Area of Circles by Anthony Or with questions added

What is the area of a circle? [b]Explore with the following applet, and answer the six questions below.[/b]

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?

triangle rectangle oval square

Question #2

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

diameter the circumference radius half of the circumference

Question #3

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

radius diameter half of the circumference the circumference

Question #4

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

multiply the radius by 2 multiply the circumference by the radius add the radius to the circumference multiply half of the circumference by the radius

Question #5

Circumference is equal to [math]\pi d[/math] and since diameter is equal to [math]2r[/math], circumference is also equal to [math]2\pi r[/math], so half of the circumference is equal to

[math]\frac{1}{2}\pi r[/math] [math]\pi r[/math] r [math]\pi rd[/math]

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...

[math]2\pi r[/math] [math]\pi dr[/math] [math]\pi r\cdot r[/math] or [math]\pi r^2[/math]