Pentagon Shape - Definition, Properties, Formulas, Examples

Pentagon Shape

A pentagon shape is a 5 sided polygon. This five sided shape has five straight sides and five interior angles, which add up to 540°. Let us learn more about the pentagon shape, the pentagon properties, pentagon shape objects, and some pentagon shape examples in this article.

1.	What is a Pentagon?
2.	Pentagon Sides and Angles
3.	Pentagon Properties
4.	Pentagon Formulas
5.	Pentagon Shape Objects
6.	Types of Pentagon
7.	FAQs on Pentagon

What is a Pentagon?

A pentagon is a geometric two-dimensional shape with five sides and five angles. The pentagon definition states that it is a 2-dimensional polygon that has 5 sides and 5 angles. Observe the figure given below which shows the shape of a pentagon.

Pentagon Sides and Angles

As seen in the figure given above, a pentagon has 5 sides and 5 interior angles. The word 'pentagon' is derived from a Greek word in which 'penta' means five, and 'gon' means angle. If it is a regular pentagon, then all its sides are equal in length and all the interior angles are 108°. In case of an irregular pentagon, the interior angles are of different measure but they all add up to 540°.

Pentagon Properties

The basic properties of a pentagon are given below which help to identify a polygon to be a pentagon.

• A pentagon has 5 sides and 5 angles.
• 5 diagonals can be drawn in a pentagon and this can be calculated using the formula, Diagonals of a pentagon: = n × (n − 3) ÷ 2 = 5 × (5 − 3) ÷ 2 = 5
• The sum of all the interior angles of a pentagon is 540° and the sum of the exterior angles of a pentagon is 360°.
• In case of a regular pentagon, each interior angle is equal to 108° and each exterior angle is equal to 72°. This can be calculated using the formulas: Interior angle of a regular pentagon: 540° ÷ n = 540° ÷ 5 = 108°, Exterior angle of a regular pentagon: = 360° ÷ n = 360° ÷ 5 = 72°

Pentagon Formulas

There are many formulas related to a pentagon. A few basic ones are given below.

• Diagonals of a pentagon: = n × (n − 3) ÷ 2 = 5 × (5 − 3) ÷ 2 = 5
• Sum of interior angles of a pentagon: = 180° × (n − 2) = 180° × (5 − 2) = 540°
• Each exterior angle of a regular pentagon: = 360° ÷ n = 360° ÷ 5 = 72°
• Each interior angle of regular pentagon: = 540° ÷ n = 540° ÷ 5 = 108°
• Area of a regular Pentagon = 1/2 × Perimeter × Apothem
• Perimeter of Pentagon = (side 1 + side 2 +side 3 + side 4 + side 5)

Pentagon Shape Objects

There are many pentagon shape objects that we come across in our daily lives, for example, the shape of okra after we cut it, a symmetrical starfish, and many more. Observe the following figure which shows a few regular and irregular pentagon shape examples.

Interesting Facts about the Pentagon Shape

• The Pentagon is the headquarters of the United States Department of Defense in Washington DC, an example of a typical Pentagon shape.
• President Roosevelt decided that a new building for the Department of War was needed during World War II.
• The interesting features of the Pentagon shape were that the architect chose the Pentagon shape for the building, which reduced the distance that people had to walk from one office to another.

Types of Pentagon

Regular Pentagon and Irregular Pentagon

A pentagon can be classified into a regular pentagon and an irregular pentagon on the basis of its angle measures and its side lengths.

• In a regular pentagon, all the interior angles are of equal measure and all the sides are of equal length.
• In an irregular pentagon, all the interior angles and the sides are of different measures.

Convex pentagon and Concave pentagon

• In a Convex pentagon, all the interior angles are less than 180°, and the vertices point outwards.
• In a Concave pentagon, one or more interior angles are more than 180°, and the vertices point inwards.

Observe the figure given below to distinguish between regular and irregular pentagons along with two other types of pentagons - concave pentagons and convex pentagons.

☛ Related Articles on Pentagon

• Angles in a Pentagon
• Area of Pentagon
• Pentagon Area Calculator
• Decagon
• Pentagonal Pyramid