Perimeter is basically arc length. You could just as easily have a line segment of length 96 as a square of perimeter 96. Then the side length is 24, and so the area is 242.242. On the other hand, if the circumference of a circle is 96, then 96=πd,96=πd, so that means that r=96/2πr=96/2π. This means that the area is (96/2)2,(96/2)2, which is different from 242