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Area of a circle from what we already know

Author:
Alfonso Garcia, Malin Christersson
Topic:
Area, Circle

An interesting surprise

In this section we will explore how to determine the area of a circle by dividing it into sections and then rearranging these sections to form a shape with an easily recognizable area. Follow the instructions and have fun!

1. Slider 1

The applet below shows a circle divided into 4 sections. As we move slider 1 the number of sections increases by multiples of 4. Move slider 1 to 3 and notice that there are now 12 sections in the circle. We will explore what happens when we play with the other two sliders in the sections below.

2. Slider 2

Set slider 1 to 5 (The circle will have 20 sections). Move slider 2 all the way to the left and describe what happens. You can change the value of slider 1 to greater numbers to help in your description.

3. Slider 3

Now move slider 3 all the way down slowly and describe what happens once it gets to the bottom. Give as much detail as possible.

4. What shape do you see?

As slider 3 moved down with a large number of sections for slider 1, what shape is created by rearranging the sections?

Tick all that apply
  • A
  • B
  • C
Check my answer (3)

5. Now, what is the area?

If you answered parallelogram in the previous question, you are correct! Write the formula for the area of a parallelogram.

6. Connecting to the circle part 1

The area of a parallelogram is The height of the parallelogram is the same as...

Tick all that apply
  • A
  • B
  • C
Check my answer (3)

7. Connecting to the circle part 2 - the base

The area of a parallelogram is The applet shows the base = Which of the following best describes why this is true?

Tick all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

8. A little algebra

Simplify the right side of this equation. This is the area of the parallelogram: Comment on your simplified equation.

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