# Lesson Area of circle and square with same circumference/perimeter

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 Geometry: Area and Surface Area Solvers Lessons Answers archive Quiz In Depth
 This Lesson (Area of circle and square with same circumference/perimeter) was created by by edjones(7569)  : View Source, ShowAbout edjones: Retired MD, likes kids and math 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 where r=radius 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. Ed This lesson has been accessed 16989 times.