Surface Area of Hexagonal Prism

The surface area of a prism is the amount of space occupied by the surface of a prism. A hexagonal prism is a prism composed of two hexagonal bases and six rectangular sides. It is an octahedron. It is a 3-D shape that has a hexagonal base and a hexagonal top. Like all three-dimensional shapes, you will learn how to calculate the surface area of a hexagonal prism. Let's learn more about its formula using solved examples!!!

The surface area of a hexagonal prism is defined as the total region covered by the surfaces of a hexagonal prism. Since it has a flat base, thus it has a total surface area as well as a curved/lateral surface area. A hexagonal prism has 8 faces, 18 edges, and 12 vertices. It has equal top and bottom bases with diagonals crossing the center point of a regular hexagon.

The surface area of a hexagonal prism is expressed in square units, common units being square meters, square centimeters, square inches, etc. Just like other three-dimensional shapes, a hexagonal prism can also have two types of areas,

• Total Surface Area (TSA)
• Lateral Surface Area (LSA)

The surface area of a hexagonal prism is the sum of the areas of its faces and its base. The surface area of a hexagonal prism gives the area of each face of the prism. If the apothem length of the prism is "a", the base length of the prism is "b" and the height of the prism is "h", the surface area of a hexagonal prism is given as:

Total Surface Area, TSA= 2(area of hexagon base) + 6(area of rectangle face) sq. units. = 6b(a + h) or 6ah + 3√3a² (in case of regular hexagonal prism)
Lateral Surface Area, LSA = Ph = 6(area of the rectangle) = 6ah sq. units

• a = base length
• a = apothem length
• h = height

In the case of a regular hexagonal prism, the Total Surface Area, TSA = 6ah + 3√3a², where a = base length and h= height of the prism. The hexagonal prism formula for calculating surface area remains the same for all kinds of hexagonal prisms. Hexagonal prisms can be regular or irregular.

• A regular hexagonal prism is a hexagonal prism having regular hexagons as bases and all the sides are the same length.
• An irregular hexagonal prism has irregular hexagonal bases, and thus the sides of its hexagon bases are not of the same length.

Let us take a hexagonal prism, having apothem length "a", the base length "b", and height "h". In order to determine we cut the hexagonal prism into its net and open it. A general formula of the lateral surface area of a prism is the product of its base and height. Thus, the lateral surface area of a hexagonal prism can be given by finding the perimeter of the base of the prism multiplied by its height. We know that the base of the hexagonal prism is in the shape of a hexagon.

Lateral Surface Area of a Hexagonal Prism

The lateral surface area of the hexagonal prism is the sum of the area of 6 rectangular faces. Therefore, the lateral surface area, L = 6ah = 6ah sq. units

Total Surface Area of a Hexagonal Prism

Total Surface Area, T = 6(area of rectangle face) + 2(area of hexagon base) sq. units. = 6ah + 3√3a²

The following steps are used to calculate the surface area of a hexagonal prism :

• Step 1: Calculate the area of the hexagonal base using the formula, 3√3a²
• Step 2: Find the area of the six rectangular faces.
• Step 3: Add all the areas together for the total surface area of a square prism, while the area of 6 rectangular faces gives the lateral area of the square prism.

Thus, the total surface area of a hexagonal prism is 6ah + 3√3a² and the lateral surface area is 6ah, in squared units.

Example: Determine the total surface area and the lateral surface area of a hexagonal prism with a base length of 4 inches and height of 11 inches.

Solution: Given a = 4 inches and h = 11 inches

Lateral Surface Area of Hexagonal Prism = 6ah = 6 × 4 × 11 = 264 square inches

Total Surface Area of Hexagonal Prism = LSA + 3√3a² = 264 + 3√3 × (4)²
⇒ TSA = 264 + 83.136
⇒ TSA = 347.136 square inches

Therefore, the total surface area of the hexagonal prism is 347.136 square inches.

What is the Surface Area of a Hexagonal Prism?

The surface area of a hexagonal prism refers to the total region covered by the surfaces of a hexagonal prism. The surface area of a hexagonal prism gives the area of each face of the prism. The unit of the surface area of a prism is expressed in square units like square meters, square centimeters, square inches, etc.

What is the Formula to Find the Surface Area of Hexagonal Prism?

The surface area of a hexagonal prism is given as Total Surface Area, T = 2(area of hexagon base) + 6(area of rectangle face) sq. units. = 6b(a + h), where the apothem length of the prism is "a", the base length of the prism is "b" and the height of the prism is "h". In the case of a regular hexagonal prism, TSA = 6ah + 3√3a²

How to Find the Total Surface Area of the Hexagonal Prism?

To find the total surface area of the hexagonal prism, follow the steps given below:

• Step 1: Check for the given information. Identify the values of apothem length, base length, and height of the prism.
• Step 2: Put these values in the formula of the surface area of a hexagonal prism, TSA = 6b(a + h)
• Step 3: Write the value of the surface area of the hexagonal prism with an appropriate unit.

How to Find the Lateral Surface Area of the Hexagonal Prism?

To find the lateral surface area of the hexagonal prism, follow the steps given below:

• Step 1: Find the values of apothem length, base length, and height of the hexagonal prism.
• Step 2: Put these values in the formula of the lateral surface area of a hexagonal prism, LSA = 6ah
• Step 3: Write the value so obtained in cubic units

How to Find the Height of the Hexagonal Prism When Its Lateral Surface Area and Apothem Length are Given?

The formula to calculate the lateral surface area of a hexagonal prism is 6ah.

• Step 1: Check for its lateral surface area and identify its apothem length.
• Step 2: Divide the lateral surface area by 6a, to find the height of the prism.

What Happens to the Lateral Surface Area of the Hexagonal Prism If Its Height is Doubled?

We know that the lateral surface area of the hexagonal prism is 6ah. If its height gets doubled, its lateral surface area will be 6a(2h), that is 2(6ah). Thus, we can conclude that its lateral surface area will also get doubled.

What Happens to the Total Surface Area of Hexagonal Prism If Length of Apothem is Doubled?

We know that the total surface area of the hexagonal prism is 6b(a + h). When apothem length is doubled, it would definitely lead to an increase in the value of the area but the area will not get doubled.