Circumradius of Pentagon Calculator

✖The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.ⓘ Edge Length of Pentagon [l_e]

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

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Circumradius of Pentagon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
r_c = l_e/10*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.
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

r_c = l_e/10*sqrt(50+(10*sqrt(5))) --> 10/10*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 00.006 seconds)

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Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< Circumradius of Pentagon Calculators

Circumradius of Pentagon given Inradius

LaTeX Go Circumradius of Pentagon = (Inradius of Pentagon)/(sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5))))

Circumradius of Pentagon

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

Circumradius of Pentagon given Edge Length using Central Angle

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

Circumradius of Pentagon given Inradius using Central Angle

LaTeX Go Circumradius of Pentagon = Inradius of Pentagon/(cos(pi/5))

< Radius of Pentagon Calculators

Circumradius of Pentagon given Edge Length using Interior Angle

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

Circumradius of Pentagon

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

Circumradius of Pentagon given Edge Length using Central Angle

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

Circumradius of Pentagon given Height and Inradius

LaTeX Go Circumradius of Pentagon = Height of Pentagon-Inradius of Pentagon

Circumradius of Pentagon Formula

LaTeX Go

Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
r_c = l_e/10*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?

Circumradius of Pentagon calculator uses Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5))) to calculate the Circumradius of Pentagon, Circumradius of Pentagon is defined as the line connecting the center and a point on circumcircle of Pentagon. Circumradius of Pentagon is denoted by r_c symbol.

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

FAQ

What is Circumradius of Pentagon?

Circumradius of Pentagon is defined as the line connecting the center and a point on circumcircle of Pentagon and is represented as r_c = l_e/10*sqrt(50+(10*sqrt(5))) or Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5))). The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

How to calculate Circumradius of Pentagon?

Circumradius of Pentagon is defined as the line connecting the center and a point on circumcircle of Pentagon is calculated using Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5))). To calculate Circumradius of Pentagon, you need Edge Length of Pentagon (l_e). 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 3 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 = Inradius of Pentagon/(cos(pi/5))

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