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Diagonal of Pentagon given Circumradius Formula

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Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon. Check FAQs

d = \frac{r c}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

d - Diagonal of Pentagon?r_c - Circumradius of Pentagon?

Diagonal of Pentagon given Circumradius Example

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Here is how the Diagonal of Pentagon given Circumradius equation looks like with Values.

Here is how the Diagonal of Pentagon given Circumradius equation looks like with Units.

Here is how the Diagonal of Pentagon given Circumradius equation looks like.

17.119 = \frac{9}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

17.119m = \frac{9m}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

17.119 = \frac{9}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

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Diagonal of Pentagon given Circumradius Solution

Follow our step by step solution on how to calculate Diagonal of Pentagon given Circumradius?

FIRST Step Consider the formula

d = \frac{r c}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

Next Step Substitute values of Variables

∴

d = \frac{9m}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

Next Step Prepare to Evaluate

∴

d = \frac{9}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

Next Step Evaluate

∴

d = 17.1190172933128m

LAST Step Rounding Answer

∴

d = 17.119m

Diagonal of Pentagon given Circumradius Formula Elements

Variables

Functions

Diagonal of Pentagon

Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Pentagon

Circumradius of Pentagon

The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Pentagon

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.

Syntax: sqrt(Number)

Other Formulas to find Diagonal of Pentagon

Go Diagonal of Pentagon

d = (1 + \sqrt{5}) \cdot \frac{l e}{2}

Go Diagonal of Pentagon given Area

d = (1 + \sqrt{5}) \cdot \sqrt{\frac{A}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Diagonal of Pentagon given Perimeter

d = (1 + \sqrt{5}) \cdot \frac{P}{10}

Go Diagonal of Pentagon given Height

d = (1 + \sqrt{5}) \cdot \frac{h}{\sqrt{5 + (2 \cdot \sqrt{5})}}

How to Evaluate Diagonal of Pentagon given Circumradius?

Diagonal of Pentagon given Circumradius evaluator uses Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10)) to evaluate 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 evaluate Diagonal of Pentagon given Circumradius using this online evaluator? To use this online evaluator for Diagonal of Pentagon given Circumradius, enter Circumradius of Pentagon (r_c) and hit the calculate button.

FAQs on Diagonal of Pentagon given Circumradius

What is the formula to find Diagonal of Pentagon given Circumradius?

The formula of Diagonal of Pentagon given Circumradius is expressed as Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10)). Here is an example- 17.11902 = 9/(sqrt((5-sqrt(5))/10)).

How to calculate Diagonal of Pentagon given Circumradius?

With Circumradius of Pentagon (r_c) we can find Diagonal of Pentagon given Circumradius using the formula - Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10)). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Diagonal of Pentagon?

Here are the different ways to Calculate Diagonal of Pentagon-

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

Can the Diagonal of Pentagon given Circumradius be negative?

No, the Diagonal of Pentagon given Circumradius, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Pentagon given Circumradius?

Diagonal of Pentagon given Circumradius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diagonal of Pentagon given Circumradius can be measured.

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