Published on 09/14/2005

#### Activity Overview

Students will compare areas of different polygons with a fixed perimeter and find the shape that gives the maximum area

#### Before the Activity

You will need to set the window and configuration of the Activity Center. 0< x <10, 0< y <22)

#### During the Activity

Count off by fives, but give each person one of the following numbers: 3, 4, 5, 6, 8.

Have each student draw a convex polygon with that number of sides and having a perimeter of 32 centimeters.

After drawing their polygon, they should take pieces of cereal and cover the polygon with as few pieces as possible. They may break the cereal into smaller pieces as necessary.

Next they should meet with other students who were assigned the same polygon and compare their results. Student's will return to their seats and compare their results with their original group.

On their calculator, students' will contribute to the Activity Center an ordered pair consisting of the number of sides of their polygon and the number of pieces of cereal required to cover it.

These points will be plotted for the whole class to see. The students should discuss what shape gave the largest perimeter. Ask whether this number would continue to increase as the number of sides increased.

Discuss what shape would have the largest possible area. You could introduce the idea of a limit. You could even draw a line representing the area of the circle so they could see the limit.

If the students are in geometry and have learned the formula for the area of a regular polygon, they could also find the actual area. Since the cereal is approximately 4 cm^2 in area, they could multiply the number of pieces by four to get an approximation of the actual area.

#### After the Activity

Review student results: