Surface Area of Hexagonal Pyramid
2026-02-28 13:07 Diff
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Last updated on September 4, 2025

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.

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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.

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

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

Find the base area of a hexagonal pyramid with a side length of 7 cm.

Explanation

Base Area = 127.30 cm²

Well explained 👍

Problem 4

Base Area = (3√3/2) × a² = (3√3/2) × 7² = 127.30 cm²

Okay, lets begin

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

Well explained 👍

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?

Base area and lateral surface area are the two components of surface area in a hexagonal pyramid.

2.What is the difference between slant height and height?

Slant height is the length from the apex to the edge of the base. Height is the perpendicular distance from the apex to the center of the base.

3.Is lateral surface area the same as the sum of the triangular face areas?

Yes, the lateral surface area is the total area of all triangular faces connecting the base to the apex.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

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

About the Author

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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