# Pentagon: Shape, Parallel lines, Angles, Examples, formula and sum of Pentagon Angles

A pentagon shape is a five-sided flat (two-dimensional) geometric shape. In geometry, we define the pentagon as a five-sided polygon with 5 straight sides and 5 interior angles totalling 540°.

## Why are there no parallel lines in a pentagon?

The geometry of this two-dimensional shape doesn’t allow a parallel line. Each line is the same length as the others, and the angle between the two lines is 108°, for 540° in inner angles. So there will be no parallel lines in this case, and it has five sides.

## Is a pentagon any five-sided shape?

A pentagon (from the Greek “pente” - five and “gonia” - angle) is any five-sided polygon or a 5-on. A regular pentagon's internal angles add up to 540°. A pentagon can be simple or complex, and it can be self-intersecting. A pentagram is an example of a self-intersecting regular pentagon (or a star pentagon).

## What is the distinction between a regular pentagon and an irregular pentagon?

Every pentagon has five straight sides, but the sides may or may not be the same length. For example, a regular pentagon comprises five equal sides and five equal angles.

## What is one of a pentagon's angles?

Every interior angle of a regular pentagon measures 108°.

## In geometry, what does the term regular pentagon mean?

When all angles and sides of a polygon are equal, we say it to be regular (otherwise, it is irregular).

## Is it possible for a pentagon to be concave?

Pentagons and other polygons can also be convex or concave. A pentagon or polygon is convex if all of its interior angles are less than 180°. It is concave if one or more interior angles are greater than 180°. A convex pentagon is usually a regular pentagon.

## What are some examples of pentagon shapes?

• The world-famous United States Department of Defense building in Washington, D.C. (The Pentagon building)
• A baseball field's home plate.
• A soccer ball has pentagonal sections.

## What is the sum of all pentagon angles?

The sum of a polygon's interior angles is 180x(n-2)°, where n is the number of sides.

Angle measurement in a Regular Polygon = 180x(n-2) / n, where n is the number of sides.

## What is the pentagon formula?

The basic formula for calculating the area of a pentagon is Area = 5/2sh, where s is the length of the pentagon’s side, and h is the apothem of a pentagon.

A pentagon's apothem is a line segment connecting the pentagon's centre to one of its sides. The apothem is parallel to the side. Every regular polygon has an apothem. It is the line drawn from the polygon's centre that is perpendicular to one of its sides. There are n apothems for a polygon with n sides.

## How is the sum of the pentagon's angles calculated out to be 540°?

To find the sum of interior angles of a pentagon, for example, we will use the formula: S=( n-2)x180°; here, n = 5. As a result, (5-2)x180° = 3x180° = 540°.

## Is there symmetry in a pentagon?

It has four sides and four symmetry lines. A regular pentagon has 5 sides and 5 symmetry lines. In a regular polygon, the number of lines of symmetry equals the number of sides.