For many geometric figures, the radius has a well-defined relationship with other measures of the figure.
The radius of a circle with area A is
The radius of the circle that passes through the three non-collinear points P1, P2, and P3 is given by
where θ is the angle ∠P1P2P3. This formula uses the law of sines. If the three points are given by their coordinates (x1,y1), (x2,y2), and (x3,y3), the radius can be expressed as
A square, for example (n
The radius r of a regular polygon with n sides of length s is given by r = Rn s, where Values of Rn for small values of n are given in the table. If s = 1 then these values are also the radii of the corresponding regular polygons.
The radius of a d-dimensional hypercube with side s is