In Geometry, the shape that is bounded by at least three straight lines or at least three interior angles is called polygon. The most common examples of polygons are

- Triangle ( 3 sided polygon)
- Quadrilateral ( 4 sided polygon)
- Pentagon ( 5 sided polygon)
- Hexagon ( 6 sided polygon)
- Heptagon ( 7 sided polygon)
- Octagon ( 8 sided polygon) and so on.

In this article, let’s discuss the seven-sided polygon called “Heptagon” with proper definition, shape, sides, properties along with its formula in detail.

Also, read: Quadrilaterals

## Heptagon Definition

A heptagon is a polygon with 7 sides and 7 angles. Sometimes the heptagon is also known as “septagon”. All the sides of a heptagon meet with each other end to end to form a shape. Therefore,

**The number of heptagon sides = 7**

## Heptagon shape

Depending on the angles and diagonals, there are different types of heptagon, such as

- Regular and Irregular Heptagon
- Convex and Concave Heptagon

### Regular and Irregular Heptagon

If a heptagon is regular, then all the angles and sides are equal, and the hexagon sides meet each other at an angle of 5π/7 radians or [128(4/7)degrees]. If the heptagon does not have equal side and angle measure, then it is known as irregular heptagon.

### Convex and Concave Heptagon

If all the diagonals lie inside the heptagon, it is known as **convex heptagon**. If some of the diagonals lie outside of the heptagon and one or more interior angles are greater than 180 degrees, then the heptagon is known as **concave heptagon**.

## Heptagon Properties

Some properties of heptagons are as follows:

- In heptagon, the sum of the interior angles is equal to 900 degrees
- The sum of exterior angles of a heptagon is 360 degrees
- For regular heptagon, the measure of the interior angle is about 128.57 degrees
- The measure of the central angle of a regular heptagon is approximately 51.43 degrees
- The number of diagonals in a heptagon is 14
- Regular heptagons are also known as convex heptagons
- The number of triangles formed in a heptagon is 5

## Area of a Heptagon

For a regular heptagon with side length “a”, then the formula to find the area of a heptagon is given as

Area of a heptagon, \(A = \frac{7}{4}a^{2}\cot \frac{\pi }{7}\) Square units

The above equation is approximately equal to

**Area of a Heptagon, A = 3.634a ^{2} square units**

## Perimeter of Heptagon

Since all the sides “a” of a regular heptagon are of equal measure, then the perimeter or circumference of a heptagon is written as,

**The perimeter of a heptagon, P = 7a units**

### Heptagon Solved problem

**Question:**

Find the area and perimeter of a regular heptagon whose side is 5 cm?

**Solution:**

Given:

The side of a heptagon, a = 5 cm

We know that

The area of a heptagon, **A = 3.634a ^{2} square units**

Substitute a = 5 cm in formula,

A = 3.634 (5)^{2}

A = 3.634 (25)

A = 90.85 cm^{2}

Therefore, the area of a heptagon is 90.85 cm^{2}

The perimeter of a heptagon, P = 7a units

P = 7(5)

P = 35 cm

Hence, the perimeter of a heptagon is 35 cm.

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## Frequently Asked Questions

### What is a Heptagon in Math?

In maths (geometry), a heptagon is a polygon with seven sides and seven angles. A heptagon has seven straight sides and seven corners i.e. vertices. It is sometimes referred to as a “septagon”.

### What are Regular and Irregular Heptagons?

Regular Heptagons: In a regular heptagon, all the angles and sides are equal.

Irregular Heptagon: In an irregular heptagon, the measure of sides and angles are not equal.

### What are Convex and Concave Heptagons?

Convex Heptagon: In a convex heptagon all its diagonals lies inside it.

Concave Heptagon: In a concave heptagon, one or more interior angles are greater than 180 degrees and some diagonals lie outside the polygon.

### What is the Angle of a Regular Heptagon?

The angle of a regular heptagon is 5π/7 radians or 128.57 degrees. In a heptagon, the sum of all seven angles is 900 degrees.