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Diagonal of Decagon across Three Sides given Inradius Formula

GoDiagonal of Decagon across Three Sides Formula

GoDiagonal of Decagon across Three Sides given Diagonal across Five Sides Formula

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Diagonal across Three Sides of Decagon is a straight line joining two non-adjacent sides which is across three sides of the Decagon. Check FAQs

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

d₃ - Diagonal across Three Sides of Decagon?r_i - Inradius of Decagon?

Diagonal of Decagon across Three Sides given Inradius Example

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Here is how the Diagonal of Decagon across Three Sides given Inradius equation looks like with Values.

Here is how the Diagonal of Decagon across Three Sides given Inradius equation looks like with Units.

Here is how the Diagonal of Decagon across Three Sides given Inradius equation looks like.

25.5195 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

25.5195m = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 15m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

25.5195 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

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Diagonal of Decagon across Three Sides given Inradius Solution

Follow our step by step solution on how to calculate Diagonal of Decagon across Three Sides given Inradius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d 3 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 15m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

d 3 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

d 3 = 25.5195242505612m

LAST Step Rounding Answer

∴

d 3 = 25.5195m

Diagonal of Decagon across Three Sides given Inradius Formula Elements

Variables

Functions

Diagonal across Three Sides of Decagon

Diagonal across Three Sides of Decagon is a straight line joining two non-adjacent sides which is across three sides of the Decagon.

Symbol: d₃

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Three Sides of Decagon

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

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 Diagonal across Three Sides of Decagon

Go Diagonal of Decagon across Three Sides

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

Go Diagonal of Decagon across Three Sides given Diagonal across Five Sides

d 3 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{d 5}{1 + \sqrt{5}}

Go Diagonal of Decagon across Three Sides given Diagonal across Four Sides

d 3 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{d 4}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Go Diagonal of Decagon across Three Sides given Diagonal across Two Sides

d 3 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot d 2}{\sqrt{10 + (2 \cdot \sqrt{5})}}

How to Evaluate Diagonal of Decagon across Three Sides given Inradius?

Diagonal of Decagon across Three Sides given Inradius evaluator uses Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))) to evaluate the Diagonal across Three Sides of Decagon, The Diagonal of Decagon across Three Sides given Inradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using inradius. Diagonal across Three Sides of Decagon is denoted by d₃ symbol.

How to evaluate Diagonal of Decagon across Three Sides given Inradius using this online evaluator? To use this online evaluator for Diagonal of Decagon across Three Sides given Inradius, enter Inradius of Decagon (r_i) and hit the calculate button.

FAQs on Diagonal of Decagon across Three Sides given Inradius

What is the formula to find Diagonal of Decagon across Three Sides given Inradius?

The formula of Diagonal of Decagon across Three Sides given Inradius is expressed as Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))). Here is an example- 25.51952 = sqrt(14+(6*sqrt(5)))/2*(2*15)/sqrt(5+(2*sqrt(5))).

How to calculate Diagonal of Decagon across Three Sides given Inradius?

With Inradius of Decagon (r_i) we can find Diagonal of Decagon across Three Sides given Inradius using the formula - Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Diagonal across Three Sides of Decagon?

Here are the different ways to Calculate Diagonal across Three Sides of Decagon-

Diagonal across Three Sides of Decagon=sqrt(14+(6*sqrt(5)))/2*Side of Decagon
Diagonal across Three Sides of Decagon=sqrt(14+(6*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5))
Diagonal across Three Sides of Decagon=sqrt(14+(6*sqrt(5)))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))

Can the Diagonal of Decagon across Three Sides given Inradius be negative?

No, the Diagonal of Decagon across Three Sides given Inradius, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Decagon across Three Sides given Inradius?

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

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