Apothem

The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word "apothem" can also refer to the length of that line segment. Regular polygons are the only polygons that have apothems. Because of this, all the apothems in a polygon will be congruent and have the same length.

For a regular pyramid, which is a pyramid whose base is a regular polygon, the apothem is the slant height of a lateral face; that is, the shortest distance from apex to base on a given face. For a truncated regular pyramid (a regular pyramid with some of its peak removed by a plane parallel to the base), the apothem is the height of a trapezoidal lateral face.

For a triangle (necessarily equilateral), the apothem is equivalent to the line segment from the midpoint of a side to any of the triangle's centers, since an equilateral triangle's centers coincide as a consequence of the definition.

Read more about Apothem:  Properties of Apothems, Finding The Apothem

Other articles related to "apothem":

Regular Polygon - Regular Convex Polygons - Area
... polygon having side s, circumradius r, apothem a, and perimeter p is given by For regular polygons with side s=1, resp ... apothem a=1, this produces the following table Number of sides Name of polygon Area when side s=1 Area when circumradius r=1 Area when apothem a=1 Exact Approximate ...
Golden-ratio - Pyramids - Mathematical Pyramids and Triangles
... A pyramid in which the apothem (slant height along the bisector of a face) is equal to φ times the semi-base (half the base width) is sometimes called a golden pyramid ... the two halves of a diagonally split golden rectangle (of size semi-base by apothem), joining the medium-length edges to make the apothem ... The slant height or apothem is 5/3 or 1.666.. ...
Finding The Apothem
... The apothem of a regular polygon can be found multiple ways, of which two are described here ... The apothem a of a regular n-sided polygon with side length s, or circumradius R, can be found using the following formula The apothem can also be found by Both formulas ...