Circumradius of Pentagon given Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10)
rc = d*sqrt((5-sqrt(5))/10)
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
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.
Diagonal of Pentagon - (Measured in Meter) - Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.
STEP 1: Convert Input(s) to Base Unit
Diagonal of Pentagon: 16 Meter --> 16 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = d*sqrt((5-sqrt(5))/10) --> 16*sqrt((5-sqrt(5))/10)
Evaluating ... ...
rc = 8.41169779390614
STEP 3: Convert Result to Output's Unit
8.41169779390614 Meter --> No Conversion Required
FINAL ANSWER
8.41169779390614 8.411698 Meter <-- Circumradius of Pentagon
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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St Joseph's College (SJC), Bengaluru
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16 Circumradius of Pentagon Calculators

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

Circumradius of Pentagon given Diagonal Formula

Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10)
rc = d*sqrt((5-sqrt(5))/10)

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 Diagonal?

Circumradius of Pentagon given Diagonal calculator uses Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10) to calculate the Circumradius of Pentagon, Circumradius of Pentagon given Diagonal is defined as the line connecting the center and a point on the circumcircle of the Pentagon. Circumradius of Pentagon is denoted by rc symbol.

How to calculate Circumradius of Pentagon given Diagonal using this online calculator? To use this online calculator for Circumradius of Pentagon given Diagonal, enter Diagonal of Pentagon (d) and hit the calculate button. Here is how the Circumradius of Pentagon given Diagonal calculation can be explained with given input values -> 8.411698 = 16*sqrt((5-sqrt(5))/10).

FAQ

What is Circumradius of Pentagon given Diagonal?
Circumradius of Pentagon given Diagonal is defined as the line connecting the center and a point on the circumcircle of the Pentagon and is represented as rc = d*sqrt((5-sqrt(5))/10) or Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10). Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.
How to calculate Circumradius of Pentagon given Diagonal?
Circumradius of Pentagon given Diagonal is defined as the line connecting the center and a point on the circumcircle of the Pentagon is calculated using Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10). To calculate Circumradius of Pentagon given Diagonal, you need Diagonal of Pentagon (d). With our tool, you need to enter the respective value for Diagonal 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 Diagonal of Pentagon. We can use 15 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 = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))
  • Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
  • Circumradius of Pentagon = Inradius of Pentagon/(cos(pi/5))
  • Circumradius of Pentagon = Height of Pentagon-Inradius of Pentagon
  • 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 = 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)))
  • Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
  • Circumradius of Pentagon = Inradius of Pentagon/(1/2-cos(3/5*pi))
  • Circumradius of Pentagon = Height of Pentagon/(3/2-cos(3/5*pi))
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