Long 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 Long Diagonal of Octagon is the length of longest diagonals or the line joining any pair of opposite vertices of the Regular Octagon.ⓘ Long Diagonal of Octagon given Inradius [d_Long]

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Long Diagonal of Octagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Diagonal of Octagon = 2*sqrt(4-(2*sqrt(2)))*Inradius of Octagon
d_Long = 2*sqrt(4-(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

Long Diagonal of Octagon - (Measured in Meter) - The Long Diagonal of Octagon is the length of longest diagonals or the line joining any pair of opposite vertices of the Regular 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_Long = 2*sqrt(4-(2*sqrt(2)))*r_i --> 2*sqrt(4-(2*sqrt(2)))*12

Evaluating ... ...

d_Long = 25.9774128070175

STEP 3: Convert Result to Output's Unit

25.9774128070175 Meter --> No Conversion Required

FINAL ANSWER

25.9774128070175 ≈ 25.97741 Meter <-- Long Diagonal of Octagon

(Calculation completed in 00.004 seconds)

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< Long Diagonal of Octagon Calculators

Long Diagonal of Octagon given Medium Diagonal

LaTeX Go Long Diagonal of Octagon = sqrt(4-(2*sqrt(2)))*Medium Diagonal of Octagon

Long Diagonal of Octagon

LaTeX Go Long Diagonal of Octagon = sqrt(4+(2*sqrt(2)))*Edge Length of Octagon

Long Diagonal of Octagon given Height

LaTeX Go Long Diagonal of Octagon = sqrt(4-(2*sqrt(2)))*Height of Octagon

Long Diagonal of Octagon given Short Diagonal

LaTeX Go Long Diagonal of Octagon = sqrt(2)*Short Diagonal of Octagon

Long Diagonal of Octagon given Inradius Formula

LaTeX Go

Long Diagonal of Octagon = 2*sqrt(4-(2*sqrt(2)))*Inradius of Octagon
d_Long = 2*sqrt(4-(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 Long Diagonal of Octagon given Inradius?

Long Diagonal of Octagon given Inradius calculator uses Long Diagonal of Octagon = 2*sqrt(4-(2*sqrt(2)))*Inradius of Octagon to calculate the Long Diagonal of Octagon, The Long Diagonal of Octagon given Inradius formula is defined as the length of the longest diagonals or the line joining any pair of opposite vertices of the Regular Octagon and calculated using the inradius of the Octagon. Long Diagonal of Octagon is denoted by d_Long symbol.

How to calculate Long Diagonal of Octagon given Inradius using this online calculator? To use this online calculator for Long Diagonal of Octagon given Inradius, enter Inradius of Octagon (r_i) and hit the calculate button. Here is how the Long Diagonal of Octagon given Inradius calculation can be explained with given input values -> 25.97741 = 2*sqrt(4-(2*sqrt(2)))*12.

FAQ

What is Long Diagonal of Octagon given Inradius?

The Long Diagonal of Octagon given Inradius formula is defined as the length of the longest diagonals or the line joining any pair of opposite vertices of the Regular Octagon and calculated using the inradius of the Octagon and is represented as d_Long = 2*sqrt(4-(2*sqrt(2)))*r_i or Long Diagonal of Octagon = 2*sqrt(4-(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 Long Diagonal of Octagon given Inradius?

The Long Diagonal of Octagon given Inradius formula is defined as the length of the longest diagonals or the line joining any pair of opposite vertices of the Regular Octagon and calculated using the inradius of the Octagon is calculated using Long Diagonal of Octagon = 2*sqrt(4-(2*sqrt(2)))*Inradius of Octagon. To calculate Long 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 Long Diagonal of Octagon?

In this formula, Long Diagonal of Octagon uses Inradius of Octagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Long Diagonal of Octagon = sqrt(4+(2*sqrt(2)))*Edge Length of Octagon
Long Diagonal of Octagon = sqrt(4-(2*sqrt(2)))*Medium Diagonal of Octagon
Long Diagonal of Octagon = sqrt(2)*Short Diagonal of Octagon

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