What term refers to a segment drawn from the center of a regular polygon perpendicular to a side?

The correct term for a segment drawn from the center of a regular polygon that is perpendicular to one of its sides is the apothem. The apothem serves as a crucial element in geometry, particularly when calculating the area of a regular polygon. It represents the shortest distance from the center to a side of the polygon, and it is particularly relevant in the context of regular polygons, which have equal sides and equal angles.

In the case of regular polygons, the apothem is crucial because it connects the center to the midpoint of a side, establishing a perpendicular relationship that is essential for geometric calculations. The formula for the area of a regular polygon involves the apothem, emphasizing its importance in various applications, including both theoretical mathematics and practical surveying.

The other terms provided highlight different concepts. A diameter relates specifically to circles, representing a line segment passing through the center and connecting two points on the circle. A radius is a segment from the center to any point on the circle, and a median refers to a segment from a vertex to the midpoint of the opposite side in a triangle. Each of those terms pertains to different geometric figures or properties, setting the apothem apart as the most suitable answer for this specific context.