CHARACTERISTICS OF REGULAR POLYGONS
Geometry
 
1. CIRCUMCIRCLES

All regular polygons have a circumcircle, i.e. they fit exactly inside a circle with all its vertices touching the circumference. The radius and centre of this circle are also the radius and centre of the regular polygon.

One way of constructing regular polygons is to divide the circumference up into equal-sized arcs and join these adjacent points on the circumference with straight lines. This gives us the corresponding inscribed regular polygon. The bigger the radius of the circle, the bigger the regular polygon constructed.

1.- Construct some different polygons and change the size of each one by making the radius bigger. 

 Introduce the values by using the arrows or writing the value directly into the space.
The radius can be given decimal values.

In which polygon are the sides and radius the same length? 

2.- Draw a hexagon in your exercise book by drawing a circle and measuring the length of the radius. Then divide the circumference into 6 using the length of the radius to make each division. Finally, join the adjacent points together with straight lines.

2. The apothem OF a regular polygon
The apothem in a regular polygon is the perpendicular line from one of the sides to the centre of the shape. It is important to know this in order to calculate the area of a polygon as it represents the height of each of the triangles formed by two radii and one side of the polygon.

3.- Increase the number of sides of the shape in this window and watch how the perpendicular line gets longer and longer until it gets closer and closer in length to the radius of the polygon.

4.- Draw a hexagon in your exercise book and work out the length of the apothem geometrically.
 
       
           
  Miguel García Reyes
 
Spanish Ministry of Education. Year 2001
 
 

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