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°.
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.
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).
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.
Every interior angle of a regular pentagon measures 108°.
When all angles and sides of a polygon are equal, we say it to be regular (otherwise, it is irregular).
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.
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.
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.
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°.
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.