Will a circle always have a greater area than a square if the circumfrance and perimeter are the same

The answer is yes. here is how:

circumference of a circle is 2pi*r

perimeter of a square is 4a, a being the length of each side.

when 2pi*r=4a, r = (2a) / pi

area of the circle is pi*r^2=pi (2a/pi) ^2 = (4/pi) * a^2

area of the square is a^2

Because 4/pi is bigger than 1, (4/pi) * a^2 is always larger than a^2