Heptagon - Definition, Types, Properties, Formula, Examples

When we look around, we see shapes everywhere. The laptop or the mobile you right now are using is rectangular in shape. The clock on your wall is most likely circular in shape. So, now if I ask you what shape is, then what will be your answer? Feeling short of words? 

Sometimes, the terms we most commonly use are the most difficult ones to define, right? So let me give you a brief definition of shape. Geometric shapes are figures which have a defined boundary, have definite angles, and dimensions. Shapes are used in math, art, architecture, and everyday life. We can categorise shapes broadly into 2D and 3D types. 2D shapes are those which have only two dimensions, length and breadth. Examples of 2D shapes are circle, rectangle, triangle, heptagon etc.

3D shapes are those which have three dimensions, the third dimension being height or depth (depending upon the shape) along with the length and breadth. Examples of 3D shapes are sphere, cube, cylinder etc.

Among these shapes is one interesting shape named heptagon which is a polygon with 7 sides. To brush up your memory, a polygon is a closed 2D (two-dimensional) shape made up of straight lines, where each line segment is called a side, and the points where sides meet are called vertices (corners). Polygons are named differently based on the number of sides in them. For instance, a triangle is a polygon with three sides, quadrilateral is a polygon with four sides and the topic of our interest today, i.e. heptagon is a polygon with seven sides.

Now, we are done with the backstory and let’s know more about the hero of today’s story i.e. heptagon.

A heptagon is a polygon with seven sides and seven angles. Its name has roots in the Greek. It is a combination of two words, “Hepta” which means seven and “Gonia” which means angle. A heptagon is  also named  a septagon  and this name has its roots in Latin where “septem” means seven.

So as per the name, a heptagon is a seven-sided closed figure made up of straight lines. A heptagon looks similar to a pentagon or hexagon, but with one more side. Heptagons may be irregular or regular. Irregular heptagons have unequal sides and/or angles. regular heptagons have equal sides and equal angles. Heptagons are also classified as convex and concave heptagons. 

In convex heptagons all interior angles are less than 180° and hence we get a common heptagon shape. In concave heptagons, at least one interior angle is more than 180°, which gives rise to star shaped heptagon.

The properties of heptagon are as follows:

1. Number of sides: 7

2. Number of vertices: 7

3. Number of angles: 7

4. Sum of interior angles: 900°

5. Each interior angle (regular heptagon): ≈ 128.57°

6. Each exterior angle (regular heptagon): ≈ 51.43°

7. Number of diagonals: 14 diagonals

We can use  formulas to calculate different properties of a heptagon. Some of these formulas are listed below.

We can find out the sum of interior angles of a heptagon by the following formula:

(n − 2) × 180° = 900°  where n is the number of sides i.e 7 for a heptagon. 

We can find out the value of each interior angle of a regular heptagon by the following formula:

900° ÷ 7≈ 128.57°

To find out the value of each interior angle of a regular heptagon by the following formula:

360° ÷ n≈ 51.43°

The numbers of diagonals for a heptagon can be deduced by using the following formula:

n(n − 3) ÷ 2    =14

Now, let’s come to some examples of a heptagon that we can see around us:

1. In currency: The new design of Indian 20-rupee coin has a heptagonal shape. It is a  great real-world example which  you can actually see and hold! Some other nations also mint heptagonal coins, such as: the British 50 pence coin (although technically a curved heptagon), and Tonga’s pa‘anga coin.

2. In Road signs: Some road signs use a heptagon structure. These are special-purpose traffic signs used in some countries for emphasis or distinction. Heptagon with its seven sides makes the sign stand out, even from a distance or in low visibility conditions. They are also used for unique hazard indicators.  Heptagons are used for such specific signs because drivers can instantly identify it as an important or unusual sign and even if faded or covered by dust, the distinct shape gives away its meaning.

3. In architecture: Certain buildings, tiles, and windows use heptagon patterns for decoration. Regular heptagons are difficult to construct accurately with a compass and straightedge, so are not very common in architecture but wherever used they give a sense of exclusivity. Some examples of use of heptagons in architecture are: The Monument of the Seven Martyrs, Sifnos Island, Greece and Garden pagodas and viewing towers in Japan or Europe. Some religious buildings also use heptagons in their architecture because the heptagon symbolises the seven chakras of energy or seven days of the week or seven heavens.

4. Medals: In some countries the medals are not circular but heptagonal. In India even, some organisations honour their champions by giving heptagonal medals only.

5. Decorative items: Heptagon being not very common gives exclusivity to the décor items and also gives a sense of balance and harmony. Mirrors, jewelleries and wall accents often use heptagon shape.

6. Religious symbols etc:  A type if heptagon which resembles a star is called heptagram and is often used in religious symbols, flags, and artworks. It looks like a seven-pointed star.

7. Geometry Models or Art Projects: In mathematics labs or school craft projects, heptagon-shaped figures are used to study angles and symmetry. Paper heptagons are used to teach polygon properties.

So, reading this you must be feeling that geometry and other areas of maths are not that boring and useless. This belief of yours will be more strongly rooted when you will join our Alphamath program where well qualified teachers teach using an engaging syllabus full of activities and fun learning. These classes are available online in both one on one and batch class format. For more details visit our website or contact our team through the given contact channels.

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