### Example

This distance is the length of the perpendicular segment drawn from the vertex of the regular pyramid to any of the sides of its base.

### Formula

The formula for the measure of the apothem of a regular polygon with *n* sides can be used to establish the relationship that provides the measure of the slant height of a right regular pyramid.

In the figure above, * S* represents the slant height of the pyramid,

*the height of the pyramid and*

**h***the apothem of the polygonal base or the radius of the circle inscribed in the base. It may be noted that since these three elements form a right triangle with a hypotenuse*

**a***, then \(S = \sqrt{h^2 + a^2}\). By using the formula for the measure*

**S***a*of the apothem of the polygonal base with

*n*sides that have a length of

*c*, the following relationship is obtained: \(S = \sqrt{h^2 + \left( \dfrac{c}{2\tan{(\frac{180}{n})}} \right)^2}\).