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# Heptagon Calculator

Heptagon — Area, Perimeter, and Side lengthUsing the heptagon calculatorOther related calculatorsFAQs

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 or septagon (its other name) 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*}

You can also use this tool to find the parameters of other regular polygons. Simply tick on the Try other regular polygons checkbox to display the number of sides variable and enter other numbers of sides.

FAQs

### 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.