Heptagon

Heptagon is a shape from the polygon family that has seven sides. “Hepta” is derived from the Greek word meaning seven and “gon”, meaning sides. It is also called Septagon.

Let’s learn about Heptagon in detail, including its types, properties, formulas and examples.

Heptagon Definition

A Heptagon is a two dimensional closed figure with seven sides and seven angles.

Heptagon not only consists of seven sides and angles but also includes different parts, which affect its structure.

Heptagon Shape

Heptagon is a polygon with seven sides and seven angles. It is also called a septagonal shape, but the use of the word Septagon is avoided.

A heptagon can be reflected with a symmetric line segment dividing the heptagon into halves and creating a congruent image.

Parts of Heptagon

The important parts which make a polygon a “heptagon” are as follows:

Parts of Heptagon	Description
Side	A straight line segment that defines the structure of a heptagon.
Vertex	A point where two line segments meet in the heptagon structure. (Plural: vertices)
Angle	The heptagon forms angles where two line segments meet, one at each vertex.
Interior and Exterior	The part enclosed inside the sides of the heptagon is known as the interior, whereas the area outside the shape is known as the exterior.
Diagonal	A line segment connecting two non-adjacent vertices. A heptagon has 14.

Heptagon Sides

The line segment which encloses the figure and forms the boundary line of shape is called a side of the heptagon. There are 7 sides in a heptagon shape. These sides can be of any length, to make a heptagonal structure.

Heptagon Angles

A Heptagon makes an angle at each of the seven vertices. For a regular heptagon, the sum of interior angles is 900° and the sum of exterior angles is 360°.

Each of the interior angle would be around 128.5 degrees and exterior angle will be 51.43 degrees.

For an irregular heptagon the interior and exterior angles will vary.

There are two types of angles in a heptagon, which are :

• Interior Angle of Heptagon
• Exterior Angle of Heptagon

Interior Angles of Heptgon

There are seven interior angles of a Heptagon and the sum of these angles is 900 degrees. In the case of regular heptagon, each angle is equal to 128.57 degrees.

Exterior Angles of Heptagon

There are seven exterior angles in a Heptagon. These exterior angles are formed when the sides of Heptagon are extended outside the Heptagon. The sum of exterior angle is 360 degrees.

Heptagon Diagonals

As heptagon has 7 vertices, the total number of diagonals can be 14. Thus, a heptagon has 14 diagonals in total.

Types of Heptagon Shape

Heptagons can be categorized into two groups, which are :

• Based on Side Length
• Based on Angle Measurement

Let’s discuss these two classifications of Heptagon in detail.

Heptagons Based on Side length

A heptagon may have the same length for all seven sides and may not have same length for all the seven sides. Hence, on the basis of Side length the Heptagons are classified as follows :

• Regular Heptagon
• Irregular Heptagon

Let’s discuss types of Heptagons based on side length in detail

Regular Heptagon

A heptagon whose sides and angles are equal is known as a regular heptagon. It is the ideal shape which has equal sides and equal angles with no parallel sides.

Regular heptagons have the following properties :

• The sum of exterior angle is equal to 360 degrees.
• The measure of interior angle is 128 degrees approximately.
• It has 14 diagonals.
• A regular heptagon can be divided into 5 triangles.
• The measure of central angle is approximately 54 degree.
• It has rotational symmetry of order 7.

Irregular Heptagon

Every object with a closed shape and seven sides is a heptagon. These sides can be of different length, at any angle. Hence, there cannot be any particular measure for irregular heptagon.

A irregular heptagon doesn’t have lines of symmetry.

Heptagon Based On Angle Measurement

On the basis of measurement of angles, Heptagon is classified as :

• Concave Heptagon
• Convex Heptagon

Let’s learn them in detail.

Concave Heptagon

In a concave heptagon, at least one of the interior angle of all the angles is greater than 180 degree. Some of the properties are listed below :

• It is a type of irregular heptagon.
• It is asymmetrical in nature
• It causes one of the corresponding diagonal to fall outside the boundary line of heptagon.

Convex Heptagon

When all interior angles of a heptagon measure less than 180 degree it is known as Convex Heptagon. It has the following properties,

• All interior angle measure less than 180 degrees.
• A regular heptagon(equal sides) is always a convex heptagon.
• A convex heptagon can be both regular or irregular heptagon.
• All diagonals lie inside the heptagon.
• They may or may not be symmetrical in nature.

