 289 $$ 5. **Simplify the fraction:** $$ \frac{162}{360} = \frac{\cancel{162}}{\cancel{360}} = \frac{9}{20} $$ 6. **Rewrite the area expression:** $$ A = \frac{9}{20} \times \pi \times 289 $$ 7. **Calculate the area:** $$ A = \frac{9 \times 289}{20} \pi = \frac{2601}{20} \pi $$ 8. **Approximate the value using $\pi \approx 3.1416$:** $$ A \approx \frac{2601}{20} \times 3.1416 = 130.05 \times 3.1416 = 408.27 $$ **Final answer:** The area of sector $CDE$ is approximately $408.27$ square units.