When drawn from the center of a polygon to the midpoint of a side, what is this segment called?

The segment drawn from the center of a polygon to the midpoint of a side is known as the apothem. In geometry, the apothem specifically refers to the shortest distance from the center of a regular polygon to one of its sides, which effectively is perpendicular to that side and bisects it. This segment is crucial in calculating various properties of polygons, such as area and perimeter.

Understanding the apothem is important as it helps to relate the polygon's dimensions to its internal angles and overall symmetry, which is especially relevant in regular polygons where all sides and angles are equal. The significance of the apothem becomes clear when calculating the area of the polygon using the formula: Area = (Perimeter × Apothem) / 2, where the apothem represents the height of the triangles that make up the area of the polygon.

This term and its use are distinct from a chord, which connects two points on a circle's circumference, a radius, which is a line from the center of the circle to any point on its circumference, and a segment, which can simply refer to any division of a line but does not specifically indicate the relationship present in this case.