Heptagon Properties

Key properties of a heptagon are :

Properties of Heptagon
Property	Description
Sides	A heptagon has seven sides, forming a closed structure.
Angles	A heptagon has seven angles. The sum of interior angles is 900 degrees (5π radians), and the sum of exterior angles is 360 degrees.
Vertex	It has 7 vertices, where each line segment joins.
Diagonals	A heptagon has 14 diagonals, which are line segments joining two non-consecutive vertices.
Sum of Interior Angles	The total sum of all angles in a heptagon is 900 degrees, calculated as (n-2) × 180°, where n is the number of sides.
Interior Angle Measure	Each angle measure in a regular heptagon is approximately 128.57 degrees, calculated as (n-2) × 180°/n.
Exterior Angle Sum	The sum of exterior angles in a heptagon is always 360 degrees, with each exterior angle being approximately 51.43 degrees.
Line of Symmetry	A heptagon has rotational symmetry of order 7 and can be symmetrically divided into congruent halves.

Heptagon Formula

There are two common Formulas of Regular Heptagon, which are :

• Perimeter of Heptagon
• Area of Heptagon

Perimeter of Heptagon

For a regular heptagon, the perimeter of heptagon can be calculated using the following formula :

Perimeter of Heptagon = 7 × Sides of Heptagon (for Regular Heptagon)

For irregular heptagons, we need to add all the seven sides individually.

Area of Heptagon

Area of a heptagon is given by the following formula,

Area of Regular Heptagon = 3.643 × (side)²

How to Draw Heptagon

Constructing a regular heptagon with the perfect 128. 57 degree of angle and equal length can be a little tricky.

Let’s follow the steps below, to construct a regular heptagon.

Step 1: Draw a circle, centered at point x. Also, it is better to leave some extra space outside the circle to make the exterior part of heptagon.

Step 2: Draw a radius connecting the center of the circle to its outer boundary. lets name the radius ,AX.

Step 3: Draw another circle centered at A, which intersects the circle at two points, B and C.

Step 4: Connect B and C. The line segment BC bisects AX.

Step 5: Draw third circle centered at C which will intersect at point D.

Step 6: Use your compass to measure the length of CD and create 7 sides.

Step 7: Join the Seven Points to get the final Heptagonal shape. Erase the unnecessary parts.

Step 8: Your Final Heptagon is constructed. There is a probability of negligible error in this method to construct a heptagon.

Related:

• Polygon
• Hexagon
• Octagon
• Geometrical Shape
• Pentagon

Heptagon Examples

Let’s solve some example problems on the properties of Heptagon.

Example 1: If the area of a regular heptagon is 714 cm², what is its side?

Solution:

Area of Heptagon = 3.643 × side × side

Here, we have area = 714 cm²

⇒ 714 = 3.643 × side × side

⇒ Side² = 714/3.63 = 196.69

⇒ Side = √196.69 ≈ 14

When we solve the above equation, we get the side equals to 14 cm, approximately.

Example 2: Find the area of the heptagon whose side is 8cm?

Solution:

We know, Area of heptagon = 3.643 (side)²

⇒ Area of heptagon = 3.643 × 8cm × 8cm = 233.1 cm²

So the area of heptagon with side 8cm will be 233.1 cm²

Example 3: Find the perimeter of the heptagon whose side is 8cm?

Solution:

Perimeter of heptagon is 7 × side.

here side = 8 cm

So, Perimeter = 7 × 8 = 56 cm

The perimeter of heptagon with side 8cm will be 56cm.

Practice Questions on Heptagon

Here is a worksheet on Heptagon for you to solve.

1. Find the area of heptagon where the side is 4cm?

2. Find the area of heptagon whose side is 9 cm?

3. The area of heptagon is 1200cm², what is the length of its each side?

4. What is the perimeter of the heptagon whose sides are 2cm, 4cm, 6cm, 3cm, 5cm, 4cm?

FAQs on Heptagon

What is Heptogon?

Heptagon is a polygon bounded by seven line segments.

How Many Sides are there in Heptagon?

A heptagon has 7 sides.

What is Difference between Regular and Irregular Heptagon?

In a regular heptagon, all angles and sides are equal, whereas irregular heptagon can have different measure of sides and angles.

What is the Sum of Internal Angles of Regular Heptagon?

For a regular heptagon (equal length of all sides) , the sum of its interior angle is 900 degrees.

What is Area of Heptagon?

Area of heptagon is equal to 3.643 × (side)²

How Many Lines of Symmetry are there in Heptagon?

Depending on if the heptagon is regular or irregular it can have 0 to 7 lines of symmetry. For regular heptagon, it is 7 line of symmetry.

How many Diagonals are there in Heptagon?

There are 14 diagonals in a heptagon

Define Concave and Convex Heptagon.

At least one of the interior angles of concave heptagon is greater than 180 degree while all the interior angles of convex heptagon are less than 180 degrees.