Types of Pentagon

Author: nitin.p070

A pentagon is a closed two dimensional figure that is the union of line segments in a plane. A pentagon has the five sides and five angles. The internal angles in a simple pentagon total 540°. A pentagram is an example of a self-intersecting pentagon. A regular pentagon has five Edges and five vertices. Internal angle of a regular pentagon is 108 degree. There are two types of pentagons : concave pentagon and convex pentagon.

In geometry an equilateral pentagon is a polygon with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique, because it is equilateral and moreover its five angles are equal.
Four intersecting equal circles arranged in a closed chain are sufficient to determine an equilateral pentagon. Each circle's center is one of four vertices of the pentagon. The remain vertex is determined by the intersection of the first and the last circle of the chain.

It is possible to describe any equilateral pentagon with only two angles a and ß with a = ß provided the fourth angle (d) is the smallest of the rest of the angles. Thus the general equilateral pentagon can be regarded as a bivariate function f(\alpha,\beta) where the rest of the angles can be obtained by using trigonometric relations. The equilateral pentagon described in this manner will be unique up to a rotation in the plane.

Types of Pentagon : Concave and Convex Pentagon:

Concave pentagon:

It is a five sided polygon. At least one interior angle is greater than 180 degrees.

This causes some of the vertices of the pentagon to points towards the center.

An alternate definition exists a line that will cut the polygon in 4 or more places.

The twelve concave pentagons can be get together to make a concave dodecahedron.

Convex pentagon:

It is a shape with 180degrees or less.

The regular pentagon is the example of the convex pentagon.

Let us see regular pentagon in detail.

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Types of Pentagon : Regular Pentagon

A shape with five equal sides and five equal angles are called as Regular Pentagon.

Properties of Regular Pentagon:

• It has five equal sides
• It has five equal angles
• It has five lines of symmetry

Angle of a Regular pentagon:

Exterior angle of any polygon is 360° and hence the exterior angle of a regular pentagon is 360°.

Regular pentagon has five sides so each exterior angle measures (360/5) = 72°.

Interior angle of a polygon is calculated by using the formula,
n - 2 (180)

Where n =number of sides.

Where n =number of sides.

Here for pentagon interior angle = (5 - 2) 180 = 540°.

For regular pentagon each side interior angle = 540 / 5 = 108°.

Area of any regular polygon is:

A = 5t2 tan (54) / 4

Derivation of the diagonal length formula:

D = T * (1+v5) / 2

Article Source: http://www.articlesbase.com/online-education-articles/types-of-pentagon-6278397.html

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