1. 10-8 Polygons and Tessellations
Learning Goal:
Students will be able to determine which polygons form a tessellation.

2. A polygon is…
a many-sided figure
a shape with three or more sides.

3. A triangle has three sides.1 3 2

4. Square
A square has four sides. 4 3 1 2

5. A pentagon has five sides.1 5 2 4 3

6. Hexagon and Heptagon
A hexagon has six sides. (Hexagon and six both have an “x”.)
A heptagon has seven sides.
heptagon
hexagon

7. Octagon An octagon has eight sides. Count the sides.
If this octagon was red and had the word “Stop” written on it, then you would know where we see a lot of octagons.

8. Nonagon An nonagon has nine sides. Count the sides.
What does the word “nonagon” sound like?

9. Decagon An decagon has ten sides. Count the sides.
How many years are in a “decade”?

10. How many degrees are in each polygon?
There is a formula!
(n-2)(180)=
n= the number of sides the polygon has

11. What is a Tessellation?
A tessellation is a tiling, kind of like the floor, except it goes on forever.
There must be no overlapping or no gaps.

12. Regular Tessellations
It must tile a floor (flat surface) with no gaps or overlapping.
The tiles must be regular polygons. (Remember that regular means all the sides and angles are congruent.)
Each vertex must look the same.
This is a vertex.

13. Things We Can Tessellate with These Rules.
Hexagons
120°+ 120°+120° = 360°
Squares
Notice that at the vertex the angles add up to 360°.
90°+ 90°+ 90°+ 90°
= 360°
Triangles
The same thing happens here.
60°+ 60°+ 60°+ 60° + 60°+ 60° = 360°

14. Guess what! Any regular polygon with more than six sides will overlap.
What Won’t Tessellate
Pentagons
It makes a gap!
108 °+108 °+108 °= 324°
Octagons
Now there is an overlap.
135 °+135 °+135 °= 405°
Guess what! Any regular polygon with more than six sides will overlap.
So the only polygons that will work are the triangle, square, and hexagon.

15. Semi-Regular Tessellations
Semi-regular tessellations are almost the same as regular tessellations, except you can use two or more regular polygons.
3, 6, 3, 6
3, 3, 3, 3, 6
Not a tessellation