# Hexagonal Pyramid Calculator

Created by Rahul Dhari
Reviewed by Madhu Raman
Last updated: Mar 17, 2022
Table of contents:

The hexagonal pyramid calculator is useful if you are looking to find out the volume and surface area of hexagonal pyramids. A pyramid is a 3D shape that has a polygonal base and an apex point that connects with all the vertices of the base. The lines joining the apex points and the base vertices are called edges. Each face of a pyramid is a triangle, and in the case of a regular pyramid, it is an isosceles triangle.
You can find more information on how to find the surface area of a hexagonal pyramid as well as its volume in the article below.

## What is a hexagonal pyramid?

A hexagonal pyramid is a three-dimensional shape that has a hexagonal base and an apex vertex. Each edge joins the vertex of the base to the apex point. In addition to this, it has six isosceles triangles as its faces. It has 12 edges and 7 vertices.

## Surface area of a hexagonal pyramid

The surface area of a hexagonal pyramid has two components —

1. Lateral surface area, $A_l$; and
2. Base surface area $A_b$.

The lateral surface area is the sum of the area of all the lateral faces. A hexagonal pyramid has 6 lateral faces which are in the shape of an isosceles triangle. To find the area of a triangle, you would need:

1. Length of the base, $a$; and
2. Height of the triangle, $l$.

The height of the triangular face of a pyramid is also known as the slant height, $h_s$. Such that the lateral surface area of a hexagonal pyramid is:

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

Similarly, the base area, $A_b$ is given by the equation:

$\scriptsize A_b = \frac {3\sqrt{3}}{2} a^2$

## Volume of a hexagonal pyramid

The volume of a hexagonal pyramid in term of base length and the pyramid height is given by the equation:

$V = \frac{\sqrt{3}}{2} a^2 h$

## Example: Using the hexagonal pyramid calculator

Find the surface area and volume of the hexagonal pyramid having base length 4 mm and height as 5 mm.

To find the volume and surface area of the hexagonal pyramid:

1. Enter the base length as 4 mm.
2. Insert the height as  5 mm.
3. The hexagonal pyramid calculator will return the following areas and volume:
• Face area = $12.166 \text{ mm}^2$;
• Base area = $41.57 \text{ mm}^2$;
• Lateral surface area = $73 \text{ mm}^2$;
• Total surface area = $114.56 \text{ mm}^2$;
• Volume = $69.28 \text{ mm}^3$;

## Other pyramid calculators

Similar to the hexagonal pyramid calculator, there are other tools based on pyramids that you can refer to learn more cool things about this 3-dimensional shape, such as:

## FAQ

### How do I find the base area for a hexagonal pyramid?

To find the base area of a hexagonal pyramid:

1. Find the square of the base length.
2. Divide the square by 2.
3. Multiply the resultant by 3.
4. Multiply the produce by square root of 3 to obtain the base area of the hexagonal pyramid.

### What is the surface area of hexagonal pyramid having side length 5 cm and height 7 cm?

The surface area of the hexagonal pyramid is 151.55 sq cm. Out of which, the 123.46 sq. cm is the lateral surface area, which is calculated as: 3 × 5 × √((0.25×25) + 49) = 123.46 sq. cm., while 64.95 sq. cm is the base area.

Rahul Dhari
Dimensions
Base length (a)
in
Pyramid height (h)
in
Results
Face area
in²
Base area
in²
Lateral surface area
in²
Total surface area
in²
Volume
cu in
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