1. **Problem statement:** Find the area of a regular dodecagon (12-sided polygon) with a radius (circumradius) of 13. Round the answer to the nearest hundredth. 2. **Formula for the area of a regular polygon using radius:** $$\text{Area} = \frac{1}{2} n R^2 \sin\left(\frac{2\pi}{n}\right)$$ where $n$ is the number of sides and $R$ is the radius. 3. **Apply the formula:** - Number of sides $n = 12$ - Radius $R = 13$ $$\text{Area} = \frac{1}{2} \times 12 \times 13^2 \times \sin\left(\frac{2\pi}{12}\right)$$ 4. **Simplify inside the sine:** $$\sin\left(\frac{2\pi}{12}\right) = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$$ 5. **Calculate the area:** $$\text{Area} = 6 \times 169 \times \frac{1}{2} = 6 \times 84.5 = 507$$ 6. **Final answer:** The area of the regular dodecagon is $507.00$ (rounded to the nearest hundredth).