Circumradius of Dodecagon given Diagonal across Four Sides Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2)
rc = (sqrt(6)+sqrt(2))/2*d4/(((3*sqrt(2))+sqrt(6))/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
Circumradius of Dodecagon - (Measured in Meter) - Circumradius of Dodecagon is the radius of a circumcircle touching each of the vertices of Dodecagon.
Diagonal Across Four Sides of Dodecagon - (Measured in Meter) - Diagonal across Four Sides of Dodecagon is a straight line joining two non-adjacent vertices across four sides of the Dodecagon.
STEP 1: Convert Input(s) to Base Unit
Diagonal Across Four Sides of Dodecagon: 33 Meter --> 33 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = (sqrt(6)+sqrt(2))/2*d4/(((3*sqrt(2))+sqrt(6))/2) --> (sqrt(6)+sqrt(2))/2*33/(((3*sqrt(2))+sqrt(6))/2)
Evaluating ... ...
rc = 19.0525588832576
STEP 3: Convert Result to Output's Unit
19.0525588832576 Meter --> No Conversion Required
FINAL ANSWER
19.0525588832576 19.05256 Meter <-- Circumradius of Dodecagon
(Calculation completed in 00.004 seconds)

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11 Circumradius of Dodecagon Calculators

Circumradius of Dodecagon given Diagonal across Four Sides
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 Area
Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*sqrt(Area of Dodecagon/(3*(2+sqrt(3))))
Circumradius of Dodecagon given Diagonal across Five Sides
Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Five Sides of Dodecagon/(2+sqrt(3))
Circumradius of Dodecagon given Inradius
Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2)
Circumradius of Dodecagon given Height
Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Height of Dodecagon/(2+sqrt(3))
Circumradius of Dodecagon given Width
Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Width of Dodecagon/(2+sqrt(3))
Circumradius of Dodecagon given Perimeter
Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/24*Perimeter of Dodecagon
Circumradius of Dodecagon
Go Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Side of Dodecagon
Circumradius of Dodecagon given Diagonal across Three Sides
Go Circumradius of Dodecagon = Diagonal Across Three Sides of Dodecagon/sqrt(2)
Circumradius of Dodecagon given Diagonal across Six Sides
Go Circumradius of Dodecagon = Diagonal Across Six Sides of Dodecagon/2
Circumradius of Dodecagon given Diagonal across Two Sides
Go Circumradius of Dodecagon = Diagonal Across Two Sides of Dodecagon/1

Circumradius of Dodecagon given Diagonal across Four Sides Formula

Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2)
rc = (sqrt(6)+sqrt(2))/2*d4/(((3*sqrt(2))+sqrt(6))/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 Circumradius of Dodecagon given Diagonal across Four Sides?

Circumradius of Dodecagon given Diagonal across Four Sides calculator uses Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2) to calculate the Circumradius of Dodecagon, The Circumradius of Dodecagon given Diagonal across Four Sides 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 diagonal across four sides. Circumradius of Dodecagon is denoted by rc symbol.

How to calculate Circumradius of Dodecagon given Diagonal across Four Sides using this online calculator? To use this online calculator for Circumradius of Dodecagon given Diagonal across Four Sides, enter Diagonal Across Four Sides of Dodecagon (d4) and hit the calculate button. Here is how the Circumradius of Dodecagon given Diagonal across Four Sides calculation can be explained with given input values -> 19.05256 = (sqrt(6)+sqrt(2))/2*33/(((3*sqrt(2))+sqrt(6))/2).

FAQ

What is Circumradius of Dodecagon given Diagonal across Four Sides?
The Circumradius of Dodecagon given Diagonal across Four Sides 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 diagonal across four sides and is represented as rc = (sqrt(6)+sqrt(2))/2*d4/(((3*sqrt(2))+sqrt(6))/2) or Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2). Diagonal across Four Sides of Dodecagon is a straight line joining two non-adjacent vertices across four sides of the Dodecagon.
How to calculate Circumradius of Dodecagon given Diagonal across Four Sides?
The Circumradius of Dodecagon given Diagonal across Four Sides 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 diagonal across four sides is calculated using Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Diagonal Across Four Sides of Dodecagon/(((3*sqrt(2))+sqrt(6))/2). To calculate Circumradius of Dodecagon given Diagonal across Four Sides, you need Diagonal Across Four Sides of Dodecagon (d4). With our tool, you need to enter the respective value for Diagonal Across Four 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 Four Sides of Dodecagon. We can use 10 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))
  • Circumradius of Dodecagon = Diagonal Across Three Sides of Dodecagon/sqrt(2)
  • Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/24*Perimeter of Dodecagon
  • Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*sqrt(Area of Dodecagon/(3*(2+sqrt(3))))
  • Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Height of Dodecagon/(2+sqrt(3))
  • Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Inradius of Dodecagon/((2+sqrt(3))/2)
  • Circumradius of Dodecagon = Diagonal Across Two Sides of Dodecagon/1
  • Circumradius of Dodecagon = (sqrt(6)+sqrt(2))/2*Width of Dodecagon/(2+sqrt(3))
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