Simple way to show students how regular polygons look when you increase the number of sides, n. With this worksheet, students are able to check the area of a regular polygon with a given side length.

1. What is a regular polygon?
2. Are regular polygons and polygons the same? If so, why? If not, why not?
3. Are triangles regular polygons?
4. What makes the area and surface area different?
5. What do you notice about your regular polygon?
6. Can you see other shapes within your regular polygon? If so, what do you see?
7. If you increase the sides of a regular polygon, will that yield more triangles? How many do you see?
8. If you decrease the vertices of a regular polygon, will that yield less triangles? How do you know?
For the following problems below, solve using pencil and paper and Geogebra as a tool. You may work with a partner or in groups.
9. If n = 4 and AB has a length of 7, what is the area?
10. If n = 3 and AB has a length of 9, what is the area?
11. If n = 12 and AB has a length of 4, what is the area?