Apothem

of a regular polygon

The segment (and its length) of a perpendicular dropped from the centre of the regular polygon onto any of its sides. The apothem of a regular $n$-gon is equal to the radius of the circle inscribed in it and is connected with the side of the polygon, $a_n$, and with its surface area $S_n$ by the relations:

$$a_n=2r_n\tan\frac\pi n,\quad S_n=nr_n^2\tan\frac\pi n.$$

The apothem of a regular pyramid is the height of its (side) face.