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103 LearnersLast updated on September 4, 2025
Surface Area of Hexagonal Pyramid
A hexagonal pyramid is a 3-dimensional shape with a hexagonal base and triangular faces that meet at a single point called the apex. The surface area of a hexagonal pyramid is the total area covered by its outer surface. This includes the base area and the lateral surface area, which consists of the triangular faces. In this article, we will learn about the surface area of a hexagonal pyramid.
What is the Surface Area of a Hexagonal Pyramid?
The surface area of a hexagonal pyramid is the total area occupied by the boundary or surface of the pyramid. It is measured in square units.
A hexagonal pyramid has a hexagonal base at the bottom and a point at the top called the apex. It has several triangular faces that connect the base to the apex.
The surface area of a hexagonal pyramid includes the area of the hexagonal base and the area of the triangular faces that form the lateral surface area.
Surface Area of a Hexagonal Pyramid Formula
A hexagonal pyramid has two main components of surface area: the base area and the lateral surface area.
To calculate the surface area, you need the base area and the lateral surface area, which depends on the slant height and the perimeter of the base.
A hexagonal pyramid has: Base Area Lateral Surface Area
Base Area of a Hexagonal Pyramid
The base area of a hexagonal pyramid is the area of the hexagonal base at the bottom of the pyramid.
The formula for the area of a regular hexagon is given by: Base Area = (3√3/2) × a² square units
Here, a is the length of a side of the hexagon.
Lateral Surface Area of a Hexagonal Pyramid
The lateral surface area is the total area of the triangular faces that connect the base to the apex. The formula for the lateral surface area of a hexagonal pyramid is:
Lateral Surface Area = (1/2) × Perimeter × Slant Height
Where the perimeter is the sum of the lengths of all sides of the hexagonal base and the slant height is the height of the triangular faces from the base to the apex.
Total Surface Area of a Hexagonal Pyramid
The total surface area of a hexagonal pyramid is the sum of the base area and the lateral surface area. It is calculated using the formula:
Total Surface Area = Base Area + Lateral Surface Area
By substituting the formulas for the base area and lateral surface area, we can find the total surface area.
Confusion between Base Area and Lateral Surface Area
Students sometimes confuse the base area with the lateral surface area. Remember, the base area refers to the hexagonal base, while the lateral surface area includes the triangular faces.
Mistake 1
Using Side Length Instead of Perimeter
Some students mistakenly use the side length of the hexagon instead of the perimeter when calculating the lateral surface area. Always remember to use the total perimeter of the hexagon.
Mistake 2
Incorrect Calculation of the Base Area
Miscalculating the base area by using an incorrect formula is a common mistake. Ensure to use the formula for a regular hexagon: (3√3/2) × a².
Mistake 3
Forgetting to Include Both Base and Lateral Surface Areas
Students often calculate only one component of the surface area. Always include both the base area and the lateral surface area when finding the total surface area.
Mistake 4
Assuming all Pyramids Have the Same Formulas
Some students assume that formulas for pyramids with different bases are the same. Ensure to use the correct formula for a hexagonal base.
Mistake 5
Solved Examples of Surface Area of Hexagonal Pyramid
Find the surface area of a hexagonal pyramid with a side length of 4 cm and a slant height of 9 cm.
Total Surface Area = 206.76 cm²
Problem 1
Given a = 4 cm, Slant Height = 9 cm. Base Area = (3√3/2) × a² = (3√3/2) × 4² = 41.57 cm² Perimeter = 6 × a = 24 cm Lateral Surface Area = (1/2) × Perimeter × Slant Height = (1/2) × 24 × 9 = 108 cm² Total Surface Area = Base Area + Lateral Surface Area = 41.57 + 108 = 149.57 cm²
Find the total surface area of a hexagonal pyramid with a side length of 6 cm and a slant height of 10 cm.
Explanation
Total Surface Area = 300.88 cm²
Problem 2
Base Area = (3√3/2) × 6² = 93.53 cm² Perimeter = 6 × 6 = 36 cm Lateral Surface Area = (1/2) × 36 × 10 = 180 cm² Total Surface Area = Base Area + Lateral Surface Area = 93.53 + 180 = 273.53 cm²
A hexagonal pyramid has a side length of 5 cm and a slant height of 8 cm. Find the total surface area.
Explanation
Total Surface Area = 235.47 cm²
Problem 3
Base Area = (3√3/2) × 5² = 64.95 cm² Perimeter = 6 × 5 = 30 cm Lateral Surface Area = (1/2) × 30 × 8 = 120 cm² Total Surface Area = Base Area + Lateral Surface Area = 64.95 + 120 = 184.95 cm²
Find the base area of a hexagonal pyramid with a side length of 7 cm.
Explanation
Base Area = 127.30 cm²
Problem 4
Base Area = (3√3/2) × a² = (3√3/2) × 7² = 127.30 cm²
The lateral surface area of a hexagonal pyramid is 150 cm², and its slant height is 12 cm. Find the perimeter.
Explanation
Perimeter = 25 cm
It is the total area that covers the outside of the pyramid, including its base and the triangular faces.
1.What are the two components of surface area in a hexagonal pyramid?
2.What is the difference between slant height and height?
3.Is lateral surface area the same as the sum of the triangular face areas?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Hexagonal Pyramid
Students often make mistakes while calculating the surface area of a hexagonal pyramid, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.
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Seyed Ali Fathima S
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Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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