The side of a square is equal in length to the diameter of a circle, which figure will have the greater area?

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Answer 1 · 2018-04-11T16:49:15

area of a circle

area of a circle: #pir^2#

the radius of a circle is half of its diameter, so #pir^2 = pi(d/2)^2#

#(d/2)^2 = d^2/4#

the area of a circle is is #d^2pi/4#.

the area of a square is the square of its side length.

if the diameter of a circle is the same as the side length, then the area of a square is #d^2#.

the side length of a square, or the diameter of a circle, cannot be negative.

#d^2 * pi/4# will always be greater than #d^2#, since #d# is always positive.