# Heptagon Calculator

Created by Rahul Dhari
Reviewed by Kenneth Alambra
Last updated: Oct 17, 2022

The heptagon calculator will assist you in finding parameters related to the heptagon shape. Be it the sides of a heptagon or perimeter or area, this calculator can help you with all of that. You can start by entering some numbers in the tool or reading on to understand what a heptagon is.

## Heptagon — Area, Perimeter, and Side length

A heptagon is a polygon with 7 sides and 7 angles. The words heptagon and septagon are from Greek and Latin origins, with "hept" and "sept" referring to 7. For a regular polygon with $n$ sides, the internal and external angles, $\alpha$ & $\beta$ are

$\alpha = \frac{(n - 2)\pi}{n}\\[1em] \beta = \frac{2\pi}{n}$

The area and the perimeter, $P$ of the heptagon ($n=7$) is

\begin{align*} \text{Area} &= \frac{n}{4} \times a^2 \times \cot \left ( \frac{\pi}{n} \right )\\[1em] \text{Area} &= \frac{7}{4} \times a^2 \times \cot \left ( \frac{\pi}{7} \right )\\[1em] \text{Area} &= 3.634 a^2\\ P &= n \times a\\ P &= 7 \times a\\ \end{align*}

## Using the heptagon calculator

Let's calculate the area of the heptagon with a side of 8 cm to understand the heptagon calculator usage.

1. Enter the length of the side, $a = 8\ \text{cm}$.

2. The perimeter of the heptagon is $8\ \text{cm}\times 7 = 56\ \text{cm}$.

3. The area of the heptagon is

\scriptsize \qquad \begin{align*} \text{Area} &= \frac{7}{4} \times a^2 \times \cot \left ( \frac{\pi}{7} \right )\\[1em] \text{Area} &= 3.634 \times 8^2 = 232.57 \text{ cm}^2 \end{align*}
1. The internal angle, $\alpha$ and exterior angle, $\beta$ are $128.57^\circ$ and $51.43^\circ$

2. The radius of the circumcircle is

\scriptsize \qquad \begin{align*} R &= \frac{a} {2\sin(\frac{\pi}{7})}\\[1em] R &= \frac{8} {2\sin(\frac{\pi}{7})} = 9.219 \text{ cm} \end{align*}
1. The radius of the incircle is
\scriptsize \qquad \begin{align*} r &= \frac{a} {2\tan(\frac{\pi}{7})}\\[1em] r &= \frac{8} {2\tan(\frac{\pi}{7})} = 8.306 \text{ cm} \end{align*}

If you like this tool, you might be interested in some of our similar polygon-related calculators:

## FAQ

### What do you mean by a heptagon?

A heptagon is a 7-sided polygon. It is also known as septagon. The prefix in the word "hept-" and "sept-" are of Greek and Latin origin, respectively.

### How many sides do a heptagon have?

A heptagon has 7 sides. Its figure has 7 sides and 7 angles. The angle between each side of a regular heptagon is 128.57°.

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

To find the area of a heptagon:

1. Find the square of the side of the heptagon.
2. Multiply the square by 3.634 to obtain the area of the heptagon.
Rahul Dhari

Name
regular septagon
Parameters
Side (a)
in
Perimeter
in
Area
in²
α
128.57
deg
β
51.43
deg
in
in
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