Area of Circles by Anthony Or with questions added
What is the area of a circle? Explore with the following applet, and answer the six questions below.
Anthony Or, GeoGebra Institute of Hong Kong.
Question #1
As you increase the number of dissected parts of the circle and rearrange them, what shape gets formed from the circle?
Question #2
The height of this new shape is equal to what measurement of the original circle?
Question #3
The base (or length) of this new shape is equal to what measurement of the original circle.
Question #4
How can you calculate the area of a circle based on its relationship to the area of the new shape?
Question #5
Circumference is equal to and since diameter is equal to , circumference is also equal to , so half of the circumference is equal to
Question #6
Based on this activity, the area of the new shape is equal to the area of the circle, which means the area of a circle is equal to...