Edge Length of Pentagon given Inradius using Interior Angle Calculator

✖The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.ⓘ Edge Length of Pentagon given Inradius using Interior Angle [l_e]

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Formula

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Edge Length of Pentagon given Inradius using Interior Angle

Formula

`"l"_{"e"} = "r"_{"i"}*sin(3/5*pi)/(1/2-cos(3/5*pi))^2`

Example

`"10.1716m"="7m"*sin(3/5*pi)/(1/2-cos(3/5*pi))^2`

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Edge Length of Pentagon given Inradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
l_e = r_i*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
This formula uses 1 Constants, 2 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Edge Length of Pentagon - (Measured in Meter) - The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.
Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = r_i*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 --> 7*sin(3/5*pi)/(1/2-cos(3/5*pi))^2

Evaluating ... ...

l_e = 10.1715953920751

STEP 3: Convert Result to Output's Unit

10.1715953920751 Meter --> No Conversion Required

FINAL ANSWER

10.1715953920751 ≈ 10.1716 Meter <-- Edge Length of Pentagon

(Calculation completed in 00.004 seconds)

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Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 16 Edge Length of Pentagon Calculators

Edge Length of Pentagon given Height using Interior Angle

Go Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))

Edge Length of Pentagon given Area using Interior Angle

Go Edge Length of Pentagon = sqrt(((2*sin(3/5*pi))*Area of Pentagon)/(5*(1/2-cos(3/5*pi))^2))

Edge Length of Pentagon given Circumradius using Interior Angle

Go Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))

Edge Length of Pentagon given Inradius using Interior Angle

Go Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2

Edge Length of Pentagon given Height using Central Angle

Go Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))

Edge Length of Pentagon given Area

Go Edge Length of Pentagon = sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))

Edge Length of Pentagon given Area using Central Angle

Go Edge Length of Pentagon = sqrt((Area of Pentagon*4*tan(pi/5))/5)

Edge Length of Pentagon given Circumradius

Go Edge Length of Pentagon = Circumradius of Pentagon*10/sqrt(50+(10*sqrt(5)))

Edge Length of Pentagon given Inradius

Go Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))

Edge Length of Pentagon given Height

Go Edge Length of Pentagon = Height of Pentagon*2/sqrt(5+(2*sqrt(5)))

Edge Length of Pentagon given Circumradius using Central Angle

Go Edge Length of Pentagon = 2*Circumradius of Pentagon*sin(pi/5)

Edge Length of Pentagon given Inradius using Central Angle

Go Edge Length of Pentagon = 2*Inradius of Pentagon*tan(pi/5)

Edge Length of Pentagon given Area and Inradius

Go Edge Length of Pentagon = (2*Area of Pentagon)/(5*Inradius of Pentagon)

Edge Length of Pentagon given Diagonal

Go Edge Length of Pentagon = Diagonal of Pentagon*2/(1+sqrt(5))

Edge Length of Pentagon given Width

Go Edge Length of Pentagon = Width of Pentagon*2/(1+sqrt(5))

Edge Length of Pentagon given Perimeter

Go Edge Length of Pentagon = Perimeter of Pentagon/5

Edge Length of Pentagon given Inradius using Interior Angle Formula

Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
l_e = r_i*sin(3/5*pi)/(1/2-cos(3/5*pi))^2

What is Pentagon?

A Pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape. In geometry, it is considered as a five-sided polygon with five straight sides and five interior angles, which add up to 540°. Pentagons can be simple or self-intersecting. A simple pentagon (5-gon) must have five straight sides that meet to create five vertices but do not intersect with each other. A self-intersecting regular pentagon is called a pentagram.

How to Calculate Edge Length of Pentagon given Inradius using Interior Angle?

Edge Length of Pentagon given Inradius using Interior Angle calculator uses Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 to calculate the Edge Length of Pentagon, The Edge Length of Pentagon given Inradius using Interior Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using inradius and interior angle. Edge Length of Pentagon is denoted by l_e symbol.

How to calculate Edge Length of Pentagon given Inradius using Interior Angle using this online calculator? To use this online calculator for Edge Length of Pentagon given Inradius using Interior Angle, enter Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Edge Length of Pentagon given Inradius using Interior Angle calculation can be explained with given input values -> 10.1716 = 7*sin(3/5*pi)/(1/2-cos(3/5*pi))^2.

FAQ

What is Edge Length of Pentagon given Inradius using Interior Angle?

The Edge Length of Pentagon given Inradius using Interior Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using inradius and interior angle and is represented as l_e = r_i*sin(3/5*pi)/(1/2-cos(3/5*pi))^2 or Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2. The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

How to calculate Edge Length of Pentagon given Inradius using Interior Angle?

The Edge Length of Pentagon given Inradius using Interior Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using inradius and interior angle is calculated using Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2. To calculate Edge Length of Pentagon given Inradius using Interior Angle, you need Inradius of Pentagon (r_i). With our tool, you need to enter the respective value for Inradius of Pentagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Edge Length of Pentagon?

In this formula, Edge Length of Pentagon uses Inradius of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -

Edge Length of Pentagon = (2*Area of Pentagon)/(5*Inradius of Pentagon)
Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))
Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))
Edge Length of Pentagon = sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))
Edge Length of Pentagon = Height of Pentagon*2/sqrt(5+(2*sqrt(5)))
Edge Length of Pentagon = Circumradius of Pentagon*10/sqrt(50+(10*sqrt(5)))
Edge Length of Pentagon = Width of Pentagon*2/(1+sqrt(5))
Edge Length of Pentagon = 2*Circumradius of Pentagon*sin(pi/5)
Edge Length of Pentagon = 2*Inradius of Pentagon*tan(pi/5)
Edge Length of Pentagon = sqrt((Area of Pentagon*4*tan(pi/5))/5)
Edge Length of Pentagon = Perimeter of Pentagon/5
Edge Length of Pentagon = Diagonal of Pentagon*2/(1+sqrt(5))
Edge Length of Pentagon = sqrt(((2*sin(3/5*pi))*Area of Pentagon)/(5*(1/2-cos(3/5*pi))^2))
Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))
Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))

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