Inradius of Dodecagon given Diagonal across Three Sides Calculator

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

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✖Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.ⓘ Inradius of Dodecagon given Diagonal across Three Sides [r_i]

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Inradius of Dodecagon given Diagonal across Three Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Inradius of Dodecagon - (Measured in Meter) - Inradius of Dodecagon is defined as the radius of the circle which is inscribed inside the Dodecagon.
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.

STEP 1: Convert Input(s) to Base Unit

Diagonal Across Three Sides of Dodecagon: 27 Meter --> 27 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = (2+sqrt(3))/2*d₃/(sqrt(3)+1) --> (2+sqrt(3))/2*27/(sqrt(3)+1)

Evaluating ... ...

r_i = 18.4413429510899

STEP 3: Convert Result to Output's Unit

18.4413429510899 Meter --> No Conversion Required

FINAL ANSWER

18.4413429510899 ≈ 18.44134 Meter <-- Inradius of Dodecagon

(Calculation completed in 00.004 seconds)

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< Inradius of Dodecagon Calculators

Inradius of Dodecagon given Diagonal across Four Sides

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

Inradius of Dodecagon given Diagonal across Two Sides

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

Inradius of Dodecagon given Diagonal across Six Sides

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

Inradius of Dodecagon given Diagonal across Three Sides

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

Inradius of Dodecagon given Diagonal across Three Sides Formula

LaTeX Go

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

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 Inradius of Dodecagon given Diagonal across Three Sides?

Inradius of Dodecagon given Diagonal across Three Sides calculator uses Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1) to calculate 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 calculate Inradius of Dodecagon given Diagonal across Three Sides using this online calculator? To use this online calculator for Inradius of Dodecagon given Diagonal across Three Sides, enter Diagonal Across Three Sides of Dodecagon (d₃) and hit the calculate button. Here is how the Inradius of Dodecagon given Diagonal across Three Sides calculation can be explained with given input values -> 18.44134 = (2+sqrt(3))/2*27/(sqrt(3)+1).

FAQ

What is Inradius of Dodecagon given Diagonal across Three Sides?

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 and is represented as r_i = (2+sqrt(3))/2*d₃/(sqrt(3)+1) or Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1). Diagonal across Three Sides of Dodecagon is a straight line joining two non-adjacent vertices across three sides of the Dodecagon.

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

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 is calculated using Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1). To calculate Inradius of Dodecagon given Diagonal across Three Sides, you need Diagonal Across Three Sides of Dodecagon (d₃). With our tool, you need to enter the respective value for Diagonal Across Three Sides 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 Inradius of Dodecagon?

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

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))

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