How to Find the Radius of a Square?

TopSquare can be defined as a regular closed quadrilateral structure which has four equal sides. In other words, square can be defined as a quadrilateral which consists of four line segments. Lengths of all line segments are equal. Points, where line segments meet, are called vertices or nodes. All four angles of Square are also same (π / 2 radians or 90º) that is four angles in square are right angles. Usually radius is related to circular shapes, but for square we can define it as distance between Centre of square to its vertex. A square with vertices P, Q, R, and S will be figured out as shown below:


Let’s consider ‘a’ as the side of square or length of Line Segment. All line segments are of equal length (which is equal to ‘a’) as shown in figure.

Perimeter of square will be given as four times the side length and mathematically, P = 4 a. Area of square will be S = a². Diagonal of a square can be defined as Line Segment joining two opposite vertices. There are two diagonals in square. In above figure, PR and QS are diagonals. Diagonals of square are perpendicular to each other and bisect the angle of square. Since all four sides are of equal length hence opposite sides are parallel to each other.
Radius of square can be defined as that line segment which is drawn from the center (O) of square to one of its vertices (nodes).

In above figure, radius is indicated by 'r' and it is half the diagonal. Let's see how to find the radius of a square. We have to calculate the diagonal using pythagoras theorem. Diagonal will be:
d²= a² + a² = 2 a²,
hence, d = a √2,
Thus radius will be,
R = d / 2 = (a √2) / 2.