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Inradius of Dodecagon given Diagonal across Three Sides Formula

GoInradius of Dodecagon given Diagonal across Two Sides Formula

GoInradius of Dodecagon given Diagonal across Four Sides Formula

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Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon. Check FAQs

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 3}{\sqrt{3} + 1}

r_i - Inradius of Dodecagon?d₃ - Diagonal Across Three Sides of Dodecagon?

Inradius of Dodecagon given Diagonal across Three Sides Example

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

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

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

18.4413 = \frac{2 + \sqrt{3}}{2} \cdot \frac{27}{\sqrt{3} + 1}

18.4413m = \frac{2 + \sqrt{3}}{2} \cdot \frac{27m}{\sqrt{3} + 1}

18.4413 = \frac{2 + \sqrt{3}}{2} \cdot \frac{27}{\sqrt{3} + 1}

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Inradius of Dodecagon given Diagonal across Three Sides Solution

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

FIRST Step Consider the formula

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 3}{\sqrt{3} + 1}

Next Step Substitute values of Variables

∴

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{27m}{\sqrt{3} + 1}

Next Step Prepare to Evaluate

∴

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{27}{\sqrt{3} + 1}

Next Step Evaluate

∴

r i = 18.4413429510899m

LAST Step Rounding Answer

∴

r i = 18.4413m

Inradius of Dodecagon given Diagonal across Three Sides Formula Elements

Variables

Functions

Inradius of Dodecagon

Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Dodecagon

Diagonal Across Three Sides of Dodecagon

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

Symbol: d₃

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal Across Three Sides of Dodecagon

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 Dodecagon

Go Inradius of Dodecagon given Diagonal across Two Sides

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 2}{\frac{\sqrt{2} + \sqrt{6}}{2}}

Go Inradius of Dodecagon given Diagonal across Four Sides

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 4}{\frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2}}

Go Inradius of Dodecagon given Diagonal across Six Sides

r i = \frac{2 + \sqrt{3}}{2} \cdot \frac{d 6}{\sqrt{6} + \sqrt{2}}

Go Inradius of Dodecagon

r i = \frac{2 + \sqrt{3}}{2} \cdot S

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

Inradius of Dodecagon given Diagonal across Three Sides evaluator uses Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1) to evaluate the Inradius of Dodecagon, The Inradius of Dodecagon given Diagonal across Three Sides formula is defined as the line connecting the incenter and any point on the incircle that touches all the edges of the Dodecagon, calculated using diagonal across three sides. Inradius of Dodecagon is denoted by r_i symbol.

How to evaluate Inradius of Dodecagon given Diagonal across Three Sides using this online evaluator? To use this online evaluator for Inradius of Dodecagon given Diagonal across Three Sides, enter Diagonal Across Three Sides of Dodecagon (d₃) and hit the calculate button.

FAQs on Inradius of Dodecagon given Diagonal across Three Sides

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

The formula of Inradius of Dodecagon given Diagonal across Three Sides is expressed as Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1). Here is an example- 18.44134 = (2+sqrt(3))/2*27/(sqrt(3)+1).

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

With Diagonal Across Three Sides of Dodecagon (d₃) we can find Inradius of Dodecagon given Diagonal across Three Sides using the formula - Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Dodecagon?

Here are the different ways to Calculate Inradius of Dodecagon-

Inradius of Dodecagon=(2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2)
Inradius of Dodecagon=(2+sqrt(3))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2)
Inradius of Dodecagon=(2+sqrt(3))/2*Diagonal Across Six Sides of Dodecagon/(sqrt(6)+sqrt(2))

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

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

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

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

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