Circumradius of Dodecagon given Height Calculator

✖Height of Dodecagon is the length of the perpendicular distance between any pair of opposite sides of the Dodecagon.ⓘ Height of Dodecagon [h]

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

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Circumradius of Dodecagon given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Height of Dodecagon/(2+sqrt(3))
r_c = (sqrt(6)+sqrt(2))/2*h/(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.
Height of Dodecagon - (Measured in Meter) - Height of Dodecagon is the length of the perpendicular distance between any pair of opposite sides of the Dodecagon.

STEP 1: Convert Input(s) to Base Unit

Height 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*h/(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 00.004 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 Height Formula

LaTeX Go

Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Height of Dodecagon/(2+sqrt(3))
r_c = (sqrt(6)+sqrt(2))/2*h/(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 Height?

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

How to calculate Circumradius of Dodecagon given Height using this online calculator? To use this online calculator for Circumradius of Dodecagon given Height, enter Height of Dodecagon (h) and hit the calculate button. Here is how the Circumradius of Dodecagon given Height 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 Height?

The Circumradius of Dodecagon given Height formula is defined as the straight line connecting the circumcenter and any point on the circumcircle that touches all vertices of the Dodecagon, calculated using height and is represented as r_c = (sqrt(6)+sqrt(2))/2*h/(2+sqrt(3)) or Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Height of Dodecagon/(2+sqrt(3)). Height of Dodecagon is the length of the perpendicular distance between any pair of opposite sides of the Dodecagon.

How to calculate Circumradius of Dodecagon given Height?

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

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