Octagon is a two-dimensional geometric shape that consists of eight sides, eight vertices, and eight internal angles. The word octagon has been derived from two Greek words ‘octa’ meaning eight, and ‘gon’ meaning side. It falls under the category of polygons. The area of a regular octagon is given as 4.828427 times the square of the length of its side.

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**Types of Octagon**

### 1. Regular Octagon

If all the eight sides of an octagon are equal in length and all the internal angles are equal in magnitude, then such an octagon is known as a regular octagon. The sum of the exterior angles of a regular octagon is equal to 360°. The magnitude of each of the interior angles of a regular octagon is equal to 135°. The angle formed at the centre of the regular octagon is equal to 45°.

### 2. Irregular Octagon

If at least two sides of an octagon vary in length, then it is known as an irregular octagon.

### 3. Concave Octagon

If at least one of the internal angles of an octagon is greater than 180°, then such an octagon is known as a concave octagon. Usually, concave octagons have a dent in their closed structure.

### 4. Convex Octagon

All the internal angles of a convex octagon have a magnitude less than 180°. Usually, the convex octagons tend to have an outward bump.

**Properties of Octagon**

1. An octagon has a total of 20 diagonals.

2. The sum of interior angles of an octagon is equal to 1080°.

3. Each interior angle of a regular octagon has a magnitude equal to 135°.

4. The exterior angles of a regular octagon are congruent to each other and have a magnitude equal to 45°.

**Examples of Octagon**

### 1. Street Signs

Street signs such as the stop signs are typically constructed in the shape of an octagon. The octagon shape is usually preferred to create road warning signs to ensure that the driver facing the back of the sign is also able to understand what the signboard indicates.

### 2. Clock

Clocks are manufactured in a variety of shapes and sizes such as cube, cuboid, hexagon, heptagon, octagon, etc.

### 3. Window

Some of the windows are shaped like an octagon to add uniqueness to the household.

### 4. Tiles

One of the most popular two-dimensional geometric shapes used to manufacture tiles is an octagon.

### 5. Glass

Some of the drinking glasses are often shaped like an octagonal prism. If you look at the base of such a glass, you can easily visualize the two-dimensional octagon geometric shape.

### 6. Buildings

Architects generally make use of the octagon geometric shape to construct buildings, homes, apartments, offices, temples, and other infrastructures.

### 7. Plate

Some of the plates and dishes are also manufactured in the shape of an octagon.

### 8. Spectacles and Sun Glasses

Octagon geometric shape is widely used to construct frames for spectacles and sunglasses.

### 9. Ornaments and Accessories

A number of ornaments and accessories such as earrings, pendants, rings, etc., are shaped like an octagon.

### 10. Medal

Medals are usually awarded to a person as a token of appreciation for his/her deed. Some of the medals are shaped like an octagon.

### 11. Umbrellas

The octagon geometric shape can be visualized by looking at an open umbrella from the top view.

### 12. Trampoline

The frame or the outer structure of a trampoline usually consists of eight sides, eight vertices, and eight internal angles, thereby forming a prominent example of octagon-shaped objects present around us.

### 13. Cookie Box

A cookie box is generally shaped like an octagon.

### 14. Boxing Ring

The boxing ring is a classic example of an octagon because it has eight sides, eight vertices, and eight internal angles.

### 15. Spider Web

Spider webs are yet another example of octagon geometric shapes.

### 16. Table

Study or dining tables are constructed in a variety of shapes out of which octagon shape is quite common.

### 17. Star

A four-pointed star pattern is a prime example of an irregular octagon because it has a total of eight sides, eight vertices, and eight unequal angles.

### 18. Musical Instruments

A number of musical instruments such as a drum, tambourine, etc., are shaped like an octagon.