What is the area of a square and how to calculate it?

The area of ​​a square is the part of the plane that is bounded by the sides of this square.
A square is a special case of a rectangle, then its area can be found as the product of one side of it by the other, and since all sides of a square are equal, its area will be equal to the square of the length of its side:
S = a².
Also, the area of ​​a square is equal to half the square of the length of its diagonal (d), that is:
S = d² / 2.
The diameter of a circle circumscribed about a square coincides with the diagonal of this square, then its area can also be found through the length of the diameter (D) of the circumscribed circle:
S = D² / 2.
Since the diameter of a circle is 2 times larger than its radius, the area of ​​a square can also be found through the radius of the circumscribed circle:
S = (2 * R) ² / 2 = (4 * R²) / 2 = 2 * R².