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Hexagonal Prism

A hexagonal prism is a 6 sided polygon with the base and top in the shape of a hexagon. In our day-to-day life, we come across various hexagonal prism examples such as pencils, nuts, gift boxes, buildings, etc. It has 8 faces, 12 vertices, and 18 edges. We see various prism-shaped examples but not all are hexagonal prism. Let us learn more about a hexagonal prism in this article.

1.	What is a Hexagonal Prism?
2.	Properties of a Hexagonal Prism
3.	Net of a Hexagonal Prism
4.	Surface Area of a Hexagonal Prism
5.	Volume of a Hexagonal Prism
6.	FAQs on Hexagonal Prism

What is a Hexagonal Prism?

A hexagonal prism is a 3D-shaped prism that has two parallel ends with the same size and shape called bases. The hexagonal prism has 6 sides known as faces, which are in the shape of parallelograms. By definition, a hexagonal prism is a prism with two bases that are in the shape of hexagons and 6 faces that are in the shape of rectangles. There are 2 different types of hexagonal prisms i.e. regular hexagonal prisms and irregular hexagonal prisms. A regular hexagonal prism is a prism with bases shaped like a hexagon with all the sides of the same length (or made up of a regular hexagon). Whereas, an irregular hexagonal prism is a prism where the sides of the hexagon bases do not have the same lengths. The angles of the regular hexagonal prism are the same, whereas, in an irregular prism the angles are not the same.

Hexagonal Prism Definition

A hexagonal prism is a polyhedron with 8 faces, 18 edges, and 12 vertices where out of the 8 faces, 6 faces are in the shape of rectangles and 2 faces are in the shape of hexagons. The top and bottom of the hexagonal prism is shaped as a hexagon and are equal to each other. In the hexagonal prism, the long diagonals always cross the center point of the hexagon starting from the vertex of the base whereas the short diagonals do not cross the center point as the diagonal is from one vertex of the base to the other.

Hexagonal Prism

Properties of a Hexagonal Prism

A hexagonal prism is a prism with two hexagon-shaped bases and six rectangular faces. The properties of a hexagonal prism are:

It has 8 faces, 18 edges, and 12 vertices
The top and bottom bases are equal to each other in length
The diagonals cross the center point of a regular hexagonal prism
In a regular hexagonal prism, all the angles of a hexagon are the same
In an irregular hexagonal prism, all the angles of a hexagon are different

Net of a Hexagonal Prism

A hexagonal prism can be formed using a net. When the object is opened flat, the net of the hexagonal prism shows the faces of the shape clearly. Once the hexagonal prism is folded, the 3D version of the prism is seen. There could be multiple nets possible for a shape, below given is one of the nets of a hexagonal prism.

Net of a Hexagonal Prism

Surface Area of a Hexagonal Prism

The surface area is the sum of the surface of the 3D object altogether. Hence, the surface area of the hexagonal prism is the combination of both the length of the base and the height of the hexagonal prism. Therefore,

Surface Area of Hexagonal Prism = 6ah + 3√3a² square units, where a is the base length and h is the height.

Volume of a Hexagonal Prism

The volume of a hexagonal prism is found by taking the area of the base along with the height and length. Therefore the formula to finding the volume is:

Volume of a Hexagonal Prism = [(3√3)/2]a²h cubic units, where a is the base length and h is the height of the prism

Volume of a Hexagonal Prism

Related Topics

Listed below are a few interesting topics related to the hexagonal prism, check it out!

Hexagonal Prism Examples

Example 1: Find the volume of a hexagonal prism with a base edge length of 5 units and a height of 10 units.

Solution: Given, a = 5 and h = 10, where a is the base length and h is the height of the hexagonal prism.

Hexagonal Prism Volume = [(3√3)/2]a²h

Volume = [(3√3)/2] × 5² × 10

Volume = [(3√3)/2] × 250

Volume = 649.51 cubic units

Therefore, the volume of the hexagonal prism is 649.51 cubic units.
Example 2: Find the surface area of a hexagonal prism with the base edge as 5 units and height as 10 units.

Solution: Given a = 5 and h = 10, where a is the base length and h is the height of the hexagonal prism.

Surface Area of Hexagonal Prism = 6ah + 3√3a²

Area = 6 × 5 × 10 + 3√3 × (5)²

Area = 300 + 129.9

Area = 429.9 square units

Therefore, the surface area of the hexagonal prism is 429.9 square units.
Example 3: Find the height of the hexagonal prism if its total surface area is 396 sq feet, apothem length is 3 feet, base length is 6 feet.

Solution:

Given, Total surface area = 396 sq feet, apothem length, a= 3 feet, and base length, b = 6 feet

Total surface area of hexagonal prism = 6b(a+h)

⇒ 6 × 6(3 + h) = 396
⇒ 36(3 + h) = 396
⇒ 3 + h = 396/36
⇒ h = 11 - 3 = 8 feet

Therefore, the height of the hexagonal prism equals 8 feet.

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Practice Questions on Hexagonal Prism

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FAQs on Hexagonal Prism

What is a Hexagonal Prism?

A hexagonal prism is a 3D-shaped figure with the top and bottom shaped like a hexagon. It is a polyhedron with 8 faces, 18 edges, and 12 vertices where out of the 8 faces, 6 faces are in the shape of rectangles and 2 faces are in the shape of hexagons. Some of the real-life examples of a hexagon prism are pencils, boxes, nuts, etc.

How many Vertices and Edges does a Hexagonal Prism Consist of?

A hexagonal prism consists of 12 vertices and 18 edges. The vertices are found both on the top and bottom of the hexagonal prism and are combined together to make a prism by 18 edges.

What is the Formula to Calculate the Surface Area of a Hexagonal Prism?

To calculate the surface area of a hexagonal prism, the formula is Surface Area of Hexagonal Prism = 6ah + 3√3a² square units, where a is the base length and h is the height.

What is the Formula to Calculate the Volume of a Hexagonal Prism?

To calculate the volume of a hexagonal prism, the formula is Hexagonal Prism Volume = [(3√3)/2]a²h cubic units, where a is the base length and h is the height of the prism

What is the Net of a Hexagonal Prism?

The net of a hexagonal prism is the 2D image through which a hexagonal prism is formed by joining the edges of the net. When the figure is opened flat we can see the faces and sides of the hexagonal prism clearly. The hexagon and rectangle in the prism can be seen with the help of a net.

How many Parallel Planes does a Hexagonal Prism have?

In a hexagonal prism, there are two parallel planes in the two bases of the prism. Since both the bases are in the shape of hexagons, the length of these bases is similar. If we cut it from anywhere parallel to the two bases, the cross-section will be in the shape of a hexagon, as we have two parallel bases in a hexagonal prism.

Does a Hexagonal Prism have a Curved Face?

No, a hexagonal prism does not have a curved surface. It is a 6 sided figure made up of polygons that include 6 rectangles and 2 hexagons.

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