1. **State the problem:** We are given the circumference of a circle as 165 mm and need to find the area of the circle, rounded to 1 decimal place. 2. **Recall the formulas:** - Circumference of a circle: $$C = 2\pi r$$ where $r$ is the radius. - Area of a circle: $$A = \pi r^2$$ 3. **Find the radius:** Given $$C = 165$$, solve for $r$: $$r = \frac{C}{2\pi} = \frac{165}{2\pi}$$ 4. **Calculate the radius value:** $$r \approx \frac{165}{6.2832} \approx 26.26$$ mm 5. **Calculate the area:** $$A = \pi r^2 \approx 3.1416 \times (26.26)^2 \approx 3.1416 \times 689.63 \approx 2164.5$$ mm$^2$ 6. **Round the answer:** Area $\approx 2164.5$ mm$^2$ to 1 decimal place. **Final answer:** The area of the circle is approximately $2164.5$ mm$^2$.