1. **State the problem:** We are given the circumference of a circle as 36.5 cm and need to find its area. 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 $$C = 36.5$$, use the circumference formula: $$36.5 = 2\pi r$$ Divide both sides by $$2\pi$$: $$r = \frac{36.5}{2\pi}$$ Show cancellation: $$r = \frac{36.5}{\cancel{2}\pi} \times \frac{1}{\cancel{2}} = \frac{36.5}{2\pi}$$ (no common factors to cancel here, so just division) 4. **Calculate the radius numerically:** Using $$\pi \approx 3.1416$$: $$r \approx \frac{36.5}{2 \times 3.1416} = \frac{36.5}{6.2832} \approx 5.81$$ cm 5. **Calculate the area:** $$A = \pi r^2 = 3.1416 \times (5.81)^2$$ $$A = 3.1416 \times 33.76 \approx 106.0$$ cm² **Final answer:** The area of the circle is approximately $$106.0$$ cm².