Diagonal of Pentagon given Circumradius Calculator

✖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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✖Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.ⓘ Diagonal of Pentagon given Circumradius [d]

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Diagonal of Pentagon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Diagonal of Pentagon - (Measured in Meter) - Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.
Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Pentagon: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = r_c/(sqrt((5-sqrt(5))/10)) --> 9/(sqrt((5-sqrt(5))/10))

Evaluating ... ...

d = 17.1190172933128

STEP 3: Convert Result to Output's Unit

17.1190172933128 Meter --> No Conversion Required

FINAL ANSWER

17.1190172933128 ≈ 17.11902 Meter <-- Diagonal of Pentagon

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< Diagonal of Pentagon Calculators

Diagonal of Pentagon given Area

LaTeX Go Diagonal of Pentagon = (1+sqrt(5))*sqrt(Area of Pentagon/sqrt(25+(10*sqrt(5))))

Diagonal of Pentagon given Circumradius

LaTeX Go Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10))

Diagonal of Pentagon

LaTeX Go Diagonal of Pentagon = (1+sqrt(5))*Edge Length of Pentagon/2

Diagonal of Pentagon given Perimeter

LaTeX Go Diagonal of Pentagon = (1+sqrt(5))*Perimeter of Pentagon/10

Diagonal of Pentagon given Circumradius Formula

LaTeX Go

Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10))
d = r_c/(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 Diagonal of Pentagon given Circumradius?

Diagonal of Pentagon given Circumradius calculator uses Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10)) to calculate the Diagonal of Pentagon, Diagonal of Pentagon given Circumradius is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using circumradius. Diagonal of Pentagon is denoted by d symbol.

How to calculate Diagonal of Pentagon given Circumradius using this online calculator? To use this online calculator for Diagonal of Pentagon given Circumradius, enter Circumradius of Pentagon (r_c) and hit the calculate button. Here is how the Diagonal of Pentagon given Circumradius calculation can be explained with given input values -> 17.11902 = 9/(sqrt((5-sqrt(5))/10)).

FAQ

What is Diagonal of Pentagon given Circumradius?

Diagonal of Pentagon given Circumradius is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using circumradius and is represented as d = r_c/(sqrt((5-sqrt(5))/10)) or Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10)). The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

How to calculate Diagonal of Pentagon given Circumradius?

Diagonal of Pentagon given Circumradius is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using circumradius is calculated using Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10)). To calculate Diagonal of Pentagon given Circumradius, you need Circumradius of Pentagon (r_c). With our tool, you need to enter the respective value for Circumradius 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 Diagonal of Pentagon?

In this formula, Diagonal of Pentagon uses Circumradius of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Diagonal of Pentagon = (1+sqrt(5))*Edge Length of Pentagon/2
Diagonal of Pentagon = (1+sqrt(5))*sqrt(Area of Pentagon/sqrt(25+(10*sqrt(5))))
Diagonal of Pentagon = (1+sqrt(5))*Perimeter of Pentagon/10

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