How Many Sides a Pentagon Has

Introduction

A geometric shape known as a pentagon has five sides and five angles. Penta means five, and gon means angle. One of the different kinds of polygons is the pentagon. A regular pentagon's interior angles add up to 540 degrees. We learn about various kinds of shapes in geometry. A polygon is a two-dimensional shape made up of straight lines and interior angles.

Examples include

• Triangle (three-sided polygon)

• Quadrilateral (four-sided polygon)

• Pentagon (five-sided polygon)

• Hexagon (six-sided polygon)

• Heptagon (seven-sided polygon)

• Octagon (eight-sided polygon), etc.

The five-sided polygon known as the "pentagon" and its proper definition, shape, sides, and properties, as well as the formula for its perimeter and area, are covered in detail in this article.

Definition

A polygon with 5 sides and 5 angles is called a pentagon. Two words, Penta and Gonia, both of which denote five angles, combine to form the word "pentagon." From end to end, the sides of a pentagon come together to form a shape.

Therefore,

The number of sides of a pentagon = 5

The shape of a pentagon

The pentagon is a polygon with five sides and five angles, just like other polygons like triangles, quadrilaterals, squares, and rectangles.

Various pentagon shapes are depending on the sides, angles, and vertices, such as

• Regular and Irregular pentagons

• Convex and Concave pentagons

Regular and Irregular Pentagon

Every side of a regular pentagon has the same length, and its five angles are all the same size. A pentagon is referred to as irregular if its side length and angle measurement are not equal.

Regular Pentagon

A regular pentagon has five congruent sides, as stated above in the definition. As a result, we can quickly determine the pentagon's perimeter. The figure below shows how this can be seen.

The perimeter of a regular pentagon is five times the length of any one of its sides because all five sides are equal in this situation.

Additionally, as shown below, we can divide a regular pentagon into five identical triangles.

In other words, the area of a regular pentagon is equal to five times the area of a triangle with sides that are equal to those of the pentagon.

Convex and Concave Pentagon

A pentagon is referred to as convex if all of its vertices point outward. A pentagon is referred to as concave if at least one of its vertices faces the interior.

Properties of a Pentagon

• The interior angles of the pentagon add up to 540 degrees.

• It is a regular pentagon if all the sides are equal and all the angles are of equal size. It is irregular if not.

• Each interior angle in the regular pentagon is 108°, while each exterior angle is 72°.

• Five equal sides make up an equilateral pentagon.

• A rectangular pentagon's interior angles add up to 540°.

Area of a Pentagon

The formula to determine the area of a pentagon is given as follows for a regular pentagon with side and apothem lengths:

Area of a Pentagon,

A= \frac{5}{2}\times \text{Side Length}\times \text{Apothem square units}

A pentagon with sides of equal length is known as a regular pentagon.

The area of the regular pentagon is given as

Area = \frac{1}{4}\sqrt{5(5+{2\sqrt{5}}))}s^{2}

Where s is the side of the Pentagon.

Perimeter of a Pentagon

Since each of the sides "a" of a regular pentagon is the same size, the circumference or perimeter of a pentagon is expressed as,

P = 5a units

Other types of pentagons exist in geometry based on their individual properties of pentagons. As follows:

Equilateral Pentagon

An equilateral pentagon is a polygon with five sides that are all the same length. All five of a pentagon's interior angles, however, can have a different set of values. As a result, they are enabling it to grow into a family of pentagons.

The regular pentagon is therefore distinctive up to similarity. Since it is an equilateral pentagon with five equal angles.

Cyclic Pentagon

A pentagon is referred to as a cyclic pentagon if all of its vertices are located on a circle's circumference. The best illustration of a cyclic pentagon is the regular pentagon. One-fourth of the square root of one of the roots of a septic equation can be used to represent the area of a cyclic pentagon. The sides of the pentagon are functions of the equation's coefficients in this case. This holds for both regular and asymmetric pentagons.