Diagonal of Dodecagon across Five 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 Five Sides of Dodecagon is a straight line joining two non-adjacent vertices across five sides of the Dodecagon.ⓘ Diagonal of Dodecagon across Five Sides given Circumradius [d₅]

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Diagonal of Dodecagon across Five Sides given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal Across Five Sides of Dodecagon = (2+sqrt(3))*(2*Circumradius of Dodecagon)/(sqrt(6)+sqrt(2))
d₅ = (2+sqrt(3))*(2*r_c)/(sqrt(6)+sqrt(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 Five Sides of Dodecagon - (Measured in Meter) - Diagonal across Five Sides of Dodecagon is a straight line joining two non-adjacent vertices across five 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

d₅ = (2+sqrt(3))*(2*r_c)/(sqrt(6)+sqrt(2)) --> (2+sqrt(3))*(2*20)/(sqrt(6)+sqrt(2))

Evaluating ... ...

d₅ = 38.6370330515627

STEP 3: Convert Result to Output's Unit

38.6370330515627 Meter --> No Conversion Required

FINAL ANSWER

38.6370330515627 ≈ 38.63703 Meter <-- Diagonal Across Five Sides of Dodecagon

(Calculation completed in 00.006 seconds)

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< Diagonal of Dodecagon across Five Sides Calculators

Diagonal of Dodecagon across Five Sides given Circumradius

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

Diagonal of Dodecagon across Five Sides given Area

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

Diagonal of Dodecagon across Five Sides given Perimeter

LaTeX Go Diagonal Across Five Sides of Dodecagon = (2+sqrt(3))*Perimeter of Dodecagon/12

Diagonal of Dodecagon across Five Sides given Inradius

LaTeX Go Diagonal Across Five Sides of Dodecagon = 2*Inradius of Dodecagon

Diagonal of Dodecagon across Five Sides given Circumradius Formula

LaTeX Go

Diagonal Across Five Sides of Dodecagon = (2+sqrt(3))*(2*Circumradius of Dodecagon)/(sqrt(6)+sqrt(2))
d₅ = (2+sqrt(3))*(2*r_c)/(sqrt(6)+sqrt(2))

What as 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 Five Sides given Circumradius?

Diagonal of Dodecagon across Five Sides given Circumradius calculator uses Diagonal Across Five Sides of Dodecagon = (2+sqrt(3))*(2*Circumradius of Dodecagon)/(sqrt(6)+sqrt(2)) to calculate the Diagonal Across Five Sides of Dodecagon, Diagonal of Dodecagon across Five Sides given Circumradius formula is defined as the line connecting two non-adjacent vertices across five sides of the Dodecagon, calculated using circumradius. Diagonal Across Five Sides of Dodecagon is denoted by d₅ symbol.

How to calculate Diagonal of Dodecagon across Five Sides given Circumradius using this online calculator? To use this online calculator for Diagonal of Dodecagon across Five Sides given Circumradius, enter Circumradius of Dodecagon (r_c) and hit the calculate button. Here is how the Diagonal of Dodecagon across Five Sides given Circumradius calculation can be explained with given input values -> 38.63703 = (2+sqrt(3))*(2*20)/(sqrt(6)+sqrt(2)).

FAQ

What is Diagonal of Dodecagon across Five Sides given Circumradius?

Diagonal of Dodecagon across Five Sides given Circumradius formula is defined as the line connecting two non-adjacent vertices across five sides of the Dodecagon, calculated using circumradius and is represented as d₅ = (2+sqrt(3))*(2*r_c)/(sqrt(6)+sqrt(2)) or Diagonal Across Five Sides of Dodecagon = (2+sqrt(3))*(2*Circumradius of Dodecagon)/(sqrt(6)+sqrt(2)). Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.

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

Diagonal of Dodecagon across Five Sides given Circumradius formula is defined as the line connecting two non-adjacent vertices across five sides of the Dodecagon, calculated using circumradius is calculated using Diagonal Across Five Sides of Dodecagon = (2+sqrt(3))*(2*Circumradius of Dodecagon)/(sqrt(6)+sqrt(2)). To calculate Diagonal of Dodecagon across Five 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 Five Sides of Dodecagon?

In this formula, Diagonal Across Five 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 Five Sides of Dodecagon = sqrt(((2+sqrt(3))*Area of Dodecagon)/3)
Diagonal Across Five Sides of Dodecagon = (2+sqrt(3))*Perimeter of Dodecagon/12
Diagonal Across Five Sides of Dodecagon = 2*Inradius of Dodecagon

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