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

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Height of Dodecagon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

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

Evaluating ... ...

h = 38.6370330515627

STEP 3: Convert Result to Output's Unit

38.6370330515627 Meter --> No Conversion Required

FINAL ANSWER

38.6370330515627 ≈ 38.63703 Meter <-- Height of Dodecagon

(Calculation completed in 00.014 seconds)

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< Height of Dodecagon Calculators

Height of Dodecagon given Diagonal across Four Sides

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

Height of Dodecagon given Diagonal across Two Sides

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

Height of Dodecagon given Diagonal across Six Sides

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

Height of Dodecagon given Diagonal across Three Sides

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

Height of Dodecagon given Circumradius Formula

LaTeX Go

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

Height of Dodecagon given Circumradius calculator uses Height of Dodecagon = (2+sqrt(3))*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2) to calculate the Height of Dodecagon, The Height of Dodecagon given Circumradius formula is defined as the perpendicular distance between any pair of opposite edges of the Dodecagon, calculated using circumradius. Height of Dodecagon is denoted by h symbol.

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

FAQ

What is Height of Dodecagon given Circumradius?

The Height of Dodecagon given Circumradius formula is defined as the perpendicular distance between any pair of opposite edges of the Dodecagon, calculated using circumradius and is represented as h = (2+sqrt(3))*r_c/((sqrt(6)+sqrt(2))/2) or Height of Dodecagon = (2+sqrt(3))*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.

How to calculate Height of Dodecagon given Circumradius?

The Height of Dodecagon given Circumradius formula is defined as the perpendicular distance between any pair of opposite edges of the Dodecagon, calculated using circumradius is calculated using Height of Dodecagon = (2+sqrt(3))*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2). To calculate Height of Dodecagon 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 Height of Dodecagon?

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

Height of Dodecagon = (2+sqrt(3))*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2)
Height of Dodecagon = (2+sqrt(3))*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1)
Height of Dodecagon = (2+sqrt(3))*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2)

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