© 2011 National Council of Teachers of Mathematics http://illuminations.nctm.org

Polygons, Perimeter, and Patterns NAME _________________________

Perry Meter likes to take walks around parks and measure how far he travels. The parks are

shaped like polygons made from “chains” of triangles placed side-by-side. In these “polygon

chains,” every other triangle is rotated 180o about its center and shifted to the right. Here is an

example of a polygon chain made with three triangles:

Complete the questions below to help Perry figure out the perimeter of each polygon so he

knows how far he walks.

1. Complete the chart below to show the perimeter of the polygons as you make them.

NAME OF POLYGON NUMBER OF TRIANGLES

IN POLYGON

PERIMETER OF

POLYGON

1 3 units

2

3

4

5

6

7

2. What would be the perimeter of the polygon chain made from 10 triangles? Explain how you

found your answer.

3. What is a mathematical rule for finding the perimeter of a chain of triangles if you know how

many triangles are in the chain?

© 2011 National Council of Teachers of Mathematics http://illuminations.nctm.org

4. If t represents the number of triangles you used to build one of the polygons, what is a

mathematical equation that could represent the perimeter of the polygon?

Perry has moved to a new city and wants to take walks around parks that are shaped like

polygons made from chains of squares that are placed side-by-side. Complete the questions

below to help Perry figure out the perimeter of the polygons so he knows how far he walks.

1. Complete the chart below to show the perimeter of the polygons as you make them.

NAME OF POLYGON NUMBER OF SQUARES

IN POLYGON

PERIMETER OF

POLYGON

1 4 units

2

3

4

5

6

7

2. What would be the perimeter of the polygon made from 10 squares? Explain how you found

your answer.

3. What is a mathematical rule for finding the perimeter of a chain of squares if you know how

many squares are in the chain?

4. If s represents the number of squares you used to build one of the polygons, what is a

mathematical equation that could represent the perimeter of the polygon?

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