How Many Sides Does Heptagon Have

# How Many Sides Does Heptagon Have

Edited By Team Careers360 | Updated on Apr 01, 2023 02:25 PM IST

## Introduction

A two-dimensional shape having seven sides and seven angles are called a heptagon. It is a member of the two-dimensional geometry polygon class. Polygons are closed geometric shapes with only straight edges. In Greek, "hepta" denotes seven, while "gonia" denotes an angle. A polygon is a shape in geometry that has at least three inner angles or straight edges surrounding it. The most typical types of polygons include

• Triangles

• Pentagons

• Hexagon

• Heptagons

• Octagon

## Properties of the heptagon

1. The inner angles of a heptagon add up to 900 degrees.

2. A heptagon's external angles add up to 360 degrees.

3. The internal angle of a standard heptagon is approximately 128.57 degrees.

4. A typical heptagon's center angle is measured at about 51.43 degrees.

5. One heptagon has fourteen diagonals.

6. Convex heptagons are another name for regular heptagons.

## Types of Heptagons

Based on their forms, heptagons can be divided into two categories.

There are various varieties of hexagons depending on the angles and diagonals, including

1. Rregular and irregular

2. Concave and Convex Heptagon

### Regular and Irregular Heptagons

The hexagon sides meet at an angle of 5π/7 radians, or [128.57degrees] if a heptagon is regular. All the angles and sides are equal. Heptagons are said to as irregular if their side and angle measurements are not equal.

### Concave and Convex Heptagon

Convex heptagons are heptagons that have all of their diagonals inside of them. The heptagon is referred to as a concave heptagon if part of the diagonals is outside the heptagon and one or more interior angles are greater than 180 degrees.

## Perimeter of Heptagon

A regular heptagon's sides "l" are all of the equal lengths, hence its perimeter or circumference is expressed as,

Heptagonal perimeter, P = 7l units

## Area of Heptagon

The formula to determine a heptagon's area is given as follows for a regular heptagon with side length "l":

A=\frac{7}{4}l^2cot\frac{\pi }{7}sq. Units

## Some uses of Heptagon from the past.

The Barbados Dollar is also heptagonal, while the United Kingdom now issues two heptagonal coins, the 20p, and 50p pieces. The cavities on the 20-cent coin are positioned identically.

A Reuleaux heptagon, which is a curvilinear heptagon with curves of constant width, is the precise shape of the coins. The sides of the heptagon are curved outward to help the coins roll smoothly when they are entered into a vending machine. The 2 Pula, 1 Pula, 50 Thebe, and 5 Thebe Botswana pula coins are also fashioned like equilateral-curve heptagons.

Additionally, Mauritius, the United Arab Emirates, Tanzania, Samoa, Papua New Guinea, So Tomé and Principe, Haiti, Jamaica, Liberia, Ghana, the Gambia, Jordan, Jersey, Guernsey, Isle of Man, Gibraltar, Guyana, Solomon Islands, Falkland Islands, and Saint Helena all have coins in the shape of Reuleaux heptagons in circulation. Zambia's 1000 Kwacha coin is a genuine heptagon.

The disc of the Brazilian 25-cent coin is engraved with a heptagon. A "7/2" heptagram was a component of some previous Georgian coats of arms, notably those used during the Soviet era.

Heptagonal floor designs are quite uncommon in architecture. The Prince Ernst Mausoleum in Stadthagen, Germany, is one outstanding illustration.

In the US, the police badge frequently has a "7/2" heptagram outline.

1. What is the sum of the interior angles of a heptagon?

The net sum of all the angles of a heptagon is 900.

2. What is the formula to calculate the perimeter of a heptagon?

Heptagonal perimeter, P = 7l units

3. What is the formula to calculate the area of a heptagon?

The formula to determine a heptagon's area is given as follows for a regular heptagon with side length "l":

A=\frac{7}{4}l^2cot\frac{\pi }{7}sq. Units

4. Regular and irregular heptagons: what are they?

Regular Heptagons: All of the angles and sides are equal, they make up a regular heptagon.

Irregular Heptagon: An irregular heptagon has unequal side and angle measurements.

5. What is the sum of the exterior angles of a heptagon?

A heptagon's external angles add up to 360 degrees.

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