## Edge Length of Pentagon given Inradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))
le = ri*10/sqrt(25+(10*sqrt(5)))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
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
le = ri*10/sqrt(25+(10*sqrt(5))) --> 7*10/sqrt(25+(10*sqrt(5)))
Evaluating ... ...
le = 10.1715953920751
STEP 3: Convert Result to Output's Unit
10.1715953920751 Meter --> No Conversion Required
10.1715953920751 10.1716 Meter <-- Edge Length of Pentagon
(Calculation completed in 00.004 seconds)
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## Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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## < 16 Edge Length of Pentagon Calculators

Edge Length of Pentagon given Height using Interior Angle
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
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
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
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
Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))
Edge Length of Pentagon given Area
Edge Length of Pentagon = sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))
Edge Length of Pentagon given Area using Central Angle
Edge Length of Pentagon = sqrt((Area of Pentagon*4*tan(pi/5))/5)
Edge Length of Pentagon given Circumradius
Edge Length of Pentagon = Circumradius of Pentagon*10/sqrt(50+(10*sqrt(5)))
Edge Length of Pentagon given Inradius
Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))
Edge Length of Pentagon given Circumradius using Central Angle
Edge Length of Pentagon = 2*Circumradius of Pentagon*sin(pi/5)
Edge Length of Pentagon given Height
Edge Length of Pentagon = Height of Pentagon*2/sqrt(5+(2*sqrt(5)))
Edge Length of Pentagon given Inradius using Central Angle
Edge Length of Pentagon = 2*Inradius of Pentagon*tan(pi/5)
Edge Length of Pentagon given Area and Inradius
Edge Length of Pentagon = (2*Area of Pentagon)/(5*Inradius of Pentagon)
Edge Length of Pentagon given Diagonal
Edge Length of Pentagon = Diagonal of Pentagon*2/(1+sqrt(5))
Edge Length of Pentagon given Width
Edge Length of Pentagon = Width of Pentagon*2/(1+sqrt(5))
Edge Length of Pentagon given Perimeter
Edge Length of Pentagon = Perimeter of Pentagon/5

## Edge Length of Pentagon given Inradius Formula

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

## 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?

Edge Length of Pentagon given Inradius calculator uses Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5))) to calculate the Edge Length of Pentagon, Edge Length of Pentagon given Inradius is defined as the length of the line connecting the two adjacent vertices of the Pentagon, calculated using inradius. Edge Length of Pentagon is denoted by le symbol.

How to calculate Edge Length of Pentagon given Inradius using this online calculator? To use this online calculator for Edge Length of Pentagon given Inradius, enter Inradius of Pentagon (ri) and hit the calculate button. Here is how the Edge Length of Pentagon given Inradius calculation can be explained with given input values -> 10.1716 = 7*10/sqrt(25+(10*sqrt(5))).

### FAQ

What is Edge Length of Pentagon given Inradius?
Edge Length of Pentagon given Inradius is defined as the length of the line connecting the two adjacent vertices of the Pentagon, calculated using inradius and is represented as le = ri*10/sqrt(25+(10*sqrt(5))) or Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5))). 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?
Edge Length of Pentagon given Inradius is defined as the length of the line connecting the two adjacent vertices of the Pentagon, calculated using inradius is calculated using Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5))). To calculate Edge Length of Pentagon given Inradius, you need Inradius of Pentagon (ri). 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 = 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 = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
• Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))) Let Others Know