A pentagon is a geometrical shape, which has 5 sides and five angles. Here, “Penta” denotes five and “gon” denotes angle. The pentagon is one of the species of polygons. The sum of every the inner angles because that a continual pentagon is 540 degrees.

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In Geometry, we study around different varieties of shapes. The two-dimensional form that is created of directly lines and also interior angle is well-known as a polygon. The examples of polygons are:

Triangle (three-sided polygon)Quadrilateral (four-sided polygon)Pentagon (five-sided polygon)Hexagon (six-sided polygon)Heptagon (seven-sided polygon)Octagon (eight-sided polygon) and also so on.

In this article, you have the right to learn around the five-sided polygon called “pentagon” with proper definition, shape, sides, properties together with its perimeter and area of a pentagon formula in detail.

Pentagon Definition

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A pentagon is a polygon with 5 sides and 5 angles. Words “pentagon” is comprised of 2 words, namely Penta and also Gonia, which way five angles. Every the political parties of a pentagon satisfy with each other end to finish to kind a shape. Therefore,

The variety of sides that a pentagon = 5

Pentagon shape

Like other polygons such together triangle, quadrilaterals, square, rectangle, etc., the pentagon is also a polygon that consists of five sides and also five angles.

Depending top top the sides, angles, and also vertices, there are different species of pentagon shapes, together as

Regular and also Irregular pentagonConvex and also Concave pentagon

Regular and Irregular Pentagon

If a pentagon is regular, then every the sides room equal in length, and also five angles room of same measures. If the pentagon does not have equal next length and angle measure, then it is recognized as an irregular pentagon.

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Regular Pentagon

As characterized above, a regular pentagon has five congruent sides. Thus, we have the right to easily uncover the perimeter of this form of pentagon. This deserve to be observed from the below given figure.

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Here, every the five sides are equal therefore the perimeter that a constant pentagon is five times the length of any kind of one that its sides.

Also, we can divide a consistent pentagon right into five similar triangles as shown below.

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Thus, we can say that the area that a consistent pentagon is same to the 5 times area the a triangle with sides the very same as the pentagon.

Convex and also Concave Pentagon

If all the vertices the a pentagon room pointing outwards, it is recognized as a convex pentagon. If a pentagon has at least one peak pointing inside, then the pentagon is well-known as a concave pentagon.

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Pentagon Properties

Some properties of the pentagon room as follows:

In the pentagon, the sum of the interior angles is equal to 540°.If every the sides room equal and all the angles space of equal measure, then it is a continuous pentagon. Otherwise, that is irregular.In the continual pentagon, each internal angle steps 108°, and each exterior angle steps 72°.An it is provided pentagon has 5 equal sides.The amount of the interior angles of a rectangular pentagon is 540°.

Area of a Pentagon

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For a consistent pentagon with side and also apothem length, climate the formula to uncover the area of a pentagon is provided as

Area of a Pentagon, A = (5/2) ×Side length ×Apothem square units

If just the side length of a pentagon is given, then

Area = 5s2 / (4 tan 36°) Square units

If only the radius of a pentagon is given, then

Area =(5/2)r2 sin 72° Square units

Perimeter of Pentagon

Since all the sides “a” that a consistent pentagon are of same measure, then the perimeter or one of a pentagon is composed as,

The perimeter of a pentagon, p = 5a units

Pentagon fixed problem

Question: Find the area and perimeter of a constant pentagon whose next is 5 cm and apothem size is 6 cm.

Solution:

Given:

The side of a pentagon, a = 5 cm

Apothem size = 6 cm

We know that

The area the a pentagon, A = (5/2) ×Side length ×Apothem square units

Substitute next = 5 cm, Apothem = 6 centimeter in formula,

A = (5/2) × 5 × 6

A = 5 × 5 × 3

A = 75

Therefore, the area of a pentagon is 75 cm2

The perimeter of a pentagon, p = 5a units

P = 5(5)

P = 25 cm

Hence, the perimeter the a pentagon is 25 cm.Based top top the properties of pentagons, there are other species of pentagons that exist in geometry. Lock are:

1. It is provided pentagon

A polygon with five sides that equal size is called an it is provided pentagon. However, all the 5 internal angle of a pentagon deserve to take a range of to adjust of values. They are thus enabling it to kind a household of pentagons. Therefore, the continuous pentagon is distinctive up come similarity. Since it is an equilateral and also equiangular (since its 5 angles room equal) pentagon.

2. Cyclic pentagon

If every the vertices that a pentagon lie on the one of a circle, then it is referred to as a cyclic pentagon. The consistent pentagon is the finest example of a cyclic pentagon. The area of a cyclic pentagon have the right to be stood for as one 4th the square source of among the roots of a septic equation. Here, the coefficients of the equation are functions of the sides of the pentagon. This uses to both regular and irregular pentagons.

Line of the opposite of a Pentagon:

When coming to the line symmetry, every polygon has a certain number of lines of symmetry. Because that example, a square has actually 4 currently of symmetry. In the same way, a regular pentagon has actually 5 currently of symmetry.

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