WHY THE AREA OF A CIRCLE IS R^{2}
(You will need your algebra to prove this!!)
 Start with a circle and cut it up into pie slices:
 Now roll it out into a line:
(C)

 Now cut the line in half and put
the second half upsidedown on the
first half:
 Now it's a RECTANGLE!! (approximately)
So the area of this
rectangle is:
C R C
A = R X  = 
2 2
 Since C = D and D = 2R then substituting 2R for D we have: C = 2R.
Putting this back in the area formula, we have:
R C R(2R)
A =  =  = RR = R^{2} <=== Notice that the 2s cancelled!
2 2
