## Circumradius of Pentagon given Edge Length using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
rc = (le*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
cos - Trigonometric cosine function, cos(Angle)
Variables Used
Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.
Edge Length of Pentagon - (Measured in Meter) - The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Pentagon: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (le*(1/2-cos(3/5*pi)))/(sin(3/5*pi)) --> (10*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
Evaluating ... ...
rc = 8.5065080835204
STEP 3: Convert Result to Output's Unit
8.5065080835204 Meter --> No Conversion Required
8.5065080835204 8.506508 Meter <-- Circumradius of Pentagon
(Calculation completed in 00.004 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 16 Circumradius of Pentagon Calculators

Circumradius of Pentagon = sqrt(50+(10*sqrt(5)))/10*sqrt((4*Area of Pentagon)/sqrt(25+(10*sqrt(5))))
Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5)))))
Circumradius of Pentagon given Edge Length using Interior Angle
Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
Circumradius of Pentagon = Width of Pentagon*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5)))
Circumradius of Pentagon given Area using Central Angle
Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5))
Circumradius of Pentagon given Area using Interior Angle
Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi)))
Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5)))
Circumradius of Pentagon given Edge Length using Central Angle
Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))
Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10)
Circumradius of Pentagon given Height using Interior Angle
Circumradius of Pentagon = Height of Pentagon/(3/2-cos(3/5*pi))
Circumradius of Pentagon given Height using Central Angle
Circumradius of Pentagon = (Height of Pentagon)/(1+cos(pi/5))

## < 9 Radius of Pentagon Calculators

Circumradius of Pentagon given Edge Length using Interior Angle
Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
Inradius of Pentagon given Edge Length using Interior Angle
Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi)
Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5)))
Circumradius of Pentagon given Edge Length using Central Angle
Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))
Inradius of Pentagon given Edge Length using Central Angle
Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))
Inradius of Pentagon given Area and Edge Length
Inradius of Pentagon = (2*Area of Pentagon)/(5*Edge Length of Pentagon)

## Circumradius of Pentagon given Edge Length using Interior Angle Formula

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

## 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 Circumradius of Pentagon given Edge Length using Interior Angle?

Circumradius of Pentagon given Edge Length using Interior Angle calculator uses Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi)) to calculate the Circumradius of Pentagon, The Circumradius of Pentagon given Edge Length using Interior Angle is defined as the length of the line joining the center of the Pentagon to point on the circumcircle of the Pentagon, calculated using edge length and interior angle. Circumradius of Pentagon is denoted by rc symbol.

How to calculate Circumradius of Pentagon given Edge Length using Interior Angle using this online calculator? To use this online calculator for Circumradius of Pentagon given Edge Length using Interior Angle, enter Edge Length of Pentagon (le) and hit the calculate button. Here is how the Circumradius of Pentagon given Edge Length using Interior Angle calculation can be explained with given input values -> 8.506508 = (10*(1/2-cos(3/5*pi)))/(sin(3/5*pi)).

### FAQ

What is Circumradius of Pentagon given Edge Length using Interior Angle?
The Circumradius of Pentagon given Edge Length using Interior Angle is defined as the length of the line joining the center of the Pentagon to point on the circumcircle of the Pentagon, calculated using edge length and interior angle and is represented as rc = (le*(1/2-cos(3/5*pi)))/(sin(3/5*pi)) or Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi)). The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.
How to calculate Circumradius of Pentagon given Edge Length using Interior Angle?
The Circumradius of Pentagon given Edge Length using Interior Angle is defined as the length of the line joining the center of the Pentagon to point on the circumcircle of the Pentagon, calculated using edge length and interior angle is calculated using Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi)). To calculate Circumradius of Pentagon given Edge Length using Interior Angle, you need Edge Length of Pentagon (le). With our tool, you need to enter the respective value for Edge Length 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 Circumradius of Pentagon?
In this formula, Circumradius of Pentagon uses Edge Length of Pentagon. We can use 18 other way(s) to calculate the same, which is/are as follows -
• Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))
• Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
• Circumradius of Pentagon = (Height of Pentagon)/(1+cos(pi/5))
• Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5)))))
• Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10)
• Circumradius of Pentagon = sqrt((Area of Pentagon*2)/(sin(2*pi/5)*5))
• Circumradius of Pentagon = sqrt(50+(10*sqrt(5)))/10*sqrt((4*Area of Pentagon)/sqrt(25+(10*sqrt(5))))
• Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5)))
• Circumradius of Pentagon = Width of Pentagon*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5)))
• Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi))) 