Section 11.6

Today in class, we learned about finding the area of regular polygons, as well as the different parts. We know that all regular polygons can be inscribed in a circle.

In the hexagon, there are some important things that you should know.

• Segments OA and OB are radii of the circle and the polygon (yes, regular polygons have radii)
  
• Segment OG is an apothem, a segment joining the center to the midpoint of any side, and forms a right angle, so OG⊥AB.
  

The octagon shows you other parts of a regular polygon.

• Center- the center of a regular polygon


• Central angle- the angle formed at the center of the polygon by two segments from adjacent vertices.
  

To sum things up, here are some important things about apothems and radii:

• all apothems of a regular polygon are congruent
  
• only regular polygons have apothems


• an apothem is a perpendicular bisector of a side


• a radius of a regular polygon is a radius of a circle circumscribed about the polygon


• a radius of a regular polygon bisects an angle of the polygon.
  

Now on to the symbols of the parts of the polygon and the formula for the area. Also, uppercase and lowercase letters mean different things.

• A- area of the polygon


• p- perimiter of a polygon


• n- number of sides in a polygon


• s- length of a side of a polygon


• r- length of a radius of a polygon


• a- length of the apothem


• θ (theta)- measure of the central angle
  

The formula for the area of a regular polygon is 1/2 ap, or one half of the apothem times the perimeter. Also, 1/2 ans can be used for the area, as the number of sides in a polygon (n) times the side length (s) equals the perimeter (p).

That's all for this section, I hope our blog is popular at the conference tomorrow!

-Jacob

P. S. I lost the game.