SOLUTION: Why does the formula for area of a circle work? Such as¼ • π • d² , why divide by 1/4 to get the area?

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Question 920327: Why does the formula for area of a circle work? Such as¼ • π • d² , why divide by 1/4 to get the area?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

area of the circle is A=pi%2Ar%5E2 where r=radius
you also know that diameter D=2r; consequently,D%5E2=%282r%29%5E2=4r%5E2

so, when you know the diameter and want to use it to find area, then you have to express r%5E2 in terms of D%5E2:
D%5E2=4r%5E2=>r%5E2=D%5E2%2F4 or r%5E2=%281%2F4%29D%5E2
then go to A=pi%2Ar%5E2 and substitute %281%2F4%29D%5E2 for r%5E2
A=pi%2A%281%2F4%29D%5E2
A+=+%28pi%2F4%29%2AD%5E2