Inradius of Dodecagon given Diagonal across Two Sides Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2)
ri = (2+sqrt(3))/2*d2/((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
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 Two Sides of Dodecagon - (Measured in Meter) - Diagonal across Two Sides of Dodecagon is a straight line joining two non-adjacent vertices across two sides of the Dodecagon.
STEP 1: Convert Input(s) to Base Unit
Diagonal Across Two Sides of Dodecagon: 20 Meter --> 20 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = (2+sqrt(3))/2*d2/((sqrt(2)+sqrt(6))/2) --> (2+sqrt(3))/2*20/((sqrt(2)+sqrt(6))/2)
Evaluating ... ...
ri = 19.3185165257814
STEP 3: Convert Result to Output's Unit
19.3185165257814 Meter --> No Conversion Required
FINAL ANSWER
19.3185165257814 19.31852 Meter <-- Inradius of Dodecagon
(Calculation completed in 00.020 seconds)

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11 Inradius of Dodecagon Calculators

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

Inradius of Dodecagon given Diagonal across Two Sides Formula

Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2)
ri = (2+sqrt(3))/2*d2/((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 Inradius of Dodecagon given Diagonal across Two Sides?

Inradius of Dodecagon given Diagonal across Two Sides calculator uses Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2) to calculate the Inradius of Dodecagon, The Inradius of Dodecagon given Diagonal across Two 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 two sides. Inradius of Dodecagon is denoted by ri symbol.

How to calculate Inradius of Dodecagon given Diagonal across Two Sides using this online calculator? To use this online calculator for Inradius of Dodecagon given Diagonal across Two Sides, enter Diagonal Across Two Sides of Dodecagon (d2) and hit the calculate button. Here is how the Inradius of Dodecagon given Diagonal across Two Sides calculation can be explained with given input values -> 19.31852 = (2+sqrt(3))/2*20/((sqrt(2)+sqrt(6))/2).

FAQ

What is Inradius of Dodecagon given Diagonal across Two Sides?
The Inradius of Dodecagon given Diagonal across Two 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 two sides and is represented as ri = (2+sqrt(3))/2*d2/((sqrt(2)+sqrt(6))/2) or Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2). Diagonal across Two Sides of Dodecagon is a straight line joining two non-adjacent vertices across two sides of the Dodecagon.
How to calculate Inradius of Dodecagon given Diagonal across Two Sides?
The Inradius of Dodecagon given Diagonal across Two 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 two sides is calculated using Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Two Sides of Dodecagon/((sqrt(2)+sqrt(6))/2). To calculate Inradius of Dodecagon given Diagonal across Two Sides, you need Diagonal Across Two Sides of Dodecagon (d2). With our tool, you need to enter the respective value for Diagonal Across Two 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 Two Sides of Dodecagon. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Inradius of Dodecagon = (2+sqrt(3))/2*Diagonal Across Three Sides of Dodecagon/(sqrt(3)+1)
  • 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))
  • Inradius of Dodecagon = (2+sqrt(3))/2*Side of Dodecagon
  • Inradius of Dodecagon = Diagonal Across Five Sides of Dodecagon/2
  • Inradius of Dodecagon = (2+sqrt(3))/24*Perimeter of Dodecagon
  • Inradius of Dodecagon = Height of Dodecagon/2
  • Inradius of Dodecagon = 1/2*sqrt((Area of Dodecagon*(2+sqrt(3)))/3)
  • Inradius of Dodecagon = (2+sqrt(3))/2*Circumradius of Dodecagon/((sqrt(6)+sqrt(2))/2)
  • Inradius of Dodecagon = Width of Dodecagon/2
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