A hexagonal prism is a three-dimensional geometric structure with two hexagonal bases connected by six rectangular faces. It is a polyhedron with eight faces, twelve vertices, and eighteen edges.
In this, article we have covered the definition of a Hexagonal prism, its definition, formulas and others in detail.
Hexagonal Prism Definition
Hexagonal Prism also known as an octahedron is a 3-D polygon with eight faces; two of the eight faces are hexagons, which are the bases of the prism, and the other six faces are rectangles, which are the lateral (or) side faces of the prism.
The top and bottom faces of the hexagonal prism are in the shape of a hexagon and are congruent with each other. The image of a Hexagonal Prism is added below:
Hexagonal PrismTypes of Hexagoanl Prism
There are two kinds of hexagonal prisms, namely, a regular hexagonal prism and an irregular hexagonal prism.
- A regular hexagonal prism is a prism that has two hexagonal bases whose all sides are of the same length. In a regular hexagonal prism, the angles also measure the same.
- An irregular hexagonal prism is a prism that has two irregular hexagonal bases. All the sides of the base do not have the same length, and the measures of each angle are different.
Hexagonal prsim formulas are covered under three heading, including:
- Lateral Surface Area of Hexagonal Prism
- Total Surface Area of Hexagonal Prism
- Volume of Hexagonal Prism
Let's learn about all of them in detail.
Surface Area of a Hexagonal Prism
Total area that is covered by the surfaces of a hexagonal prism is referred to as its surface area. The surface area of a prism is measured in terms of square units such as sq. m, sq. cm, sq. in, etc.
A hexagonal prism has two types of areas just like other three-dimensional shapes: lateral surface area (LSA) and total surface area (TSA).
Let us consider a hexagonal prism that has an apothem length "a", a base length "s", and a height "h". We know that the general formula to calculate the lateral surface area of a prism is the product of its base and height. So, the lateral surface area of the prism of a hexagonal prism is determined by calculating the product of the perimeter of the base of the hexagonal prism and its height.
The formula to determine the lateral surface area of the hexagonal prism is equal to the sum of the areas of its six rectangular faces. Thus,
Lateral Surface Area of Hexagonal Prism (LSA) = 6sh sq. units.
where,
- "s" is Length of Base Edge
- "h" is Height of Prism
Surface Area of a Hexagonal PrismThe formula to determine the surface area of a hexagonal prism is given as follows:
Total Surface Area, TSA = 2×(Area of hexagonal base) + 6×(Area of rectangular faces) = 6s(a + h).
Total Surface Area of Hexagonal Prism (TSA) = 6s(a + h) sq. units.
where:
- "a" is Apothem Length
- "s" is Length of Base Edge
- "h" is Height of Prism
The formula to determine the surface area of a hexagonal prism in the case of a regular hexagonal prism, TSA = 6sh + 3√3s2.
Total Surface Area of Hexagonal Prism (TSA) = 6sh + 3√3s2 sq. units.
where:
- "s" is Length of Base Edge
- "h" is Height of Prism
Volume of a Hexagonal Prism
The volume of a hexagonal prism is the amount of space enclosed by it in three-dimensional space. It is also referred to as the amount of substance that it can hold, which is the capacity of a hexagonal prism. The formula for the volume of a hexagonal prism is equivalent to the product of its base area and height, which is measured in terms of cubic units such as cm3, m3, in3, etc.
The formula for finding the volume of a hexagonal prism is given as follows,
Volume of Hexagonal Prism (V) = Base Area × Height
Volume of a Hexagonal PrismThe formula for calculating the volume of a hexagonal prism when the length of the edge of the base and height of the prism is known is given as follows.
Volume of Hexagonal Prism (V) = [(3√3)/2]s2h
where:
- "s" is Length of Base Edge
- "h" is Height of Prism
The formula for calculating the volume of a hexagonal prism when the apothem length, length of the edge of the base, and height of the prism are known is given as follows.
Volume of Hexagonal Prism (V) = 3ash
where:
- "a" is Apothem Length
- "s" is Length of Base Edge
- "h" is Height of Prism
Example on Volume of a Hexagonal Prism
Example 1: Calculate the volume of a hexagonal prism with a base edge length of 15 cm and a height of 12 cm.
Solution:
Given data,
- Length of the base edge (s) = 15 cm
- Height of the prism (h) = 12 cm
We know that,
Volume of a hexagonal prism = [(3√3)/2]s2h
= (3/2) × (1.732) × (15)2 × 12
= 7,014.805 cu. cm
Hence, the volume of the hexagonal prism is 7,014.805 cu. cm.
Example 2: Determine the volume of the hexagonal prism if its height is 10 inches and its base area is given as 60 sq. in.
Solution:
Given data,
- Base area = 60 sq. in
- Height of the prism (h) = 10 inches
We know that
Volume of the hexagonal prism (V) = Base area × height
= 60 × 10 = 600 cu. in
Hence, the volume of the hexagonal prism is 600 cu. in.
Example 3: Calculate the volume of a hexagonal prism if its height is 13 cm, the length of each side of the base is 10 cm, and the apothem length is 8 cm.
Solution:
Given data,
- Length of the base edge length (s) = 10 cm
- Apothem length (a) = 8 cm
- Height of the prism (h) = 13 cm
We know that
Volume of the hexagonal prism (V) = 3ash cubic units
= 3 × 8 × 10 × 13 = 3,120 cu. cm
Hence, the volume of the hexagonal prism is 3,120 cu. cm.
Example 4: Find the total surface area of a hexagonal prism if the length of each side of the base is 8 cm and the height is 10 cm.
Solution:
Given data,
- Length of the base edge (s) = 8 cm
- Height of the prism (h) = 10 cm
We know that,
Total surface area of the hexagonal prism = 6sh + 3√3s2
= 6 × 8 × 10 + 3√3 × (8)2
= 480 + 3√3 × 64
= 480 + 332.554 = 812.554 sq. cm
Thus, the total surface area of the hexagonal prism is 812.554 sq. cm.
Example 5: Determine the lateral surface area of a hexagonal prism with a base edge length of 12 cm and a height of 9 cm.
Solution:
Given data,
- Length of the base edge length (s) = 12 cm
- Height of the prism (h) = 9 cm
We know that,
Lateral surface area of a hexagonal prism = 6sh sq. units
LSA = 6 × 12 × 9
LSA = 648 sq. cm
Hence, the volume of the hexagonal prism is 648 sq. cm.
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