This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).

Dr. Sarah's Java Sketchpad Worksheet on Areas of Polygons

1. If the perimeters of polygons are approximately equal, as seen below, what happens to the area of a polygon as the number of sides increases?

2. Explain why a circle is the shape that maximizes the area of an enclosed regular region when using a given amount of fencing.

3. Notice that the perimeters of the polygons are approximately equal, but not exactly equal. What happens if you drag the red points to change the size of the polygons in order to try and get perimeter of each polygon to exactly match the circumference of the circle? Try this below!

4. Set the circumference of the circle below equal to each of the equations for the perimeter of an equilateral triangle, a square, a pentagon, a hexagon, and then an octagon. Algebraically solve each of these expressions.

5. Compare your answers in 3. and 4. and discuss.

Drag a red point to change the size of a figure. The area and perimeter will change as the figure changes.

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