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# Hexagonal Prism      LIVE
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## 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

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

2. The top and bottom bases are hexagonal.

3. The rest of the 6 faces are rectangular in shape.

4. The diagonals intersect each other at the center point.

5. 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.

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Last updated date: 24th Sep 2023
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## 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.