# Hexagonal Prism

AA hexagonal prism is a three-dimensional solid consisting of two identical hexagonal bases joined together by six lateral faces. The lateral faces are rectangular in shape. It has 8 faces, 18 edges, and 12 vertices.

The shape of pencils, weights, and nuts are some real-life examples of a hexagonal prism.

A 2-dimensional net can be used to construct a hexagonal prism to understand the shape.

A hexagonal prism can be regular or irregular based on the uniformity of its cross-section. It can also be right or oblique, depending on the alignment of its bases.

## Regular and Irregular Hexagonal Prisms

1. Regular Hexagonal Prism â€“ Its 2 bases are regular hexagons.
2. Irregular Hexagonal Prism â€“ Its 2 bases are not regular hexagons.

## Right and Oblique Hexagonal Prisms

1. Right Hexagonal Prism â€“ It has all the lateral faces perpendicular to the bases. Thus every lateral face is rectangular.
2. Oblique Hexagonal Prism â€“ Its lateral faces are not perpendicular to its bases. So, every lateral face is parallelogram-shaped.

Like all other polyhedrons, we can calculate the surface area and volume of a hexagonal prism.

## Formulas

### Surface Area

The formula is given below:

Total Surface Area (TSA) = 6ab + 6bh, here a = apothem, b = base edge, h = height

As we know,

Total Surface Area (TSA) = 2 Ã— Base Area + Base Perimeter Ã— height

Also,

Lateral Surface Area (LSA) is the sum of the areas of all the faces except the bases.

âˆ´ LSA = Base Perimeter Ã— height

Here, Base Perimeter = 6b

âˆ´ TSA= 6ab + LSA, here LSA = 6bh

Let us solve an example to understand the concept better.

Find the lateral and total surface area of a hexagonal prism with a base edge of 9 cm, an apothem of 7.79 cm, Â and a height of 9.5 cm.

Solution:

As we know,
Lateral Area (LSA) = 6bh, here b = 9 cm, h = 9.5 cm
âˆ´LSA =6 Ã— 9 Ã— 9.5
= 513 cm2
Total Surface Area (TSA) = 6ab + LSA, Â Â here a = 7.79 cm, b = 9 cm, h = 9.5 cm
âˆ´ TSA = 6 Ã— 7.79 Ã— 9 + 513
= 933.66cm2

### Volume

The formula is given below:

Volume (V) = 3abh, here a = apothem, b = base edge, h = height

Let us solve an example to understand the concept better.

Find the volume of a hexagonal prism with a base edge of 7 cm, an apothem of 6.06 cm, and a height of 4 cm.

Solution:

As we know,
Volume (V) = 3abh, here a = 6.06 cm, b = 7 cm, h = 4 cm
âˆ´V = 3 Ã— 6.06 Ã— 7 Ã— 4
= 509.04 cm3

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