Lesson Area of circle and square with same circumference/perimeter
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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 so {{{C=2pi*r=y}}} where r=radius divide 2*pi into each side: {{{r=y/2pi}}} {{{A=pi*r^2=pi*(y/2pi)^2}}} 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. Ed {{{graph(500,500,-10,10,-10,10,(x/4)^2,3.14159*(x/(2*3.14159))^2)}}}
