## Properties of Hexagonal Prism

This tool calculates the basic geometric properties of a right prism, with a regular hexagonal base. Enter the shape dimensions 'a' and 'h' below. The calculated results will have the same units as your input. Please use consistent units for any input.

 a = h = Geometric properties: Volume = Surface area = Base area = Lateral surface area =

## Definitions

### Geometry

The prism is a solid object enclosed by two parallel planar polygonal bases and a lateral prismatic surface. Hexagonal prism is a special case of the general prism, which may have any arbitrary polygonal base. With a hexagon base, the number of faces, edges and vertices (NF, NE, NV respectively) is given by the formulas:

$\begin{split} NF & = 8 \\ NE & = 18 \\ NV & = 12 \end{split}$

The volume of a prism is given by the formula:

$V = A_b h$

where $$A_b$$ the surface area of the base and h the height of the prism. Forregular hexagon , the base area is given by:

$A_b = \frac{3 a^2}{2 \tan{30^{\circ}}}$

where $$a$$ the length of an edge of the base hexagon.

The surface area of one lateral face of the prism, is equal to:

$A_{f0} = a h$

Since there are 6 lateral faces and two bases, the total surface area of the hexagonal prism is:

$A = 2A_b + 6 A_{f0}$