March 17: How do we find the area of regular polygons? (AIM)

Aim: How do we find the area of regular polygons? 

• Regular polygons are polygons with all sides and all angles equal.

• Some examples usually used as regular polygons are:

• Pentagons - 5 (1/2 x a s)

There are 5 equal
triangles, with equal
side lengths. 

• Hexagons - 6 (1/2 x a s)

 

• Heptagons - 7 (1/2 x a s) 

• But there's a shorter way to know this. Also remember that in any case n is number of sides, s is side length, and a is apothem [distance from center of polygon to the side].

This table shows that
the formula is 1/2 times
the # of sides, apothem,
and side length. 

• Also there's another rule for finding the area of a regular polygon. It's 1/2 x P x a. In this case P is the perimeter and a is the apothem. 

• Now try this problem:

1. What is n and the areas of this figure? 

Sources Cited:

1. John Schnatterly AKA -->  http://johnschnatterly.blogspot.com/
2. http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/jenna2.html
3. http://www.kathykwylie.com/blog/2010/10/geometric-shapes-in-quilts-hexagons/
4. http://mryipsmathclass.blogspot.com/2010_11_01_archive.html
5. http://www.trueknowledge.com/q/facts_about__pentagon