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

(3-19-2012)Aim: How do we find the area of regular polygons?

Area of an isosceles triangle with altitude a, and base s.

Area of a regular polygon
You can divide a regular polygon into congruent isosceles triangle by drawing segments in a vertex.

https://www.cdli.ca/courses/math1204/unit06_org02_ilo02/les02_002.gif 




Area of each isoscles triangle with altitude regular pentagon
A= sa/2(?)-number or amount of sides the figure has or 1/2as(?)-number or amount of sides the figure has 
a--altitude
s--side
A--area

Perimeter: (?)s
(?)--number of sides
s--side value

http://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Class%20Notes/Chapter%2011/Lesson11-5/RegularPentagon.gif









For pentagon: A=sa/2(5)--Because there are five sides of the pentagon
Perimeter formula for pentagon: 5s



Area of hexagon
as/2(6) or 1/2as(6)
Perimeter:6s

http://jwilson.coe.uga.edu/emt668/EMAT6680.2003.fall/Montgomery/EMAT6690/Instructional%20Unit/Area/InstructUnitArea_files/image217.gif





Regular Polygon Area Conjecture
           The area of a polygon is given by the formula 1/2P*a, where a is the area, p is the perimeter. Also the formula that is more frequently used  1/2nas or nas/2 in which a is the apothem. The apothem is a perpendicular segment from the center to the side of the polygon.
Example:

 




http://www.capitan.k12.nm.us/teachers/shearerk/images/Apothem-hexagon.gif


S stands for the length of each side and n  is the number of sides of the polygon. 

Eamples:
1.
A=?
s=25in
a=25.8in
n=8in

A=nas/2
(8*25.8*25)/2
(5160)/2
Answer: 2580 in^2

2.
P=200cm
a=40.2cm
A=?

A=1/2P*a
1/2(200*40.2)
1/2(8040)
Answer:4020cm^2
 
TRY IT YOURSELF
 A=868
s=?
a=15.5
n=7

Answer:

s=16