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.
Hexagonal Prism
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.
Hexagonal Prism Net
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
Regular and Irregular Hexagonal Prisms
Regular Hexagonal Prism – Its 2 bases are regular hexagons.
Irregular Hexagonal Prism – Its 2 bases are not regular hexagons.
Right and Oblique Hexagonal Prisms
Right and Oblique Hexagonal Prisms
Right Hexagonal Prism – It has all the lateral faces perpendicular to the bases. Thus every lateral face is rectangular.
Oblique Hexagonal Prism – 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 × Base Area + Base Perimeter × height
Also,
Lateral Surface Area (LSA) is the sum of the areas of all the faces except the bases.
∴ LSA = Base Perimeter × height
Here, Base Perimeter = 6b
∴ 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, and a height of 9.5 cm.
Solution:
As we know, Lateral Area (LSA) = 6bh, here b = 9 cm, h = 9.5 cm ∴LSA =6 × 9 × 9.5 = 513 cm2 Total Surface Area (TSA) = 6ab + LSA, here a = 7.79 cm, b = 9 cm, h = 9.5 cm ∴ TSA = 6 × 7.79 × 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 ∴V = 3 × 6.06 × 7 × 4 = 509.04 cm3
