Develop the formula for finding the area of a circle by breaking a circle into pieces and rearranging them.
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
When the circle is rearranged and the number of parts increases, what shape do the rearranged parts start to look like?
The formula for the area of a parallelogram is [math]\textsf{Area}=\textsf{base}\times\textsf{height}[/math]. If a circle is rearranged into many parts that appear like a parallelogram, what is the measure of the height and what is the measure of the base?
How does the formula for the area of a circle relate to the formula for the area of the parallelogram created by rearranging the sectors of the circle?