## An Introduction to Hexagonal Prism

A 3-D solid figure with flat surfaces and two identical bases is a prism. The prism is named after the shape of the base. The base is a polygon like a triangle, square, hexagon, etc. The other faces of a prism can be rectangles or parallelograms. This information concludes that a hexagonal prism will have hexagonal bases.

Depending on the shape of the base, a prism can be of two types: Regular prism and Irregular prism. A regular prism will have a regular-shaped polygon as its base; that is, the length of the edges will be equal. An irregular prism will have an irregularly shaped base; that is, the length of the edges will be unequal.

Based on the angle between the bases and the faces, there are two prisms: The right prism and the oblique prism. If the faces are rectangular and perpendicular to the bases in a prism, it is called a right prism. If the faces are not perpendicular to the bases, it is called an oblique prism.

## What is a Hexagonal Prism?

A prism with bases in a hexagon shape is called a hexagonal prism. It is a 3D polyhedron having 2 hexagonal bases and 6 rectangular faces. Some real-life examples of hexagonal prisms are nuts, pencils, weights etc. It has 8 faces, of which 2 are hexagonal, the top and bottom faces, and the rest 6 faces are rectangular. It has 18 edges and 6 vertices.

There can be two types of hexagonal prisms, that is, regular and irregular prisms. A regular hexagonal prism has a hexagonal-shaped base of the same length. An irregular hexagonal prism does not have sides with the same length and same angles.

## Hexagonal Prism Faces, Edges and Vertices

The number of faces, edges and vertices defines any 3-dimensional figure.

The vertex is a point where two edges meet. It is simply a corner point.

The faces are the individual flat surfaces of a solid.

The edges are the line segments that act as an interface between two faces.

The hexagonal prism has 8 faces: 2 - hexagonal, top and bottom; 6 rectangular side faces

The hexagonal prism has 18 edges.

The hexagonal prism has 6 vertices.

## Properties of a Hexagonal Prism

The hexagonal prism has 8 faces, 12 vertices, and 18 edges.

The top and bottom bases are hexagonal.

The rest of the 6 faces are rectangular in shape.

The diagonals intersect each other at the center point.

All the angles are equal in a regular prism while the angles are different in an irregular prism.

## Surface Area of a Hexagonal Prism

The different shapes in geometry can be measured using different measures like area volume, perimeter, etc.

The surface area is defined as the quantity that expresses the extent of a 2-D figure or planar lamina. For a 3D figure, we individually calculate the area of each face and add them up to get the total surface area.

The unit of area is (length)2.

The surface area of a hexagonal prism is the sum of the area of 6 rectangular faces and the 2 hexagonal faces.

Let a hexagonal prism with height h and base side a, then

Total area of rectangular faces = 6ah

Total area of hexagonal faces = \[3\sqrt 3 {a^2}\]

Thus, total area = \[6ah + 3\sqrt 3 {a^2}\]

## Volume of a Hexagonal Prism

Volume of a solid is the amount of 3D space occupied by it.

The unit of volume is (length)3.

Let a hexagonal prism with height h and base side a, then,

Volume of a hexagonal prism = \[\dfrac{{3\sqrt 3 }}{2}{a^2}h\]

## Net of a Hexagonal Prism

The net of a 3D shape is what it would look like if opened and laid flat as a 2D object. The 3D version of the shape will appear once it is folded. The figure given below shows the net of a hexagonal prism.

Net of hexagonal prism

## Solved Examples

Q1. Calculate the volume of a hexagonal prism with a base edge of 6 units and having a height of 12 units.

Ans. Given a = 6 units and h = 12 units.

We know, the volume of a hexagonal prism = \[\dfrac{{3\sqrt 3 }}{2}{a^2}h\]

Now, put the values of a and h in the above formula.

Volume = \[\dfrac{{3\sqrt 3 }}{2}{\left( 6 \right)^2}\left( {12} \right){\rm{ unit}}{{\rm{s}}^3}\]

=1122 units3

Q2. Given a hexagonal prism with volume 150 \[cm^3\] and base area 10 cm2. Calculate the height of the prism.

Ans. Given volume = 150 \[cm^3\] and base area = 10 cm2

We know that volume = base area \[ \times \] height

Using the given values in the equation.

150 = 10 \[ \times \] height

Height = 15 cm

## Practice Questions

Q1. Given the base area and height of a hexagonal prism as 250 cm2 and 20 cm respectively. Calculate the volume of the hexagonal prism.

Ans. 5000 \[cm^3\]

Q2. The base edge of a hexagonal prism is 3 cm, and the height is 5 cm. Calculate the surface area and volume of the hexagonal prism.

Ans. 136.76 cm2 , 116.91 cm3

## Interesting Facts

Hexagonal prism is a polyhedron.

Hexagonal prism can also be called an octahedron.

The base of a regular hexagonal prism has all the angles equal to 120 degrees, and the rectangular side faces have all angles equal to 90 degrees.

## Key Features

A 3D solid figure with flat surfaces and two identical bases is known as a prism. The prism is named after the shape of the base. The base is a polygon like a triangle, square, hexagon etc. The other faces of a prism can be rectangles or parallelograms.

A prism with bases in a hexagon shape is called a hexagonal prism.

The hexagonal prism has 8 faces, 12 vertices, and 18 edges.

The surface area of a hexagonal prism is \[6ah + 3\sqrt 3 {a^2}\].

The volume of a hexagonal prism is \[\dfrac{{3\sqrt 3 }}{2}{a^2}h\].

## Summary

A 3-D solid figure with flat surfaces and two identical bases is known as a prism. A prism with bases in a hexagon shape is called a hexagonal prism. The hexagonal prism has 8 faces, 12 vertices, and 18 edges. The surface area and volume of a hexagonal prism is \[6ah + 3\sqrt 3 {a^2}\] and \[\dfrac{{3\sqrt 3 }}{2}{a^2}h\] respectively.

## List of Related Articles

Formula of Prism

## FAQs on Hexagonal Prism

1. How many right angles does a regular hexagonal prism have?

A rectangle has 4 right angles, and a hexagonal prism has 6 rectangles. So in total, there are 24 right angles in a hexagonal prism.

2. Can we call a hexagonal prism a polyhedron?

A 3-D figure in which all the faces are polygons is known as a polyhedron. The hexagonal prism has 6 rectangles and 2 hexagons as its faces, all of which are polygons. Thus, we can call a hexagonal prism a polyhedron.

3. Why do we call a hexagonal prism an octahedron?

Octahedron is a 3-D shape with 8 faces. A hexagonal prism has 8 faces, so it can be said to be an octahedron.