IM 7.3.8 Lesson: Relating Area to Circumference

A circular field is set into a square with an 800 m side length. Estimate the field's area.

1. The top circle is separated into fourths. Arrange the fourths so that straight sides are next to each other, but the curved edges are alternately on top and on bottom. Pause here so your teacher can review your work.
2. The bottom circle is separated into eighths. Arrange the eighths next to each other, like you did with the fourths.

What polygon does the shape made of the circle pieces most resemble?

How could you find the area of this polygon?

Imagine a circle made of rings that can bend but not stretch. Watch the animation below. What polygon does the new shape resemble?

How does the area of the polygon in the app above compare to the area of the circle?

How can you find the area of the polygon?

State, in detailed steps, how you could find the polygon’s area in terms of the circle’s measurements. Show your thinking. Organize it so it can be followed by others.

After you finish, trade papers with a partner and check each other’s work. If you disagree, work to reach an agreement. Discuss:

• Do you agree or disagree with each step?
• Is there a way they can make the explanation clearer?

Elena wants to tile the top of a circular table. The diameter of the table top is 28 inches. What is its area?

A box contains 20 square tiles that are 2 inches on each side. How many boxes of tiles will Elena need to tile the table?