Short Diagonal of Octagon given Inradius Calculator

✖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 [r_i]

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✖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 given Inradius [d_Short]

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Formula

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Short Diagonal of Octagon given Inradius

Formula

`"d"_{"Short"} = 2*sqrt(2-sqrt(2))*"r"_{"i"}`

Example

`"18.3688m"=2*sqrt(2-sqrt(2))*"12m"`

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Short Diagonal of Octagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Diagonal of Octagon = 2*sqrt(2-sqrt(2))*Inradius of Octagon
d_Short = 2*sqrt(2-sqrt(2))*r_i
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Inradius of Octagon: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Short = 2*sqrt(2-sqrt(2))*r_i --> 2*sqrt(2-sqrt(2))*12

Evaluating ... ...

d_Short = 18.3688047535243

STEP 3: Convert Result to Output's Unit

18.3688047535243 Meter --> No Conversion Required

FINAL ANSWER

18.3688047535243 ≈ 18.3688 Meter <-- Short Diagonal of Octagon

(Calculation completed in 00.004 seconds)

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< 8 Short Diagonal of Octagon Calculators

Short Diagonal of Octagon given Medium Diagonal

Go Short Diagonal of Octagon = sqrt(2-sqrt(2))*Medium Diagonal of Octagon

Short Diagonal of Octagon given Perimeter

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

Short Diagonal of Octagon

Go Short Diagonal of Octagon = sqrt(2+sqrt(2))*Edge Length of Octagon

Short Diagonal of Octagon given Inradius

Go Short Diagonal of Octagon = 2*sqrt(2-sqrt(2))*Inradius of Octagon

Short Diagonal of Octagon given Height

Go Short Diagonal of Octagon = sqrt(2-sqrt(2))*Height of Octagon

Short Diagonal of Octagon given Area

Go Short Diagonal of Octagon = sqrt(Area of Octagon/(sqrt(2)))

Short Diagonal of Octagon given Long Diagonal

Go Short Diagonal of Octagon = Long Diagonal of Octagon/(sqrt(2))

Short Diagonal of Octagon given Circumradius

Go Short Diagonal of Octagon = sqrt(2)*Circumradius of Octagon

Short Diagonal of Octagon given Inradius Formula

Short Diagonal of Octagon = 2*sqrt(2-sqrt(2))*Inradius of Octagon
d_Short = 2*sqrt(2-sqrt(2))*r_i

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 Short Diagonal of Octagon given Inradius?

Short Diagonal of Octagon given Inradius calculator uses Short Diagonal of Octagon = 2*sqrt(2-sqrt(2))*Inradius of Octagon to calculate the Short Diagonal of Octagon, The Short Diagonal of Octagon given Inradius formula is defined as the length of the smallest diagonals or the line joining a vertex and any of the vertices that come next to the adjacent vertices of the first vertex of the Octagon and calculated using the inradius of the Octagon. Short Diagonal of Octagon is denoted by d_Short symbol.

How to calculate Short Diagonal of Octagon given Inradius using this online calculator? To use this online calculator for Short Diagonal of Octagon given Inradius, enter Inradius of Octagon (r_i) and hit the calculate button. Here is how the Short Diagonal of Octagon given Inradius calculation can be explained with given input values -> 18.3688 = 2*sqrt(2-sqrt(2))*12.

FAQ

What is Short Diagonal of Octagon given Inradius?

The Short Diagonal of Octagon given Inradius formula is defined as the length of the smallest diagonals or the line joining a vertex and any of the vertices that come next to the adjacent vertices of the first vertex of the Octagon and calculated using the inradius of the Octagon and is represented as d_Short = 2*sqrt(2-sqrt(2))*r_i or Short Diagonal of Octagon = 2*sqrt(2-sqrt(2))*Inradius of Octagon. 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.

How to calculate Short Diagonal of Octagon given Inradius?

The Short Diagonal of Octagon given Inradius formula is defined as the length of the smallest diagonals or the line joining a vertex and any of the vertices that come next to the adjacent vertices of the first vertex of the Octagon and calculated using the inradius of the Octagon is calculated using Short Diagonal of Octagon = 2*sqrt(2-sqrt(2))*Inradius of Octagon. To calculate Short Diagonal of Octagon given Inradius, you need Inradius of Octagon (r_i). With our tool, you need to enter the respective value for Inradius 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 Short Diagonal of Octagon?

In this formula, Short Diagonal of Octagon uses Inradius of Octagon. We can use 7 other way(s) to calculate the same, which is/are as follows -

Short Diagonal of Octagon = sqrt(2+sqrt(2))*Edge Length of Octagon
Short Diagonal of Octagon = Long Diagonal of Octagon/(sqrt(2))
Short Diagonal of Octagon = sqrt(2-sqrt(2))*Medium Diagonal of Octagon
Short Diagonal of Octagon = sqrt(2-sqrt(2))*Height of Octagon
Short Diagonal of Octagon = sqrt(2+sqrt(2))*Perimeter of Octagon/8
Short Diagonal of Octagon = sqrt(Area of Octagon/(sqrt(2)))
Short Diagonal of Octagon = sqrt(2)*Circumradius of Octagon

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