Diagonal of Dodecagon across Three Sides given Inradius Calculator

✖Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.ⓘ Inradius of Dodecagon [r_i]

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✖Diagonal across Three Sides of Dodecagon is a straight line joining two non-adjacent vertices across three sides of the Dodecagon.ⓘ Diagonal of Dodecagon across Three Sides given Inradius [d₃]

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Diagonal of Dodecagon across Three Sides given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Inradius of Dodecagon/((2+sqrt(3))/2)
d₃ = (sqrt(3)+1)*r_i/((2+sqrt(3))/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 Three Sides of Dodecagon - (Measured in Meter) - Diagonal across Three Sides of Dodecagon is a straight line joining two non-adjacent vertices across three sides of the Dodecagon.
Inradius of Dodecagon - (Measured in Meter) - Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Dodecagon: 19 Meter --> 19 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₃ = (sqrt(3)+1)*r_i/((2+sqrt(3))/2) --> (sqrt(3)+1)*19/((2+sqrt(3))/2)

Evaluating ... ...

d₃ = 27.8179306876173

STEP 3: Convert Result to Output's Unit

27.8179306876173 Meter --> No Conversion Required

FINAL ANSWER

27.8179306876173 ≈ 27.81793 Meter <-- Diagonal Across Three Sides of Dodecagon

(Calculation completed in 00.004 seconds)

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< Diagonal of Dodecagon across Three Sides Calculators

Diagonal of Dodecagon across Three Sides given Area

LaTeX Go Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*sqrt(Area of Dodecagon/(3*(2+sqrt(3))))

Diagonal of Dodecagon across Three Sides given Inradius

LaTeX Go Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Inradius of Dodecagon/((2+sqrt(3))/2)

Diagonal of Dodecagon across Three Sides given Circumradius

LaTeX Go Diagonal Across Three Sides of Dodecagon = sqrt(2)*Circumradius of Dodecagon

Diagonal of Dodecagon across Three Sides

LaTeX Go Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Side of Dodecagon

Diagonal of Dodecagon across Three Sides given Inradius Formula

LaTeX Go

Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Inradius of Dodecagon/((2+sqrt(3))/2)
d₃ = (sqrt(3)+1)*r_i/((2+sqrt(3))/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 Three Sides given Inradius?

Diagonal of Dodecagon across Three Sides given Inradius calculator uses Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Inradius of Dodecagon/((2+sqrt(3))/2) to calculate the Diagonal Across Three Sides of Dodecagon, The Diagonal of Dodecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Dodecagon, calculated using inradius. Diagonal Across Three Sides of Dodecagon is denoted by d₃ symbol.

How to calculate Diagonal of Dodecagon across Three Sides given Inradius using this online calculator? To use this online calculator for Diagonal of Dodecagon across Three Sides given Inradius, enter Inradius of Dodecagon (r_i) and hit the calculate button. Here is how the Diagonal of Dodecagon across Three Sides given Inradius calculation can be explained with given input values -> 27.81793 = (sqrt(3)+1)*19/((2+sqrt(3))/2).

FAQ

What is Diagonal of Dodecagon across Three Sides given Inradius?

The Diagonal of Dodecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Dodecagon, calculated using inradius and is represented as d₃ = (sqrt(3)+1)*r_i/((2+sqrt(3))/2) or Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Inradius of Dodecagon/((2+sqrt(3))/2). Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.

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

The Diagonal of Dodecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Dodecagon, calculated using inradius is calculated using Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Inradius of Dodecagon/((2+sqrt(3))/2). To calculate Diagonal of Dodecagon across Three Sides given Inradius, you need Inradius of Dodecagon (r_i). With our tool, you need to enter the respective value for Inradius 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 Three Sides of Dodecagon?

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

Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*Side of Dodecagon
Diagonal Across Three Sides of Dodecagon = sqrt(2)*Circumradius of Dodecagon
Diagonal Across Three Sides of Dodecagon = (sqrt(3)+1)*sqrt(Area of Dodecagon/(3*(2+sqrt(3))))

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