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.**