Diagonal of Decagon across Three Sides given Inradius Calculator

✖Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.ⓘ Inradius of Decagon [r_i]

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✖Diagonal across Three Sides of Decagon is a straight line joining two non-adjacent sides which is across three sides of the Decagon.ⓘ Diagonal of Decagon across Three Sides given Inradius [d₃]

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Diagonal of Decagon across Three Sides given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5)))
d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_i)/sqrt(5+(2*sqrt(5)))
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

Diagonal across Three Sides of Decagon - (Measured in Meter) - Diagonal across Three Sides of Decagon is a straight line joining two non-adjacent sides which is across three sides of the Decagon.
Inradius of Decagon - (Measured in Meter) - Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Decagon: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_i)/sqrt(5+(2*sqrt(5))) --> sqrt(14+(6*sqrt(5)))/2*(2*15)/sqrt(5+(2*sqrt(5)))

Evaluating ... ...

d₃ = 25.5195242505612

STEP 3: Convert Result to Output's Unit

25.5195242505612 Meter --> No Conversion Required

FINAL ANSWER

25.5195242505612 ≈ 25.51952 Meter <-- Diagonal across Three Sides of Decagon

(Calculation completed in 00.004 seconds)

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< Diagonal of Decagon across Three Sides Calculators

Diagonal of Decagon across Three Sides given Diagonal across Two Sides

LaTeX Go Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(2*sqrt(5)))

Diagonal of Decagon across Three Sides given Diagonal across Four Sides

LaTeX Go Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))

Diagonal of Decagon across Three Sides given Diagonal across Five Sides

LaTeX Go Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5))

Diagonal of Decagon across Three Sides

LaTeX Go Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*Side of Decagon

Diagonal of Decagon across Three Sides given Inradius Formula

LaTeX Go

Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5)))
d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_i)/sqrt(5+(2*sqrt(5)))

What is a Decagon?

Decagon is a polygon with ten sides and ten vertices. A decagon, like any other polygon, can be either convex or concave, as illustrated in the next figure. A convex decagon has none of its interior angles greater than 180°. To the contrary, a concave decagon (or polygon) has one or more of its interior angles greater than 180°. A decagon is called regular when its sides are equal and also its interior angles are equal.

How to Calculate Diagonal of Decagon across Three Sides given Inradius?

Diagonal of Decagon across Three Sides given Inradius calculator uses Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))) to calculate the Diagonal across Three Sides of Decagon, The Diagonal of Decagon across Three Sides given Inradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using inradius. Diagonal across Three Sides of Decagon is denoted by d₃ symbol.

How to calculate Diagonal of Decagon across Three Sides given Inradius using this online calculator? To use this online calculator for Diagonal of Decagon across Three Sides given Inradius, enter Inradius of Decagon (r_i) and hit the calculate button. Here is how the Diagonal of Decagon across Three Sides given Inradius calculation can be explained with given input values -> 25.51952 = sqrt(14+(6*sqrt(5)))/2*(2*15)/sqrt(5+(2*sqrt(5))).

FAQ

What is Diagonal of Decagon across Three Sides given Inradius?

The Diagonal of Decagon across Three Sides given Inradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using inradius and is represented as d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_i)/sqrt(5+(2*sqrt(5))) or Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))). Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

How to calculate Diagonal of Decagon across Three Sides given Inradius?

The Diagonal of Decagon across Three Sides given Inradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using inradius is calculated using Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Inradius of Decagon)/sqrt(5+(2*sqrt(5))). To calculate Diagonal of Decagon across Three Sides given Inradius, you need Inradius of Decagon (r_i). With our tool, you need to enter the respective value for Inradius of Decagon 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 Diagonal across Three Sides of Decagon?

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

Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*Side of Decagon
Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5))
Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*Diagonal across Four Sides of Decagon/sqrt(5+(2*sqrt(5)))

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