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.

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.

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°.

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°

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)

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.

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

What is Pentagon Shape in Geometry?

A two-dimensional shape with 5 sides is known as a pentagon. We call it a 5 sided polygon because it consists of 5 sides and 5 angles.

What is a 5 Sided Shape Called?

A 5 sided shape is called a pentagon. If all five sides are equal then we call it a regular pentagon, whereas if any two of the sides are different in measurement, we call it an irregular pentagon.

Is a Pentagon a Parallelogram?

No, a pentagon is not a parallelogram, it is a five-sided polygon. A parallelogram has only four sides.

What is the Similarity Between a Quadrilateral and a Pentagon Shape?

A quadrilateral and a pentagon both are polygons and the sum of their exterior angles is equal to 360°.

Does a Pentagon have Parallel Sides?

A regular pentagon has no parallel lines, but an irregular pentagon may have 1 or 2 pairs of parallel lines.

How Many Angles are there in a Pentagon?

A pentagon has five interior angles and 5 corresponding exterior angles. In the case of a regular pentagon, each of these five interior angles measures 108º each and each of the 5 exterior angles measures 72º.

How Many Lines of Symmetry Does a Pentagon Shape Have?

A regular pentagon shape has 5 lines of symmetry although an irregular pentagon has no lines of symmetry.

How to find the Exterior Angle of a Pentagon?

Each exterior angle of a regular pentagon can be calculated using the formula 360 ÷ n, here n = 5, so, 360 ÷ 5 = 72°. Therefore, each exterior angle of a regular pentagon is 72°. In case of an irregular pentagon, each exterior angle can be calculated according to the value of the corresponding interior angle. Since the exterior angle and the interior angle form a linear pair their sum will always be 180°.

What is a Regular Pentagon?

A regular pentagon is a pentagon in which all the 5 sides are of equal length and all the interior angles are of equal measure. Each interior angle of a regular pentagon is equal to 108° and each exterior angle of a regular pentagon is 72°.

What is the Angle Sum Property of Pentagon?

The angle sum property of a polygon is expressed using the formula, S = (n − 2) × 180°, where 'n' equals to the number of sides in that particular polygon. According to this property, the sum of the interior angles of any polygon can be calculated with the help of this formula. So, let us apply this to a pentagon in which n = 5. After substituting the value, we get, S = (n − 2) × 180° = S = (5 - 2) × 180° = 540°. This means the sum of the interior angles of a pentagon is always 540°.

What is the Sum of Interior Angles of a 5 sided Polygon?

The sum of the interior angles of a 5 sided polygon, which is a pentagon, is always 540°. This applies to a regular pentagon and an irregular pentagon.

How to Find the Area of a Pentagon?

The area of a regular pentagon can be calculated using the formula, Area of pentagon = 1/2 × perimeter × apothem. Another formula which is used to find the area of a regular pentagon is, \(A = \frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}\) where 's' is the length of one side of the regular pentagon. In the case of an irregular pentagon, the area can be calculated by dividing the pentagon into other smaller polygons.

How to Find the Perimeter of a Pentagon?

We know that a pentagon is a 5 sided polygon. The perimeter of a pentagon can be calculated by adding the lengths of all the 5 sides. The perimeter of a pentagon is expressed in linear units like inches, centimeters, yards, and so on.