Relationship Between Perimeter And Area

Geometry Level 2

A circle with perimeter x cm x \text{ cm} has an area of x cm 2 . x \text{ cm}^2.
A square with perimeter y cm y \text{ cm} has an area of y cm 2 . y \text{ cm}^2.
Which of these shapes has a larger area, the circle or the square? (That is, x > y x>y or x < y ? x<y? )

The square The circle

Chung Kevin by Chung Kevin , 46, Australia

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1 solution

Marta Reece
May 12, 2018

x = A ∘ = π r 2 = 2 π r ⟹ r = 2 , x = 4 π x=A_\circ=\pi r^2=2\pi r\implies r=2, x=4\pi

y = a 2 = 4 a ⟹ a = 4 , y = 16 y=a^2=4a\implies a=4, y=16

y > x \boxed{y>x}

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