Inradius of Octagon given Short Diagonal Calculator

✖The Short Diagonal of Octagon is the length of smallest diagonals or the line joining a vertex and any one of the vertices that coming next to the adjacent vertices of the first vertex of the Octagon.ⓘ Short Diagonal of Octagon [d_Short]

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✖The Inradius of Octagon is the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle.ⓘ Inradius of Octagon given Short Diagonal [r_i]

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Formula

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Inradius of Octagon given Short Diagonal

Formula

`"r"_{"i"} = sqrt((2+sqrt(2))/8)*"d"_{"Short"}`

Example

`"11.75907m"=sqrt((2+sqrt(2))/8)*"18m"`

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Inradius of Octagon given Short Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon
r_i = sqrt((2+sqrt(2))/8)*d_Short
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 Octagon - (Measured in Meter) - The Inradius of Octagon is the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touch the circle.
Short Diagonal of Octagon - (Measured in Meter) - The Short Diagonal of Octagon is the length of smallest diagonals or the line joining a vertex and any one of the vertices that coming next to the adjacent vertices of the first vertex of the Octagon.

STEP 1: Convert Input(s) to Base Unit

Short Diagonal of Octagon: 18 Meter --> 18 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = sqrt((2+sqrt(2))/8)*d_Short --> sqrt((2+sqrt(2))/8)*18

Evaluating ... ...

r_i = 11.7590666838874

STEP 3: Convert Result to Output's Unit

11.7590666838874 Meter --> No Conversion Required

FINAL ANSWER

11.7590666838874 ≈ 11.75907 Meter <-- Inradius of Octagon

(Calculation completed in 00.004 seconds)

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< 9 Inradius of Octagon Calculators

Inradius of Octagon given Long Diagonal

Go Inradius of Octagon = ((sqrt(2+sqrt(2)))/4)*Long Diagonal of Octagon

Inradius of Octagon given Short Diagonal

Go Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon

Inradius of Octagon given Circumradius

Go Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon

Inradius of Octagon given Area

Go Inradius of Octagon = sqrt(((1+sqrt(2))/8)*Area of Octagon)

Inradius of Octagon

Go Inradius of Octagon = ((1+sqrt(2))/2)*Edge Length of Octagon

Inradius of Octagon given Perimeter

Go Inradius of Octagon = (1+sqrt(2))*Perimeter of Octagon/16

Inradius of Octagon given Medium Diagonal

Go Inradius of Octagon = Medium Diagonal of Octagon/2

Inradius of Octagon given Height

Go Inradius of Octagon = Height of Octagon/2

Inradius of Octagon given Width

Go Inradius of Octagon = Width of Octagon/2

Inradius of Octagon given Short Diagonal Formula

Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon
r_i = sqrt((2+sqrt(2))/8)*d_Short

What is an Octagon?

Octagon is a polygon in geometry, which has 8 sides and 8 angles. That means the number of vertices is 8 and the number of edges is 8. All the sides are joined with each other end-to-end to form a shape. These sides are in a straight line form; they are not curved or disjoint with each other. Each interior angle of a regular octagon is 135° and each exterior angle will be 45°.

How to Calculate Inradius of Octagon given Short Diagonal?

Inradius of Octagon given Short Diagonal calculator uses Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon to calculate the Inradius of Octagon, The Inradius of Octagon given Short Diagonal formula is defined as the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touching the circle and calculated using the short diagonal of the Octagon. Inradius of Octagon is denoted by r_i symbol.

How to calculate Inradius of Octagon given Short Diagonal using this online calculator? To use this online calculator for Inradius of Octagon given Short Diagonal, enter Short Diagonal of Octagon (d_Short) and hit the calculate button. Here is how the Inradius of Octagon given Short Diagonal calculation can be explained with given input values -> 11.75907 = sqrt((2+sqrt(2))/8)*18.

FAQ

What is Inradius of Octagon given Short Diagonal?

The Inradius of Octagon given Short Diagonal formula is defined as the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touching the circle and calculated using the short diagonal of the Octagon and is represented as r_i = sqrt((2+sqrt(2))/8)*d_Short or Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon. The Short Diagonal of Octagon is the length of smallest diagonals or the line joining a vertex and any one of the vertices that coming next to the adjacent vertices of the first vertex of the Octagon.

How to calculate Inradius of Octagon given Short Diagonal?

The Inradius of Octagon given Short Diagonal formula is defined as the radius of incircle of the Regular Octagon or the circle that contained by the Octagon with all edges touching the circle and calculated using the short diagonal of the Octagon is calculated using Inradius of Octagon = sqrt((2+sqrt(2))/8)*Short Diagonal of Octagon. To calculate Inradius of Octagon given Short Diagonal, you need Short Diagonal of Octagon (d_Short). With our tool, you need to enter the respective value for Short Diagonal of Octagon 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 Octagon?

In this formula, Inradius of Octagon uses Short Diagonal of Octagon. We can use 8 other way(s) to calculate the same, which is/are as follows -

Inradius of Octagon = ((1+sqrt(2))/2)*Edge Length of Octagon
Inradius of Octagon = (sqrt(2+sqrt(2))/2)*Circumradius of Octagon
Inradius of Octagon = ((sqrt(2+sqrt(2)))/4)*Long Diagonal of Octagon
Inradius of Octagon = Medium Diagonal of Octagon/2
Inradius of Octagon = Height of Octagon/2
Inradius of Octagon = (1+sqrt(2))*Perimeter of Octagon/16
Inradius of Octagon = sqrt(((1+sqrt(2))/8)*Area of Octagon)
Inradius of Octagon = Width of Octagon/2

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