Designing Your Area
Exploring Patterns
Slowly move each slider from left to right on each applet below. Record your findings on your handout. Use what you notice to find the area of each regular polygon.
Regular Octagon
Regular Heptagon
Regular Hexagon
Regular Pentagon
Regular Quadrilateral
Regular Triangle
Area of an Regular n-gons
You have observed the regular polygons above and found the area of each polygon. Look at your table and see if you could find a pattern that would work for finding the area of a 20-sided regular polygon or a 53-gon. Use words and/or variables to write a relationship that would help you find the area of any regular n-gon.
Remember: an n-gon is a polygon with n sides.
A Different Method
Slowly move the slider from left to right on the applet below. This is a different approach to calculating the area of a regular polygon. Can you write a different equation, using words and/or variables, that would also help find the area of a regular polygon?