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Circumradius of Pentagon Formula

GoCircumradius of Pentagon given Edge Length using Central Angle Formula

GoCircumradius of Pentagon given Edge Length using Interior Angle 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 = \frac{l e}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

r_c - Circumradius of Pentagon?l_e - Edge Length of Pentagon?

Circumradius of Pentagon Example

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

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

Here is how the Circumradius of Pentagon equation looks like.

8.5065 = \frac{10}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

8.5065m = \frac{10m}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

8.5065 = \frac{10}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

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Circumradius of Pentagon Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r c = 8.5065080835204m

LAST Step Rounding Answer

∴

r c = 8.5065m

Circumradius of Pentagon 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

Edge Length of Pentagon

The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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 Edge Length using Interior Angle

r c = \frac{l e \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}{\sin (\frac{3}{5} \cdot π)}

Go Circumradius of Pentagon given Height and Inradius

r c = h - r i

Other formulas in Circumradius of Pentagon category

Go Inradius of Pentagon

r i = \frac{l e}{10} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

Go Inradius of Pentagon given Area and Edge Length

r i = \frac{2 \cdot A}{5 \cdot l e}

Go Inradius of Pentagon given Circumradius and Height

r i = h - r c

Go Inradius of Pentagon given Edge Length using Central Angle

r i = \frac{l e}{2 \cdot \tan (\frac{π}{5})}

How to Evaluate Circumradius of Pentagon?

Circumradius of Pentagon evaluator uses Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5))) to evaluate 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 evaluate Circumradius of Pentagon using this online evaluator? To use this online evaluator for Circumradius of Pentagon, enter Edge Length of Pentagon (l_e) and hit the calculate button.

FAQs on Circumradius of Pentagon

What is the formula to find Circumradius of Pentagon?

The formula of Circumradius of Pentagon is expressed as Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5))). Here is an example- 8.506508 = 10/10*sqrt(50+(10*sqrt(5))).

How to calculate Circumradius of Pentagon?

With Edge Length of Pentagon (l_e) we can find Circumradius of Pentagon using the formula - Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*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=(Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))
Circumradius of Pentagon=Height of Pentagon-Inradius of Pentagon

Can the Circumradius of Pentagon be negative?

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

Which unit is used to measure Circumradius of Pentagon?

Circumradius of Pentagon 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 can be measured.

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