Circumradius of Dodecagon given Diagonal across Five Sides Calculator

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

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✖Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.ⓘ Circumradius of Dodecagon given Diagonal across Five Sides [r_c]

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Circumradius of Dodecagon given Diagonal across Five Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Circumradius of Dodecagon - (Measured in Meter) - Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.
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.

STEP 1: Convert Input(s) to Base Unit

Diagonal Across Five Sides of Dodecagon: 37 Meter --> 37 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = (sqrt(6)+sqrt(2))/2*d₅/(2+sqrt(3)) --> (sqrt(6)+sqrt(2))/2*37/(2+sqrt(3))

Evaluating ... ...

r_c = 19.1526093375865

STEP 3: Convert Result to Output's Unit

19.1526093375865 Meter --> No Conversion Required

FINAL ANSWER

19.1526093375865 ≈ 19.15261 Meter <-- Circumradius of Dodecagon

(Calculation completed in 00.020 seconds)

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< Circumradius of Dodecagon Calculators

Circumradius of Dodecagon given Diagonal across Four Sides

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

Circumradius of Dodecagon given Diagonal across Five Sides

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

Circumradius of Dodecagon

LaTeX Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Side of Dodecagon

Circumradius of Dodecagon given Diagonal across Six Sides

LaTeX Go Circumradius of Dodecagon = Diagonal Across Six Sides of Dodecagon/2

Circumradius of Dodecagon given Diagonal across Five Sides Formula

LaTeX Go

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

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 Circumradius of Dodecagon given Diagonal across Five Sides?

Circumradius of Dodecagon given Diagonal across Five Sides calculator uses Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Five Sides of Dodecagon/(2+sqrt(3)) to calculate the Circumradius of Dodecagon, The Circumradius of Dodecagon given Diagonal across Five Sides formula is defined as the straight line connecting circumcenter and any point on the circumcircle that touches all vertices of Dodecagon, calculated using diagonal across five sides. Circumradius of Dodecagon is denoted by r_c symbol.

How to calculate Circumradius of Dodecagon given Diagonal across Five Sides using this online calculator? To use this online calculator for Circumradius of Dodecagon given Diagonal across Five Sides, enter Diagonal Across Five Sides of Dodecagon (d₅) and hit the calculate button. Here is how the Circumradius of Dodecagon given Diagonal across Five Sides calculation can be explained with given input values -> 19.15261 = (sqrt(6)+sqrt(2))/2*37/(2+sqrt(3)).

FAQ

What is Circumradius of Dodecagon given Diagonal across Five Sides?

The Circumradius of Dodecagon given Diagonal across Five Sides formula is defined as the straight line connecting circumcenter and any point on the circumcircle that touches all vertices of Dodecagon, calculated using diagonal across five sides and is represented as r_c = (sqrt(6)+sqrt(2))/2*d₅/(2+sqrt(3)) or Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Five Sides of Dodecagon/(2+sqrt(3)). Diagonal across Five Sides of Dodecagon is a straight line joining two non-adjacent vertices across five sides of the Dodecagon.

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

The Circumradius of Dodecagon given Diagonal across Five Sides formula is defined as the straight line connecting circumcenter and any point on the circumcircle that touches all vertices of Dodecagon, calculated using diagonal across five sides is calculated using Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Five Sides of Dodecagon/(2+sqrt(3)). To calculate Circumradius of Dodecagon given Diagonal across Five Sides, you need Diagonal Across Five Sides of Dodecagon (d₅). With our tool, you need to enter the respective value for Diagonal Across Five 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 Circumradius of Dodecagon?

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

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

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