The radius of the figure is $ 13 \mathrm{~mm}$. It follows that a two thirds of a circle has area $\frac{2}{3} \pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle.
Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: The radius of the figure is $ 13 \mathrm{~mm}$. It follows that a two thirds of a circle has area $\frac{2}{3} \pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle.
Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: The radius of the figure is $ 13 \mathrm{~mm}$. It follows that a two thirds of a circle has area $\frac{2}{3} \pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle.