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# Septagon|Definition & Meaning

## Definition

A **septagon **is a polygon with exactly **seven **sides. It may be regular (all sides and angles equal) or irregular (if any side or angle is not equal to the others). **Septagons **are also called **septagons**, where “sept” comes from ** septem **and

*septua-*in

**Latin**, and “

**hept**” from

**hepta**in

**Greek**.

*Septem*means “seven,” and the other two are numerical prefixes for “seven.”

A **polygon **is a shape in geometry that has at least **three **inner angles or straight edges surrounding it. They have no **curves **and are **closed shapes **constructed of **straight lines**.

The most prevalent polygons are:

- Triangle (3-sided polygon)
- Quadrilateral (4-sided polygon)
- Pentagon (5-sided polygon)
- Hexagon (6-sided polygon)
- septagon (7-sided polygon)
- Octagon (8-sided polygon) and so forth

A **polygon **is a closed, two-dimensional form with **any number **of straight sides. To put it simply, a **septagon **is a polygon with **seven **sides.

## Septagon Sides

The lengths of the **seven **straight edges that make up a **septagon’s **seven sides might vary or remain constant. These sides come together but do not **overlap **or **intersect**. A seven-sided enclosed **polygon **is created when the septagon’s sides converge at its vertices.

## Septagon Angles

**Seven **interior angles make up a **septagon**, and the total of all seven interior angles is **900°**. There are some **obtuse **and **sharp **angles in the figure. **Septagons **can be regular or **asymmetrical**, and both types of septagons have a sum of **outside angles **that is equal to **360°**.

Now let us examine more about the septagon’s **interior** and **exterior** angles.

### Interior Angles of a Regular Septagon

The **interior **angle formula, which is (n – 2) 180º where n is the number of sides in the **polygon**, can be used to calculate the sum of **interior** angles of a regular polygon. Thus, n = 7 for a septagon. A regular septagon’s interior angles are calculated as (7 – 2) 180° = 900°. A regular septagon’s interior angles are therefore equal to 900/7, or 128.57º

### Exterior Angles of a Regular Septagon

The formula for the sum of **exterior **angles states that a regular **polygon’s **total exterior angle is **360 **degrees. As a result, the total of all the outside angles of a standard **septagon** is 360 degrees. A regular septagon’s exterior angles are, therefore, equal to 360/7, or **51.43 degrees**.

## Septagon Diagonals

**Fourteen **diagonals make up a **septagon**. As opposed to a **concave** septagon, which has at minimum one diagonal outside the figure, a **convex** septagon has diagonals that are inside the figure.

## Types of Shape of Septagon

The **sides **and **angles **of a septagon can be used to classify the shape.

Septagons can be categorized into the following groups according to their side lengths:

### Regular Septagon

A** septagon **with equal sides and angles is referred to as a **regula**r septagon. The total internal **angle **of a polygon, where n is the number of sides, is equal to **(n – 2) 180°**. The sum of a septagon’s interior angles is **(7 – 2) 180° = 5 x 180° = 900° **because it has **seven **sides. A regular septagon has an internal angle value of **900°/7 = 128.57°.**

### Irregular Septagon

A **septagon **is said to be **irregular **if its sides and angles are of varied sizes. An irregular septagon will have different values for each of its internal angles. But an irregular septagon’s internal angles added together equal **900°**.

Septagons can be categorized in the following ways based on angle measurements:

### Convex Septagon

All of the inner angles in a **convex** septagon are fewer than **180** degrees. They might be septagons that are regular or irregular. The convex septagon’s vertices are all inclined toward the outside.

### Concave Septagon

A **concave** septagon has at least one internal angle that is more than **180** degrees. They might be septagons that are regular or irregular. In a concave septagon, at least one vertex faces inward.

## Properties of a Septagon

We now have a fundamental understanding of what a **septagon** is, so let’s examine some of its key characteristics.

**Seven sides**,**seven edges**, and**seven vertices**make up a septagon.- A septagon’s
**internal angles**add up to**900 degrees**. - A regular
**septagon**has**interior angles**with values of**128.57°**on each side. - A septagon’s
**exterior angles**add up to**360 degrees**. - A septagon can have a
**maximum**of**14**diagonal lines. - A typical septagon has a
**central**angle that is**51.43 degrees**or so in diameter. - Since all of the
**interior**angles of a regular septagon are fewer than**180 degrees**, it is often referred to as a**convex**septagon.

## Regular Septagon Formulas

A regular **septagon **can be represented using a variety of **formulas**. Let’s explore how to calculate a normal septagon’s **area **and **perimeter **using the septagon formulas.

### Perimeter of a Septagon

We are aware that a typical **septagon **has seven equal-length **sides**. As a result, the normal septagon’s **perimeter **is stated as **7** side length. By using this concept, the **perimeter **of a regular septagon having side length “a” is given as

Perimeter = 7a

### Area of a Septagon

The overall **area **encompassed by a **septagon **is referred to as the polygon’s area. The following **equation **can be used to compute the **area **of a regular **septagon **with side length “a”:

Area = (7a^2/4) cot (π/7)

It is possible to write this equation more concisely as:

Area = 3.634a^2

where “a” stands for the side length. This can be used to determine the size of a standard **septagon**.

## Summary of a Septagon

The following points summarize the characteristics of a septagon.

- There are 7 vertices, 7 interior angles, and 7 edges in a
**septagon**. - The septagon’s
**exterior**angles add up to**360°**while its**interior**angles add up to**900°**. - The number of sides distinguishes between two types of
**septagons**:**regular**and**irregular**. While on the basis of angles, it is classified into**convex**and**concave**septagons.

## Examples Involving the Formulas of Septagon

### Example 1

A regular **septagon** has a 52 cm perimeter. How far does each side extend?

### Solution

Considering that a regular **septagon’s** perimeter is 52 cm. We are aware that a regular septagon’s **perimeter **is provided as 7 Side length. Let ‘a’ units be the side length.

Thus:

7a = 52

a = 52/7

= 7.42 cm

Consequently, the septagon’s length is **7.42 cm** on each side.

### Example** 2**

Calculate the **area** of a regular **septagon** with 13 cm of each side length.

### Solution

Given that a regular **septagon **has sides that are 13 cm long, we are aware that the formula can be used to get the **area** of a regular septagon:

Area = 3.634a^2

= 3.634(13)^2

= 568.516 square cm.

Resultantly, **568.516 square cm **is equal to the** area **of a regular **septagon **with a side length of 13 cm.

*All images/mathematical drawings were created with GeoGebra.*