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Diagonal of Dodecagon across Four Sides given Circumradius Formula

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Diagonal across Four Sides of Dodecagon is a straight line joining two non-adjacent vertices across four sides of the Dodecagon. Check FAQs

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

d₄ - Diagonal Across Four Sides of Dodecagon?r_c - Circumradius of Dodecagon?

Diagonal of Dodecagon across Four Sides given Circumradius Example

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

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

Here is how the Diagonal of Dodecagon across Four Sides given Circumradius equation looks like.

34.641 = \frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2} \cdot \frac{20}{\frac{\sqrt{6} + \sqrt{2}}{2}}

34.641m = \frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2} \cdot \frac{20m}{\frac{\sqrt{6} + \sqrt{2}}{2}}

34.641 = \frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2} \cdot \frac{20}{\frac{\sqrt{6} + \sqrt{2}}{2}}

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2D Geometry » fx Diagonal of Dodecagon across Four Sides given Circumradius

Diagonal of Dodecagon across Four Sides given Circumradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d 4 = \frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2} \cdot \frac{20m}{\frac{\sqrt{6} + \sqrt{2}}{2}}

Next Step Prepare to Evaluate

∴

d 4 = \frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2} \cdot \frac{20}{\frac{\sqrt{6} + \sqrt{2}}{2}}

Next Step Evaluate

∴

d 4 = 34.6410161513776m

LAST Step Rounding Answer

∴

d 4 = 34.641m

Diagonal of Dodecagon across Four Sides given Circumradius Formula Elements

Variables

Functions

Diagonal Across Four Sides of Dodecagon

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

Symbol: d₄

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal Across Four Sides of Dodecagon

Circumradius of Dodecagon

Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius 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 Diagonal Across Four Sides of Dodecagon

Go Diagonal of Dodecagon across Four Sides

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

Go Diagonal of Dodecagon across Four Sides given Area

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

Go Diagonal of Dodecagon across Four Sides given Inradius

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

Go Diagonal of Dodecagon across Four Sides given Perimeter

d 4 = \frac{(3 \cdot \sqrt{2}) + \sqrt{6}}{2} \cdot \frac{P}{12}

How to Evaluate Diagonal of Dodecagon across Four Sides given Circumradius?

Diagonal of Dodecagon across Four Sides given Circumradius evaluator uses Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2) to evaluate the Diagonal Across Four Sides of Dodecagon, Diagonal of Dodecagon across Four Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across four sides of the Dodecagon, calculated using circumradius. Diagonal Across Four Sides of Dodecagon is denoted by d₄ symbol.

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

FAQs on Diagonal of Dodecagon across Four Sides given Circumradius

What is the formula to find Diagonal of Dodecagon across Four Sides given Circumradius?

The formula of Diagonal of Dodecagon across Four Sides given Circumradius is expressed as Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). Here is an example- 34.64102 = ((3*sqrt(2))+sqrt(6))/2*20/((sqrt(6)+sqrt(2))/2).

How to calculate Diagonal of Dodecagon across Four Sides given Circumradius?

With Circumradius of Dodecagon (r_c) we can find Diagonal of Dodecagon across Four Sides given Circumradius using the formula - Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Diagonal Across Four Sides of Dodecagon?

Here are the different ways to Calculate Diagonal Across Four Sides of Dodecagon-

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

Can the Diagonal of Dodecagon across Four Sides given Circumradius be negative?

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

Which unit is used to measure Diagonal of Dodecagon across Four Sides given Circumradius?

Diagonal of Dodecagon across Four 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 Dodecagon across Four Sides given Circumradius can be measured.

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