Concept Byte: Exploring the Area of a Circle

Use With Lesson 10-7

ACTIVITY

You can use transformations to find the formula for the area of a circle.

Activity

• Step 1 Use a compass to draw a large circle. Fold the circle horizontally and then vertically. Cut the circle into four wedges on the fold lines.

  

• Step 2 Fold each wedge into quarters. Cut each wedge on the fold lines. You will have 16 wedges.

  

• Step 3 Tape the wedges to a piece of paper to form the figure shown below. The figure resembles a parallelogram.

  

1. How does the area of the parallelogram compare with the area of the circle?
2. The base of the parallelogram is formed by arcs of the circle. Explain how the length b relates to the circumference C of the circle.
3. Explain how the length b relates to the radius r of the circle.
4. Write an expression for the area of the parallelogram in terms of r to write a formula for the area of a circle.

Exercises

Repeat Steps 1 and 2 from the activity. Tape the wedges to a piece of paper to form another figure that resembles a parallelogram, as shown below.

5. What are the base and height of the figure in terms of r?
6. Write an expression for the area of the figure to write a formula for the area of a circle. Is this expression the same as the one you wrote in the activity?

Table of Contents