# Dodecagon Area Calculator

Created by Kenneth Alambra
Reviewed by Rahul Dhari
Last updated: Aug 28, 2022

If you're looking for a quick and easy way to calculate the area of a regular dodecagon, this dodecagon area calculator is for you. A dodecagon is a 12-sided regular polygon, and as a regular polygon, a dodecagon follows the same properties as other regular polygons.

In this calculator, you'll be able to explore:

• How to find the area of a dodecagon;
• How to use this dodecagon area calculator; and
• Some examples of dodecagon area calculation.

## How to find the area of a dodecagon

A dodecagon is a regular polygon which means to find the area of a regular dodecagon, we can use the area formula of any regular polygon, as shown below:

$\small A = \frac{1}{2}\times n\times a\times r$

Where:

• $A$ is the area of a regular polygon;
• $n$ is the regular polygon's number of sides;
• $a$ is the length of the regular polygon's side;
• $r$ is the apothem (or incircle radius) of the regular polygon.

To use this formula to find a dodecagon area, we can denote as $A_\text{dodecagon}$, we need to use $12$ for $n$, and we can also utilize the relationship between $r$, $a$, and $n$ to arrive at this equation:

\small \begin{align*} A_\text{dodecagon} &= \frac{1}{2}\times n\times a\times r\\\\ &= \frac{1}{2}\times n\times a\times \frac{a}{\tan(\frac{\pi}{n})\times 2}\\\\ &= \frac{1}{2}\times 12\times \frac{a^2}{\tan(\frac{180\degree}{12})\times 2}\\\\ &= 6\times \ \frac{a^2}{\tan(15\degree)\times 2}\\\\ &= \frac{3\times a^2}{\tan(15\degree)}\\\\ \end{align*}

We can further simplify this equation by taking the quotient of $3$ and $\tan(15\degree)$ to have:

\small \begin{align*} A_\text{dodecagon} &= \frac{3\times a^2}{\tan(15\degree)}\\\\ &= 11.19615242\times a^2 \end{align*}

Using this formula for an example, let's say we have a dodecagon with a side that measures $10\ \text{cm}$. Substituting $10\ \text{cm}$ into our dodecagon area formula, we get:

\small \begin{align*} A_\text{dodecagon} &= \frac{3\times a^2}{\tan(15\degree)}\\\\ &= \frac{3\times (10\ \text{cm})^2}{\tan(15\degree)}\\\\ &= 1119.615242\ \text{cm}^2\\ &≈ 1119.6\ \text{cm}^2 \end{align*}

## How to use this dodecagon area calculator

This dodecagon area calculator is very easy to use and only requires one step to find the area of any dodecagon. And that is to:

• Enter at least one of the measurements of your dodecagon. You can enter your dodecagon's:
• Side (a);
• Perimeter (which is only $12\times a$);
• Circumcircle radius (R) (equal to $\frac{a}{2\times \sin(15\degree)}$); or
• Apothem (r).

You can also click on the advanced mode button below our tool to access the secret feature of this calculator. In the advanced mode of this tool, you will see the Number of sides variable, where you can enter other values to find the area of other regular polygons. Isn't that amazing? 😊

## Other regular polygon tools

Craving for more polygon-related knowledge? Don't worry. We've got a list of other related tools waiting for you:

## FAQ

### How do I find the area of a dodecagon?

To find the area of a dodecagon:

1. Take the square of its side measurement. Let's say its side measures 8 cm. We then have: 8 cm × 8 cm = 64 cm².
2. Multiply the product by 3/tan( 15°) or 11.19615242 to find the dodecagon area: 64 cm² × 11.19615242 = 716.5537545 cm² ≈ 716.6 cm².

### What is the area of a dodecagon with a side of 1 cm?

The area of a dodecagon with a 1-cm side is roughly 11.196 cm². To find that value, we can use the dodecagon area formula: dodecagon area = 11.19615242 × (side measurement)².

Since the dodecagon's side measures 1 cm, we get:
dodecagon area = 11.19615242 × (1 cm)²
= 11.19615242 × 1 cm²
= 11.19615242 cm²
≈ 11.196 cm²

Kenneth Alambra

Name
regular dodecagon
α
150
deg
β
30
deg
Input at least one measurement
Side (a)
in
Perimeter
in
in
in
Result
Area
in²
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