Hexagonal Pyramid Surface Area Calculator

Created by Mehjabin Abdurrazaque
Reviewed by Dominik Czernia, PhD
Last updated: Jun 05, 2023

In this hexagonal pyramid surface area calculator, we help you find the surface area, the lateral area, and the base area of your hexagon-based pyramid.

We also guide you on how to find the surface area of a hexagonal pyramid by hand and show you the formula for the surface area of a regular hexagonal pyramid. Keep reading!

What is a hexagonal based pyramid?

The hexagonal pyramid is a hexagon-based pyramid. Its base has 6 edges and hence, six isosceles (in some cases, equilateral) triangular faces.

• Altitude or height (h): The distance between the center of the hexagonal base and the common vertex.
• Base edge or base length (a): The length of the base's side.
• Slant height (l): The altitude or the distance between the midpoint of the base edge and the vertex.
• Apothem (ap): The distance between the midpoint of the base edge and the center of the hexagonal base.

🙋 In Greek, hexa denotes the number 6 and gon means corner. Thus, hexagon is a shape having six corners!

How do I find the surface area of a hexagonal pyramid?

The total surface area of a hexagonal pyramid (SA) is the sum of the area of its hexagonal base (BA) and the areas of its six triangular faces (FA):

SA = BA + (6 × FA)

The formula for the surface area of a regular hexagonal pyramid using base edge (a) and height (h) is:

$SA = \frac{3\sqrt{3}}{2}a^2+3a\sqrt{h^2+\frac{3a^2}{4}}$

How do I calculate the lateral area of a hexagonal pyramid?

The lateral surface area (LSA) of a hexagonal pyramid is the sum of the areas of its 6 triangular faces. We calculate a hexagonal-based pyramid using the formula:

$LSA = 3a\sqrt{h^2+\frac{3a^2}{4}}$

How do I calculate the base area of hexagonal pyramid?

A hexagonal pyramid has a hexagonal base. Therefore, the base area of the hexagonal pyramid is half of the product of its base perimeter (P) and apothem (ap):

• BA = ap×P/2

In terms of the base edge of the pyramid or the length of the hexagon's side (a), the base area is:

$BA = \frac{3\sqrt{3}}{2}a^2$

💡 The base area of a hexagonal pyramid is 2.598 times the square of its base length (a).

How do I find the face area of a hexagonal pyramid?

The face area of a hexagonal pyramid is the area of one of its six triangular faces.

In terms of the height (h) and base edge (a) of the pyramid, we calculate the pyramid's face area as:

$FA = \frac{a}{2}\sqrt{h^2+\frac{3a^2}{4}}$

How to use the hexagonal pyramid surface area calculator

⚠️ We use base edge or base length and height of the pyramid to estimate the areas in this surface area of a regular hexagonal pyramid calculator.

To find the surface area of a hexagonal pyramid using our tool:

1. Choose the desired units from the drop-down list for each variable. For example, base length and height of a hexagonal pyramid are 5 cm each. Select cm for lengths and cm2 for areas.
2. Enter the base length in the input box for Base edge (a) - 5 cm.
3. Enter the height of the pyramid in the input box for Height (h) - 5 cm.
4. Our hexagonal pyramid surface area calculator displays the following measurements immediately:
• Slant height (l) - 6.61 cm;
• Base perimeter (P) - 30 cm;
• Total surface area (SA) - 164.17 cm2;
• Base area (BA) - 64.95 cm2; and
• Lateral surface area (LSA) - 99.22 cm2.

And that's it! Our right hexagonal pyramid calc finds A (surface area) in no time.

FAQ

How do I calculate the surface area of hexagonal pyramids using slant height?

You can calculate the surface area (SA) of a hexagonal pyramid with slant height (l) using the formula:

SA = 3×ap×a + 3×a×l

where ap is the apothem of the pyramid and a is the base, and l is the slant height of the pyramid.

How do I find the base area of a pyramid with side of length 4cm?

The given pyramid has an area of 41.568 cm2 if you consider the hexagon-based pyramid. The base area (BA) of a hexagonal pyramid is 2.598 times the square of its base length (a):

BA = 2.598 × a2

Now when you know how to find surface area of a hexagonal pyramid, be sure to check out our other pyramid calculators:

Mehjabin Abdurrazaque

Base edge (a)
in
Slant height (l)
in
Height (h)
in
Base perimeter (P)
in
Surface area
Total surface area (SA)
in²
Base surface area (BA)
in²
Lateral surface area (LSA)
in²
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