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Circumradius of Pentagon given Width 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 = w \cdot \frac{\sqrt{50 + (10 \cdot \sqrt{5})}}{5 \cdot (1 + \sqrt{5})}

r_c - Circumradius of Pentagon?w - Width of Pentagon?

Circumradius of Pentagon given Width Example

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

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

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

8.4117 = 16 \cdot \frac{\sqrt{50 + (10 \cdot \sqrt{5})}}{5 \cdot (1 + \sqrt{5})}

8.4117m = 16m \cdot \frac{\sqrt{50 + (10 \cdot \sqrt{5})}}{5 \cdot (1 + \sqrt{5})}

8.4117 = 16 \cdot \frac{\sqrt{50 + (10 \cdot \sqrt{5})}}{5 \cdot (1 + \sqrt{5})}

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Circumradius of Pentagon given Width Solution

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

FIRST Step Consider the formula

r c = w \cdot \frac{\sqrt{50 + (10 \cdot \sqrt{5})}}{5 \cdot (1 + \sqrt{5})}

Next Step Substitute values of Variables

∴

r c = 16m \cdot \frac{\sqrt{50 + (10 \cdot \sqrt{5})}}{5 \cdot (1 + \sqrt{5})}

Next Step Prepare to Evaluate

∴

r c = 16 \cdot \frac{\sqrt{50 + (10 \cdot \sqrt{5})}}{5 \cdot (1 + \sqrt{5})}

Next Step Evaluate

∴

r c = 8.41169779390614m

LAST Step Rounding Answer

∴

r c = 8.4117m

Circumradius of Pentagon given Width 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

Width of Pentagon

Width of Pentagon is the measurement or extent of horizontal distance from left to right of the Pentagon.

Symbol: w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width 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 Width?

Circumradius of Pentagon given Width evaluator uses Circumradius of Pentagon = Width of Pentagon*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5))) to evaluate the Circumradius of Pentagon, The Circumradius of Pentagon given Width formula is defined as the line joining the center and a point on the circumcircle of the pentagon, calculated using width. Circumradius of Pentagon is denoted by r_c symbol.

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

FAQs on Circumradius of Pentagon given Width

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

The formula of Circumradius of Pentagon given Width is expressed as Circumradius of Pentagon = Width of Pentagon*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5))). Here is an example- 8.411698 = 16*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5))).

How to calculate Circumradius of Pentagon given Width?

With Width of Pentagon (w) we can find Circumradius of Pentagon given Width using the formula - Circumradius of Pentagon = Width of Pentagon*sqrt(50+(10*sqrt(5)))/(5*(1+sqrt(5))). 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 Width be negative?

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

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

Circumradius of Pentagon given Width 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 Width can be measured.

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