Diagonal of Dodecagon across Four Sides given Circumradius Calculator

✖Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.ⓘ Circumradius of Dodecagon [r_c]

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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.ⓘ Diagonal of Dodecagon across Four Sides given Circumradius [d₄]

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Diagonal of Dodecagon across Four Sides given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2)
d₄ = ((3*sqrt(2))+sqrt(6))/2*r_c/((sqrt(6)+sqrt(2))/2)
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Diagonal Across Four Sides of Dodecagon - (Measured in Meter) - Diagonal across Four Sides of Dodecagon is a straight line joining two non-adjacent vertices across four sides of the Dodecagon.
Circumradius of Dodecagon - (Measured in Meter) - Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Dodecagon: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₄ = ((3*sqrt(2))+sqrt(6))/2*r_c/((sqrt(6)+sqrt(2))/2) --> ((3*sqrt(2))+sqrt(6))/2*20/((sqrt(6)+sqrt(2))/2)

Evaluating ... ...

d₄ = 34.6410161513776

STEP 3: Convert Result to Output's Unit

34.6410161513776 Meter --> No Conversion Required

FINAL ANSWER

34.6410161513776 ≈ 34.64102 Meter <-- Diagonal Across Four Sides of Dodecagon

(Calculation completed in 00.004 seconds)

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< Diagonal of Dodecagon across Four Sides Calculators

Diagonal of Dodecagon across Four Sides given Circumradius

LaTeX Go Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2)

Diagonal of Dodecagon across Four Sides given Area

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

Diagonal of Dodecagon across Four Sides given Inradius

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

Diagonal of Dodecagon across Four Sides

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

Diagonal of Dodecagon across Four Sides given Circumradius Formula

LaTeX Go

Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2)
d₄ = ((3*sqrt(2))+sqrt(6))/2*r_c/((sqrt(6)+sqrt(2))/2)

What is Dodecagon?

A regular Dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry and rotational symmetry of order 12. It can be constructed as a truncated hexagon, t{6}, or a twice-truncated triangle, tt{3}. The internal angle at each vertex of a regular dodecagon is 150°.

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

Diagonal of Dodecagon across Four Sides given Circumradius calculator uses Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2) to calculate 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 calculate Diagonal of Dodecagon across Four Sides given Circumradius using this online calculator? To use this online calculator for Diagonal of Dodecagon across Four Sides given Circumradius, enter Circumradius of Dodecagon (r_c) and hit the calculate button. Here is how the Diagonal of Dodecagon across Four Sides given Circumradius calculation can be explained with given input values -> 34.64102 = ((3*sqrt(2))+sqrt(6))/2*20/((sqrt(6)+sqrt(2))/2).

FAQ

What is Diagonal of Dodecagon across Four Sides given Circumradius?

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 and is represented as d₄ = ((3*sqrt(2))+sqrt(6))/2*r_c/((sqrt(6)+sqrt(2))/2) or Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.

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

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 is calculated using Diagonal Across Four Sides of Dodecagon = ((3*sqrt(2))+sqrt(6))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). To calculate Diagonal of Dodecagon across Four Sides given Circumradius, you need Circumradius of Dodecagon (r_c). With our tool, you need to enter the respective value for Circumradius of Dodecagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Diagonal Across Four Sides of Dodecagon?

In this formula, Diagonal Across Four Sides of Dodecagon uses Circumradius of Dodecagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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