If the perimeter of a square has the same length as the circumference of a circle which has the larger area?
Let perimeter of a square=x
Then each side (s) is 1/4 of the perimeter. s=x/4 and the area A=s^2=(x/4)^2=x^2/16
Let circle circumference (C)=y
divide 2*pi into each side:
The area of a circle is the green line in the graph; the area of the square is purple. The area of a circle is larger than the area of a square for all identical lengths of perimeter and circumference. They approach each other as they approach zero.
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