# Hexagonal prism

The hexagonal prism is that polyhedron made up of two faces that are hexagons, in addition to six lateral faces that are parallelograms.

We must remember that the prism is a type of polyhedron formed by two parallel faces that are polygons identical to each other.

Let us also remember that a polyhedron is a three-dimensional figure made up of a finite number of faces that are polygons.

It is worth mentioning that the hexagonal prism can be regular when its bases are regular hexagons (with interior sides and angles, all of the same measure)

It is worth mentioning that the regular hexagonal prism would not be a regular polyhedron properly speaking, since not all its faces are identical to each other. However, it could be said that it is a semi-regular polyhedron.

Another point to take into account is that the hexagonal prism can be straight or oblique, as we can see in the figure below.

## Elements of the hexagonal prism

The elements of a quadrangular prism are:

- Bases: They are two parallel and identical hexagons. The hexagon ABCDEF and the hexagon GHIJKL in the image below.
- Side faces: They are the six parallelograms that join the two bases.
- Edges: They are the 18 segments that join two faces of the prism. AB, BC, CD, DE, EF, AF, GH, HI, IJ, JK, KL, LG, AL, BG, CH, DI, EJ and FK.
- Vertices: It is the point where three faces of the figure meet. There are a total of twelve: A, B, C, D, E, F, G, H, I, J, K and L.
- Height: The distance that separates the two bases of the figure. If the prism is straight, the height is equal to the length of the edge of the lateral faces.

## Area and volume of the hexagonal prism

To better understand the characteristics of the hexagonal prism, we can calculate the following measurements:

- Area: To find the area of the prism, the area of the bases (Ab) and the lateral area (AL) must be calculated, that is, of the body of the polyhedron

If we are facing a regular quadrangular prism, the bases are regular hexagons, whose area, as we calculated in our hexagon article, would be the following (where L is the side of the hexagon):

Likewise, the lateral faces are rectangles, so their area is calculated by multiplying the length of their continuous sides. Now, if we look closely at the figure, one of the sides will be the height of the prism (h) and the other will coincide with the side of the base (L). Thus, we multiply the area of each rectangle by six to find the entire lateral area:

Therefore, the area of the regular hexagonal prism will be:

Also, if the prism were oblique, the formula would be the following, where Ab is the area of the base, P is the perimeter of the straight section (the hexagon ABCDEF) and a is the lateral edge (see image below):

It is worth mentioning that the straight section is the intersection of a plane with the prism, so that it forms a right angle (of 90º) with the lateral edges (with each one of them).

- Volume: As a general rule, to calculate the volume of a hexagonal prism, the area of one of its bases is multiplied by the height of the polyhedron.

If the hexagonal prism were regular, we would replace the area of the base with the formula indicated a few lines above:

## Hexagonal prism example

Suppose we have a regular hexagonal prism whose bases have one side that is 14 meters. Also, the height of the prism is 22 meters. What is the area and volume of the figure?

Remember that each side face has one side that coincides with the side of the base and the other would be equal to the height of the prism.