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A circular field is set into a square with an 800-m side length.
A square where the vertical distance is labeled 800 meters. The largest possible circle is drawn inside the square with a line segment is that begins from the center of the circle to a point on the edge of the circle.
What is the field’s area? Record an estimate that is:
| too low | about right | too high |
|---|---|---|
Your teacher will give you a page with two circles on it and a piece of paper that is a different color.
Follow these instructions to create a visual display:
Cut out both circles, cutting around the thick outline.
Fold and cut one of the circles 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.
Fold and cut the fourths in half to make eighths. Arrange the eighths next to each other, like you did with the fourths.
Pause here so your teacher can review your work.
After you finish gluing your shapes, answer the following questions.
How do the areas of the two shapes compare?
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.
Here are some special objects that might be seen at a Lakota powwow, or wacipi (wah-CHEE-pee).
A hoop drum has a radius of 7 inches. What is the area of the drum?
A beaded medallion has a diameter of 6 centimeters. What is the area of the medallion?
The word squared means “to the second power.” This is because a square with side length has an area of , or .