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Circumradius of Pentagon given Diagonal Formula

GoCircumradius of Pentagon given Edge Length using Central Angle Formula

GoCircumradius of Pentagon given Inradius Formula

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

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

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

Circumradius of Pentagon given Diagonal Example

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

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

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

8.4117 = 16 \cdot \sqrt{\frac{5 - \sqrt{5}}{10}}

8.4117m = 16m \cdot \sqrt{\frac{5 - \sqrt{5}}{10}}

8.4117 = 16 \cdot \sqrt{\frac{5 - \sqrt{5}}{10}}

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Circumradius of Pentagon given Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = 16m \cdot \sqrt{\frac{5 - \sqrt{5}}{10}}

Next Step Prepare to Evaluate

∴

r c = 16 \cdot \sqrt{\frac{5 - \sqrt{5}}{10}}

Next Step Evaluate

∴

r c = 8.41169779390614m

LAST Step Rounding Answer

∴

r c = 8.4117m

Circumradius of Pentagon given Diagonal Formula Elements

Variables

Functions

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

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

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 Circumradius of Pentagon

Go Circumradius of Pentagon given Edge Length using Central Angle

r c = \frac{l e}{2 \cdot \sin (\frac{π}{5})}

Go Circumradius of Pentagon given Inradius

r c = \frac{r i}{\frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}}

Go Circumradius of Pentagon

r c = \frac{l e}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

Go Circumradius of Pentagon given Inradius using Central Angle

r c = \frac{r i}{\cos (\frac{π}{5})}

How to Evaluate Circumradius of Pentagon given Diagonal?

Circumradius of Pentagon given Diagonal evaluator uses Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10) to evaluate 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 r_c symbol.

How to evaluate Circumradius of Pentagon given Diagonal using this online evaluator? To use this online evaluator for Circumradius of Pentagon given Diagonal, enter Diagonal of Pentagon (d) and hit the calculate button.

FAQs on Circumradius of Pentagon given Diagonal

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

The formula of Circumradius of Pentagon given Diagonal is expressed as Circumradius of Pentagon = Diagonal of Pentagon*sqrt((5-sqrt(5))/10). Here is an example- 8.411698 = 16*sqrt((5-sqrt(5))/10).

How to calculate Circumradius of Pentagon given Diagonal?

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

What are the other ways to Calculate Circumradius of Pentagon?

Here are the different ways to Calculate Circumradius of Pentagon-

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)))

Can the Circumradius of Pentagon given Diagonal be negative?

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

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

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

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