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Heptagon Area Calculator

Created by Kenneth Alambra
Reviewed by Michael Darcy
Last updated: Jan 18, 2024


In this heptagon area calculator, you will learn a lot of things like:

  • How to find the area of a heptagon;
  • How to derive the heptagon area formula; and
  • How to use this heptagon area calculator.

Heptagon (or septagon) is a seven-sided polygon, and despite being very rarely used in design due to its odd number of sides, we're here to discuss how to calculate its area. Ready to learn? Then keep on reading. 🙂

How to calculate the area of a heptagon

Finding the area of a heptagon is very easy. All we have to do is utilize the regular polygon area formula presented below:

A=n×a24×tan(πn)\small A = \frac{n\times a^2}{4\times\tan(\frac{\pi}{n})}

Where:

  • AA is the area of a regular polygon;
  • nn is the number of sides of the regular polygon; and
  • aa is the length of the regular polygon's side.

Substituting 77 for nn, we now have the heptagon area formula:

Aheptagon=n×a24×tan(πn)=7×a24×tan(π7)=1.75×a2tan(180°7)\small \begin{align*} A_\text{heptagon} &= \frac{n\times a^2}{4\times\tan(\frac{\pi}{n})}\\[1.5em] &= \frac{7\times a^2}{4\times\tan(\frac{\pi}{7})}\\[1.5em] &= \frac{1.75\times a^2}{\tan(\frac{180\degree}{7})} \end{align*}

If you don't have a scientific calculator to enter trigonometric functions like the tangent function in our equation, you can use this simplified heptagon area formula:

Aheptagon=3.633912444×a2\small A_\text{heptagon} = 3.633912444\times a^2

As an example heptagon area calculation, let's consider a septagon with a side 6 cm6\ \text{cm} in length. Using our heptagon area formula, we get:

Aheptagon=1.75×a2tan(180°7)=1.75×(6 cm)2tan(180°7)=130.820848 cm2130.82 cm2\small \begin{align*} A_\text{heptagon} &= \frac{1.75\times a^2}{\tan(\frac{180\degree}{7})}\\\\ &= \frac{1.75\times (6\ \text{cm})^2}{\tan(\frac{180\degree}{7})}\\\\ &= 130.820848\ \text{cm}^2\\ &≈ 130.82\ \text{cm}^2 \end{align*}

How to use this heptagon area calculator

Our heptagon area calculator is straightforward and intuitive. To use our tool, you only have to:

  • Input at least one of any of the following measurements of your heptagon:
    • Side (a);
    • Perimeter (equal to 7×a7\times a);
    • Circumcircle radius (R) (equal to a2×sin(180°7)\frac{a}{2 \times \sin(\frac{180\degree}{7})}); or
    • Incircle radius or apothem (r) (equal to a2×tan(180°7)\frac{a}{2\times\tan(\frac{180\degree}{7})}).

FAQ

How do I find the area of a heptagon?

To find the area of a heptagon:

  1. Take the measurement of its side. Say we have a heptagon with a side that measures 4 cm.
  2. Square that measurement to obtain: 4 cm × 4 cm = 16 cm².
  3. Multiply that square by 1.75/tan(180°/7) or 3.633912444 to find the heptagon area of 16 cm² × 3.633912444 = 58.1425991 cm² ≈ 58.14 cm².

What is the area of a heptagon with a 2 feet side?

The area of a heptagon with a side that measures 2 feet is around 14.536 ft². Using the heptagon area formula:
heptagon area = 3.633912444 × side².
= 3.633912444 × (2 ft)²
= 3.633912444 × 4 ft²
= 14.53564978 ft²
≈ 14.536 ft²

Kenneth Alambra
regular polygon with sides, angles,circumcircle and incircle radii marked.








Name
regular heptagon
α
128.57
deg
β
51.43
deg
Input at least one measurement
Side (a)
in
Perimeter
in
Circumcircle radius (R)
in
Incircle radius/ apothem (r)
in
Result
Area
in²
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