Formula For Perimeter Of Pentagon

Perimeter of Pentagon

The perimeter of a pentagon is the sum of all its sides. A pentagon is a polygon with v sides, five vertices, and five interior angles that add up to 540°. Pentagons can be regular or irregular depending upon the length of the sides. Permit us study more almost the perimeter of pentagon in this article.

1.	What is the Perimeter of a Pentagon?
2.	Perimeter of Pentagon Formula
3.	Perimeter of Pentagon with Radius
iv.	FAQs on Perimeter of Pentagon

What is the Perimeter of a Pentagon?

The perimeter of a pentagon is the total measure of its purlieus and it is calculated by calculation the length of all its sides. Since a pentagon is a five-sided polygon, all the five sides tin be added to find its perimeter. The perimeter of a pentagon is expressed in linear units similar inches, yards, centimeters, and then on.

Regular and Irregular Pentagon

A regular pentagon is a pentagon in which all v sides are of equal length and all the interior angles are of equal measure. An irregular pentagon is 1 in which the sides are not equal and the angles are non of equal measure.

Properties of a Regular Pentagon

The word 'pentagon' is derived from the Greek word 'Penta' which means '5', and 'gon' which means 'angle'. At that place are some bones properties that assistance u.s. to identify a pentagon. Observe the post-obit regular pentagon to relate to its properties given below.

Perimeter of a Pentagon-regular pentagon

We tin can identify and distinguish a regular pentagon with the aid of the following backdrop:

Pentagon is a polygon with 5 sides.
It has 5 diagonals.
The sum of all the interior angles of a pentagon is 540°
Each interior angle of a regular pentagon is 108°
Each exterior bending of a regular pentagon is 72°

Now, let u.s. read nearly the formulas that are used to find the perimeter of a pentagon. The formulas differ co-ordinate to the known dimensions.

Perimeter of Pentagon Formula

We know that the perimeter of a pentagon is the sum of the lengths of all its sides. Now, if information technology is a regular pentagon, it means all v sides are of equal length. Let us consider a regular pentagon of side length 'a'. In this case, the perimeter can exist calculated with the assist of the formula, Perimeter = a + a + a + a + a, which is 5a. Therefore, the basic formula for the perimeter of a regular pentagon is given below.

Perimeter of pentagon = Sum of all its sides

Example 1: Observe the perimeter of a regular pentagon that has a side length of 7 units.

Solution:

The side length (a) of the given pentagon = 7 units.

Using the perimeter of pentagon formula, Perimeter = 5a = five × seven = 35 units.

Example two: Find the perimeter of a pentagon in which the length of the sides are 5 units, four units, vii units, 3 units, and vi units.

Solution:

In gild to find the perimeter of the irregular pentagon, we will add all the five sides, perimeter = 5 + 4 + 7 + three + 6 = 25 units.

Therefore, the perimeter of the pentagon is 25 units.

Perimeter of Pentagon with Radius

The perimeter of a pentagon can be calculated if the radius of the pentagon is given. This is the case when a pentagon is inscribed in a circle as shown below. In such cases, the radius is the line drawn from the heart of the polygon to 1 of its vertices. It is also referred to equally the circumradius. The perimeter of this pentagon can exist calculated once the side length is known with the help of the formula: Side length = 2r × Sin(180/n), where 'r' is the radius and 'n' represents the number of sides. After getting the side length, the perimeter can be easily calculated with the formula, Perimeter = 5a.

Perimeter of pentagon inscribed in a circle

Instance: Find the perimeter of a regular pentagon inscribed in a circumvolve with a radius of 5 units.

Solution: Given, radius = 5 units, number of sides = v

Let us first calculate the side length of the pentagon with the help of the formula: Side length = 2r × Sin(180/n)

On substituting the given values in the formula, nosotros get, Side length = 2r × Sin(180/northward) = Side length = 2 × 5 × Sin(180/five) = ten × Sin(180/5) = 10 × Sin 36 = ten × 0.58779 = 5.8 units. After this, the perimeter of the regular pentagon can exist calculated using the formula, Perimeter = 5a = 5 × 5.8 = 29 units.

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Perimeter of Pentagon Formula Examples

Instance 1: Find the perimeter of a regular pentagon if the length of the side of the pentagon is x units.

Solution: Given side length (a) = 10 units

Using the formula for the perimeter of pentagon, P = 5a ⇒ v × 10 = fifty units
Respond: The perimeter of the pentagon is fifty units.
Example ii: Detect the perimeter of a pentagon that has the following side lengths: three units, 7 units, 8 units, 9 units, and vi units.

