Explore the relationship between the radius and area of a circle by following these steps.

✓ 1. Press Continue to rearrange the sectors of the circle to form a shape resembling a parallelogram.

✓ 2. If we divide the circle into more sectors, the bottom shape more closely resembles a parallelogram. Press Continue to repeat the last step with 16 sectors.

✓ 3. The formula for the area of a parallelogram is base − height base × height 2 × base × height .

✓ 4. The height of the parallelogram is 2 πr r .

✓ 5. The formula for the circumference of the circle is π πr 2πr .

✓ 6. The base of the parallelogram-like figure is half the circumference of the circle, or ##b = \frac{\sf 1}{\sf 2}({\sf 2} \pi r) = \pi r.## Therefore, the area of the figure wil be A = πr (r)(2πr) (r)(πr) .

✓ 7. Simplifying the formula for area in the previous step yields the formula for the area of a circle. ##A = (r)(\pi r) = \pi r^2##