Shape 

Copyright David & Cynthia Thomas, 2009

Perimeter & Area of Polygons--Directed Activity: Perimeter vs. Area of Regular Pentagons

Focus	Area of a Regular Pentagon
Technologies	The Geometers Sketchpad and model 3_RegPolygonArea.gsp
Background	Figure 3.22 shows six regular polygons and lists their respective perimeters and areas.  In addition, a line segment called the apothem is drawn from the center of each polygon perpendicular to one side.  The radius of the polygon is the same as the radius of the circle in which it is inscribed.  Figure 3.22: Area vs. Perimeter of Regular Polygons
Tasks	- For polygons with a given radius, as the number of sides increases what happens to the § Perimeter of the polygon? § Area of the polygon? § Apothem of the polygon? - Using The Geometers Sketchpad, measure the apothem of each polygon. - Find an algebraic relationship between the perimeter, area, and apothem of each polygon. - What happens to that relationship if you change the radius?