What Is a Decagon?
A decagon is defined as a polygon with 10 sides, 10 interior angles, and 10 vertices.
What Are the Different Types of Decagons?
There are two types of decagons – regular and irregular.
- Regular Decagons – These decagons have sides of equal length and have equal angles. The interior angles add up to 1440° and the exterior angles add up to 360 degrees. A regular decagon has 35 diagonals.
- Irregular Decagon – These decagons are made of sides that are of unequal lengths and unequal angle measures.
Here are a few examples of regular and irregular decagons.
Solved Examples
Example 1: Which of the following is not a decagon?
Solution:
As we can see, there are both regular and irregular polygons. Three polygons have 10 sides and there is one shape that has 7 sides.
A seven-sided polygon is known as a heptagon and not a decagon.
Hence, the shape in the image is not a decagon.
Example 2: Alison enjoys collecting rare coins. She came across a unique coin and called it a decagon in shape. Is Alison right?
Solution:
As we know, a decagon has 10 sides and 10 interior angles. The given coin has 6 sides and it represents a hexagon.
Hence, the coin is not a decagon and Alison’s conclusion is not right.
Example 3: What is the measure of each interior angle of a regular decagon?
Solution:
Sum of all interior angles of regular decagon = 1440°
Number of sides = 10
Measure of each interior angle \(= \frac{Sum\text{ }of\text{ }all\text{ }interior\text{ }angles}{Number\text{ }of\text{ }sides}\)
\(= \frac{1440^{\circ }}{10}\)
\(= 144^{\circ }\)
Hence, each interior angle of a regular decagon measures 144°.
Some real-life examples of a decagon are umbrellas, coasters, and coins.
The word ‘decagon’ was found during the 16th century and is derived from the Latin word ‘decagonum’.
A decagon has 10 interior angles.
The exterior angles of a decagon add up to 360°.