Final answer:
A square inscribed in a circle has its sides equal to the diameter of the circle, and the area of the square is larger than half the area of the circle but smaller than the area of the circle. The perimeter of the circle is between 2 and 4 times the length of a side of the square.
Step-by-step explanation:
When constructing a square inscribed in a circle, the square fits within the circle in such a way that the length of each side of the square is equal to the diameter of the circle.
In other words, the diagonals of the square are also the diameters of the circle. The area of the square will be less than the area of the circle, but greater than half the area of the circle.
The perimeter of the circle will be between 2 times the length of a side of the square and 4 times the length of a side of the square.