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?

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The height of this new shape is equal to what measurement of the original circle?

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The base (or length) of this new shape is equal to what measurement of the original circle.

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How can you calculate the area of a circle based on its relationship to the area of the new shape?

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Circumference is equal to and since diameter is equal to , circumference is also equal to , so half of the circumference is equal to

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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...

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