march 19,2012

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

STEP 1:
when finding the area of a regular polygon we first need to notice what kind of polygon we are working with.

in the image oin the right is a hexagon.
in the hexangon if a teacher or a person were to say what is the area of the hexagon then look its a hexagon.

STEP 2 : KNOW WHAT AN APOTHEM IS :)

LEts ssay this is a regents problem and thety tell you to find the area of the polygon.First know the formula.

The formula :

NAS

   2
N: number of sides
A: apothem
S: the base
and divide that by 2.





many might not know what an aopothem is :)
so ill tell you :)
an apothem is the distance between the sides of the polygon to the center.
in this case the apothem is 2.

STEP 3:COUNT THE SIDES ! FOR N  :):D
 Like i said before
N is the number of sides
in this case since its a hexagon  there is six sides

like in the image shown in the left ------>















STEP 4: THE S IS NEXT :)
                     
 So from step 2 and step 3 we know that  N ISTHE NUMBER OF SIDES
A IS THE LENGTH BETWEEN THE SIDES AND THE CENTER

THE S :
the s is the base and dont get confuse just because its the base it doesnt mean that its in the bottom the base is anywhere that the number is next to a side.
in this case the s would be 6.

STEP 5: PLUG IT IN !!! YAY ^O^

now that we know what an apothem , n, and s is we can plug the numbers in the formula for area.
SO...... now we apply the new knwodleg we now know and solve the problem :)
ALSO DONT FORGET TO
 SHOW WORK !

FORMULA :
NAS
  2
PLUG IN :
 6*2*6 
    2
multiply first :
6*6= 36*2 =72
THEN DIVIDE:
72 
2
Final answer is
36 because 72/2  is 36
so the final area would be 36.


YOU SHOULD KNOW :
what an apothem is now :)
how to calculate the area of any polygon because the formula:
NAS
  2
works for every polygon


there might be a case where the area was already given to you: in that case plug in the area and dop it like a equation 


for example:
A= 72 
a=6
n=6
find the S


then we plug in the equation 


72= 6*6*s
          2
To get rid of the two in the other side of the equation you multiply 72*2 which equals 144. then also multiply 6*6 which are the other side of the equation. once that's done divide 144/36 which gives us 4 and that would be the S= the base :).


NOW YOU TRY:D

If we have an area of 20 and the apothem of 2 and there are 2 sides what is the S ?