Circumradius of Pentagon given Perimeter Calculator

✖The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.ⓘ Circumradius of Pentagon given Perimeter [r_c]

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Circumradius of Pentagon given Perimeter

Formula

`"r"_{"c"} = "P"/50*sqrt(50+(10*sqrt(5)))`

Example

`"8.506508m"="50m"/50*sqrt(50+(10*sqrt(5)))`

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Circumradius of Pentagon given Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5)))
r_c = P/50*sqrt(50+(10*sqrt(5)))
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.
Perimeter of Pentagon - (Measured in Meter) - The Perimeter of Pentagon is the total distance around the edge of the Pentagon.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Pentagon: 50 Meter --> 50 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = P/50*sqrt(50+(10*sqrt(5))) --> 50/50*sqrt(50+(10*sqrt(5)))

Evaluating ... ...

r_c = 8.5065080835204

STEP 3: Convert Result to Output's Unit

8.5065080835204 Meter --> No Conversion Required

FINAL ANSWER

8.5065080835204 ≈ 8.506508 Meter <-- Circumradius of Pentagon

(Calculation completed in 00.004 seconds)

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Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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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 Interior Angle

Go Circumradius of Pentagon = sqrt((2*Area of Pentagon)/(5*sin(3/5*pi)))

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

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 Perimeter Formula

Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5)))
r_c = P/50*sqrt(50+(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 Circumradius of Pentagon given Perimeter?

Circumradius of Pentagon given Perimeter calculator uses Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5))) to calculate the Circumradius of Pentagon, The Circumradius of Pentagon given Perimeter formula is defined as the line connecting the center and a point on circumcircle of Pentagon, calculated using perimeter. Circumradius of Pentagon is denoted by r_c symbol.

How to calculate Circumradius of Pentagon given Perimeter using this online calculator? To use this online calculator for Circumradius of Pentagon given Perimeter, enter Perimeter of Pentagon (P) and hit the calculate button. Here is how the Circumradius of Pentagon given Perimeter calculation can be explained with given input values -> 8.506508 = 50/50*sqrt(50+(10*sqrt(5))).

FAQ

What is Circumradius of Pentagon given Perimeter?

The Circumradius of Pentagon given Perimeter formula is defined as the line connecting the center and a point on circumcircle of Pentagon, calculated using perimeter and is represented as r_c = P/50*sqrt(50+(10*sqrt(5))) or Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5))). The Perimeter of Pentagon is the total distance around the edge of the Pentagon.

How to calculate Circumradius of Pentagon given Perimeter?

The Circumradius of Pentagon given Perimeter formula is defined as the line connecting the center and a point on circumcircle of Pentagon, calculated using perimeter is calculated using Circumradius of Pentagon = Perimeter of Pentagon/50*sqrt(50+(10*sqrt(5))). To calculate Circumradius of Pentagon given Perimeter, you need Perimeter of Pentagon (P). With our tool, you need to enter the respective value for Perimeter 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 Perimeter 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 = 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 = 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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