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Diagonal of Decagon across Three Sides given Circumradius 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 c}{1 + \sqrt{5}}

d₃ - Diagonal across Three Sides of Decagon?r_c - Circumradius of Decagon?

Diagonal of Decagon across Three Sides given Circumradius Example

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

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

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

25.8885 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

25.8885m = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16m}{1 + \sqrt{5}}

25.8885 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

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Diagonal of Decagon across Three Sides given Circumradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d 3 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16m}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

d 3 = \frac{\sqrt{14 + (6 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

Next Step Evaluate

∴

d 3 = 25.8885438199983m

LAST Step Rounding Answer

∴

d 3 = 25.8885m

Diagonal of Decagon across Three Sides given Circumradius 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

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 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 Circumradius?

Diagonal of Decagon across Three Sides given Circumradius evaluator uses Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)) to evaluate the Diagonal across Three Sides of Decagon, The Diagonal of Decagon across Three Sides given Circumradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using circumradius. Diagonal across Three Sides of Decagon is denoted by d₃ symbol.

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

FAQs on Diagonal of Decagon across Three Sides given Circumradius

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

The formula of Diagonal of Decagon across Three Sides given Circumradius is expressed as Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)). Here is an example- 25.88854 = sqrt(14+(6*sqrt(5)))/2*(2*16)/(1+sqrt(5)).

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

With Circumradius of Decagon (r_c) we can find Diagonal of Decagon across Three Sides given Circumradius using the formula - Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+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 Circumradius be negative?

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

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

Diagonal of Decagon across Three Sides given Circumradius 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 Circumradius can be measured.

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