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Inradius of Decagon given Circumradius Formula

GoInradius of Decagon Formula

GoInradius of Decagon given Diagonal across Five Sides Formula

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Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon. Check FAQs

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot r c}{1 + \sqrt{5}}

r_i - Inradius of Decagon?r_c - Circumradius of Decagon?

Inradius of Decagon given Circumradius Example

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Here is how the Inradius of Decagon given Circumradius equation looks like with Values.

Here is how the Inradius of Decagon given Circumradius equation looks like with Units.

Here is how the Inradius of Decagon given Circumradius equation looks like.

15.2169 = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

15.2169m = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16m}{1 + \sqrt{5}}

15.2169 = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

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Inradius of Decagon given Circumradius Solution

Follow our step by step solution on how to calculate Inradius of Decagon given Circumradius?

FIRST Step Consider the formula

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot r c}{1 + \sqrt{5}}

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16m}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

Next Step Evaluate

∴

r i = 15.2169042607225m

LAST Step Rounding Answer

∴

r i = 15.2169m

Inradius of Decagon given Circumradius Formula Elements

Variables

Functions

Inradius of Decagon

Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Decagon

Circumradius of Decagon

Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Decagon

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 Inradius of Decagon

Go Inradius of Decagon

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot S

Go Inradius of Decagon given Diagonal across Five Sides

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

Go Inradius of Decagon given Diagonal across Four Sides

r i = \frac{d 4}{2}

Go Inradius of Decagon given Diagonal across Three Sides

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot d 3}{\sqrt{14 + (6 \cdot \sqrt{5})}}

How to Evaluate Inradius of Decagon given Circumradius?

Inradius of Decagon given Circumradius evaluator uses Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)) to evaluate the Inradius of Decagon, The Inradius of Decagon given Circumradius formula is defined as the length of the straight line from the center to any point on the incircle of the Decagon, calculated using circumradius. Inradius of Decagon is denoted by r_i symbol.

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

FAQs on Inradius of Decagon given Circumradius

What is the formula to find Inradius of Decagon given Circumradius?

The formula of Inradius of Decagon given Circumradius is expressed as Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)). Here is an example- 15.2169 = sqrt(5+(2*sqrt(5)))/2*(2*16)/(1+sqrt(5)).

How to calculate Inradius of Decagon given Circumradius?

With Circumradius of Decagon (r_c) we can find Inradius of Decagon given Circumradius using the formula - Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Inradius of Decagon?

Here are the different ways to Calculate Inradius of Decagon-

Inradius of Decagon=sqrt(5+(2*sqrt(5)))/2*Side of Decagon
Inradius of Decagon=sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5))
Inradius of Decagon=Diagonal across Four Sides of Decagon/2

Can the Inradius of Decagon given Circumradius be negative?

No, the Inradius of Decagon given Circumradius, measured in Length cannot be negative.

Which unit is used to measure Inradius of Decagon given Circumradius?

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

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