POLYGONS“MANY” “SIDES”

A polygon is a 2-dimensional shape.

This means that polygons have both length and width.

WIDTH

L

E

N

G

T

H

Polygons are closed shapes, and they are made of at least 3 line

segments (straight lines).

Why is this shape NOT a polygon?

This shape is NOT “closed.”

Why can’t a polygon have only 2 sides?

With only 2 sides, the shape could not be “closed.”

Is this shape a polygon?

As a matter of fact, this IS a polygon.

This shape is “closed,” and it has 12 sides.

However, this is a special type of polygon called “concave.”

It’s called “concave” because some of the sides are “caved in.”

and you can draw a line segment outside of the figure when

connecting two vertices.

For our purposes, we will be discussing only convex polygons

and not concave polygons.

We will learn the names for the first eight polygons.

A one-sided polygon is called…?

That’s a trick question. There is no such thing as a one-sided

polygon. Remember, polygons must have at least 3 sides.

A 3-sided polygon is called a triangle.

You can remember the prefix “tri” by thinking of a tricycle. A

tricycle has 3 wheels.

                                

A 4-sided polygon is called a quadrilateral.

You can remember the prefix “quad” by thinking “times four.”

Quadruple means x 4

A 5-sided polygon is called a pentagon.

You can remember this name by thinking about the building in

Washington, D.C.

A six-sided polygon is called a hexagon.

You can remember that a hexagon has six sides because the words hexagon and six both have

the letter “x.”

The hexagon is the polygon of choice for bees.

A 7-sided polygon is called a heptagon.

An 8-sided polygon is called an octagon.

You can remember the prefix “oct” by thinking of an octopus.

A 9-sided polygon is called a nonagon.

You can remember that a nonagon has nine sides because

the words nonagon and nine both have two “ns.”

A 10-sided polygon is called a decagon.

You can remember the prefix “dec” by thinking about a

decade.

19911992

19931994

19951996

19971998

19992000

TEN YEARS

Let’s explore the diagonals of a polygon.

Diagonals from 1 vertex of a quadrilateral.

Diagonals from 1 vertex of a pentagon.

Diagonals from 1 vertex of a hexagon.

None, this is a trick question

Another interesting characteristic of TOTAL diagonals in polygons:

A diagonal in a polygon connects two vertices (corners).

A quadrilateral has 2 total diagonals.

A pentagon has 5 total diagonals.

A hexagon has 9 total diagonals.

Now let’s chart our findings and look for a pattern.

Polygon Total Number of Diagonals

3 (Triangle) 0

4 (Quadrilateral) 2

5 (Pentagon) 5

6 (Hexagon) 9

Now let’s chart our findings and look for a pattern.

Polygon Total Number of Diagonals

3 (Triangle) 0

4 (Quadrilateral) 2

5 (Pentagon) 5

6 (Hexagon) 9

Here’s the formula:

Total diagonals =

Number of vertices X

Diagonals from a single vertex÷ 2

T = n x (n 3)

Using the formula try finding the number of total diagonals in a regular decagon:

• T = n x (n 3)

This concludes my show on polygons.

The End.