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Circumradius of Pentagon given Height 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 = \frac{h}{5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}})}

r_c - Circumradius of Pentagon?h - Height of Pentagon?

Circumradius of Pentagon given Height Example

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

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

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

8.2918 = \frac{15}{5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}})}

8.2918m = \frac{15m}{5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}})}

8.2918 = \frac{15}{5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}})}

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Circumradius of Pentagon given Height Solution

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

FIRST Step Consider the formula

r c = \frac{h}{5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}})}

Next Step Substitute values of Variables

∴

r c = \frac{15m}{5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}})}

Next Step Prepare to Evaluate

∴

r c = \frac{15}{5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}})}

Next Step Evaluate

∴

r c = 8.29179606750063m

LAST Step Rounding Answer

∴

r c = 8.2918m

Circumradius of Pentagon given Height 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

Height of Pentagon

Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height 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 Height?

Circumradius of Pentagon given Height evaluator uses Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))) to evaluate the Circumradius of Pentagon, Circumradius of Pentagon given Height is defined as the line joining the center and a point on a circumcircle of the Pentagon, calculated using height. Circumradius of Pentagon is denoted by r_c symbol.

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

FAQs on Circumradius of Pentagon given Height

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

The formula of Circumradius of Pentagon given Height is expressed as Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))). Here is an example- 8.291796 = 15/(5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))).

How to calculate Circumradius of Pentagon given Height?

With Height of Pentagon (h) we can find Circumradius of Pentagon given Height using the formula - Circumradius of Pentagon = Height of Pentagon/(5*(sqrt(5+(2*sqrt(5)))/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=(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 Height be negative?

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

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

Circumradius of Pentagon given Height 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 Height can be measured.

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