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# Polys: What is a Polygon?

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Source:
Author: Janice VanCleave

### Problem

What is a polygon?

### Materials

• marking pen
• ruler
• rectangular dishwashing sponge
• scissors
• poster paint (any color)
• small bowl
• sheet of white construction paper

### Procedure

1. Use the pen and ruler to draw a line across the center of the sponge, dividing the sponge into two equal sections.
2. Draw a triangle on one section of the sponge.
3. Cut out the two indicated shapes drawn on the sponge. Keep the triangle for this experiment and the rectangular piece for the following "Let's Explore" experiment. Discard the remaining sponge pieces.
4. Pour about 1/2 inch (1.25 cm) of paint into the bowl.
5. Look at the sides of the triangle. Dip one of the large triangular faces into the bowl of paint, and make a print of this face on the paper.
6. Turn the sponge over and make a print of the opposite face.
7. Repeat steps 5 and 6 to make prints of the remaining sides of the sponge.

### Results

Five prints with two different kinds of shapes are made.

### Why?

A polygon is a closed figure (a geometric figure that begins and ends at the same point) formed by three or more straight line segments that are joined only where the ends of the line segments meet. Each of these endpoints is connected to only two line segments. A polygon made of three sides is called a triangle. The sum of the angles created by the three sides of a triangle is always 180 degrees. A polygon made of four sides with two pairs of parallel sides and right angles (angles that measure 90 degrees) is called a rectangle. Two of the prints made with the sponge are triangles and three are rectangles.

### Let's Explore

A quadrilateral is a four-sided polygon formed by four line segments. One type of quadrilateral is a parallelogram, which has two pairs of parallel sides. A rectangle is an example of a parallelogram. How many different-size parallelogram prints can be made by the rectangular sponge from the experiment? Repeat the experiment, using the rectangular sponge and a different color of paint. Science Fair Hint: Use the prints to prepare a display representing polygons.

### Show Time!

1. There are three basic types of quadrilaterals: the trapezium, which has no parallel sides; the trapezoid, which has one pair of parallel sides; and the parallelogram. Prepare and display a chart representing the different types of quadrilaterals and examples of each, such as the one shown here. Prepare a legend giving a description of each example. For information, see pages 37-42 in Janice VanCleave's Geometry for Every Kid. (New York: Wiley, 1994).
2. A rhomboid is a parallelogram that has no right angles and only opposite sides are congruent (the same). A rhomboid is like a flexible rectangle with its top pushed to one side and its bottom to the other. The shape of a rhomboid can be changed into that of an equal-size rectangle by cutting off a triangle from one side and placing it on the opposite side. Demonstrate this by drawing a large rhomboid on a sheet of paper. Use a ruler to draw a perpendicular dashed line from the top left vertex (point where two lines meet) of the rhomboid to its base. This line forms a triangle shape. Draw stripes across the triangle then cut along the dashed line and move the cutaway triangle to the opposite side of the rhomboid.
3. Polyhedrons are three-dimensional figures with flat surfaces called faces. These faces are polygons. Display drawings of polyhedrons, such as a house or a cereal box. Label the different polygons on the drawings.

### Check it Out!

A tanagram is a Chinese puzzle made by cutting a square into seven polygons: five triangles, one square, one rhomboid. The pieces can be arranged to form the original square as well as a great variety of other polygons. For information about making and creating different polygons with a tanagram, see pages 101-104 in Margaret Kenda and Phyllis S. Williams's Math Wizardry for Kids (Hauppauge, NY: Barron's, 1995).