What is the radius of a polygon?

The radius of a polygon, particularly in the context of a regular polygon, is defined as the segment that connects the center of the polygon to one of its vertices. This measurement is crucial because it helps in understanding the overall size and shape of the polygon.

For regular polygons, where all sides and angles are equal, the radius also represents the distance from the center to the outermost points of the shape. This concept is similar to the radius of a circle, which is the distance from the center to any point on its circumference. In practical applications, knowing the radius allows for calculating the area and perimeter of the polygon, as well as understanding its symmetry and properties related to inscribed shapes and circumscribed circles.

In contrast, the other options do not accurately describe the radius. For instance, a segment from the center to the side of the polygon defines the apothem, not the radius. The length of the longest side is a different measurement that does not pertain to the radius. Lastly, a line that bisects the polygon refers to a median or altitude instead of the radius. Thus, the accurate definition of a polygon's radius is the segment from the center to one of its vertices.