Solution: Since the side lengths of the pentagon are different, information technology is an irregular pentagon. The side lengths are given as 3 units, seven units, viii units, 9 units, and 6 units.

Using the formula for the perimeter of pentagon, P = sum of all its sides = 3 + seven + 8 + ix + vi = 33 units.

Respond: Therefore, the perimeter of the pentagon is 33 units.
Example 3: State truthful or false with respect to the perimeter of a pentagon:

a.) The perimeter of a pentagon is the sum of the lengths of all its sides.

b.) If the side of a regular pentagon is vii units, then the perimeter of the pentagon will be 28 units.

Solution:

a.) True, the perimeter of a pentagon is the sum of the lengths of all its sides.

b.) False, if the side of a regular pentagon is 7 units, so the perimeter of the pentagon will be 35 units.

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Practice Questions on Perimeter of Pentagon

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FAQs on Perimeter of Pentagon

What is the Perimeter of a Pentagon?

The perimeter of a pentagon is the total measure of its purlieus and information technology is calculated by adding the length of all its sides. If information technology is a regular pentagon the formula to find its perimeter is, P = 5a, where 'a' is the length of the side. In the instance of an irregular pentagon, where all the sides are of different lengths, the formula is, P = sum of all its sides. The perimeter of a pentagon is expressed in linear units similar inches, yards, centimeters, and so on.

How to Find the Perimeter of a Pentagon?

The perimeter of a pentagon can exist calculated with the help of the basic formula, Perimeter of pentagon = sum of its sides. Sometimes, the side length of a regular pentagon is not known and other dimensions like the radius are given. In such cases, the side length is calculated with the assistance of the formula, Side length = 2r × Sin(180/n), where 'r' is the radius and 'n' represents the number of sides. After getting the side length, the perimeter can be calculated with the formula, Perimeter = 5a.

What is the Formula of the Perimeter of a Pentagon?

The basic formula that is used to discover the perimeter of pentagon is, P = sum of its sides. If it is a regular pentagon, the formula can exist written every bit, P = 5a, where 'a' is the length of its side. If information technology is an irregular pentagon, all its sides tin be added to become the perimeter.

How to Find the Perimeter of a Pentagon with Radius?

The perimeter of pentagon can be calculated if the radius of the pentagon is given. This is the case when a pentagon is inscribed in a circumvolve. In such cases, the radius is the line drawn from the centre of the polygon to one of its vertices. It is also referred to as the circumradius. The perimeter of this pentagon can be calculated after finding the side length with the aid of the formula: Side length = 2r × Sin(180/n), where 'r' is the radius and 'north' represents the number of sides. Afterward getting the side length, the perimeter can be calculated with the formula, Perimeter = 5a.

How to Find the Perimeter of a Pentagon with Apothem?

The perimeter of a pentagon can exist calculated if the apothem of the pentagon is given. Apothem is a perpendicular line segment fatigued from the heart of the pentagon to the side of the pentagon. If the apothem of a pentagon is given, the side length tin can be calculated with the formula, Side length = 2 × apothem length × tan(180/due north), where 'n' represents the number of sides. After getting the side length, the perimeter of the pentagon tin can exist calculated with the formula, P = 5a.

How to Find the Perimeter of a Pentagon with Area?

The perimeter of a regular pentagon can be calculated if the area and the apothem of a pentagon is given. The expanse and the apothem can help to detect the side length of the pentagon with the help of the formula, Area = v/two × side length × apothem. After substituting the values in the formula the side length tin be calculated. Once the side length is known, the perimeter of the pentagon tin can be institute with the formula, Perimeter = 5 × side length

How to Observe the Perimeter of a Pentagon with Different Sides?

If the sides of a pentagon are not equal in measure, it is termed as an irregular pentagon. In this case, the perimeter of the pentagon can be calculated by using the basic formula, Perimeter = sum of its sides. For example, the different sides of a pentagon are of the lengths, 3 units, 4 units, 2 units, 5 units and 6 units, the perimeter of the pentagon volition exist, P = iii + iv + 2 + 5 + 6 = 20 units.

How to Find the Perimeter of a Regular Pentagon?

If all the sides of a pentagon are of equal length, it is known every bit a regular pentagon. In this case, the perimeter of the pentagon tin can be calculated with the help of the formula, Perimeter = 5 × side length. For instance, if ane side of a regular pentagon is 8 units, its perimeter will be, P = v × 8 = 40 units.