Diagonal of Decagon across Three Sides given Circumradius Calculator

✖Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.ⓘ Circumradius of Decagon [r_c]

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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 Circumradius [d₃]

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Diagonal of Decagon across Three Sides given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5))
d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_c)/(1+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.
Circumradius of Decagon - (Measured in Meter) - Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Decagon: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_c)/(1+sqrt(5)) --> sqrt(14+(6*sqrt(5)))/2*(2*16)/(1+sqrt(5))

Evaluating ... ...

d₃ = 25.8885438199983

STEP 3: Convert Result to Output's Unit

25.8885438199983 Meter --> No Conversion Required

FINAL ANSWER

25.8885438199983 ≈ 25.88854 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 Circumradius Formula

LaTeX Go

Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5))
d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_c)/(1+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 Circumradius?

Diagonal of Decagon across Three Sides given Circumradius calculator uses Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)) to calculate the Diagonal across Three Sides of Decagon, The Diagonal of Decagon across Three Sides given Circumradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using circumradius. Diagonal across Three Sides of Decagon is denoted by d₃ symbol.

How to calculate Diagonal of Decagon across Three Sides given Circumradius using this online calculator? To use this online calculator for Diagonal of Decagon across Three Sides given Circumradius, enter Circumradius of Decagon (r_c) and hit the calculate button. Here is how the Diagonal of Decagon across Three Sides given Circumradius calculation can be explained with given input values -> 25.88854 = sqrt(14+(6*sqrt(5)))/2*(2*16)/(1+sqrt(5)).

FAQ

What is Diagonal of Decagon across Three Sides given Circumradius?

The Diagonal of Decagon across Three Sides given Circumradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using circumradius and is represented as d₃ = sqrt(14+(6*sqrt(5)))/2*(2*r_c)/(1+sqrt(5)) or Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)). Circumradius of Decagon is the radius of a circumcircle touching each of the Decagon's vertices.

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

The Diagonal of Decagon across Three Sides given Circumradius formula is defined as the straight line joining two non-adjacent vertices across the three sides of the Decagon, calculated using circumradius is calculated using Diagonal across Three Sides of Decagon = sqrt(14+(6*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)). To calculate Diagonal of Decagon across Three Sides given Circumradius, you need Circumradius of Decagon (r_c). With our tool, you need to enter the respective value for Circumradius 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 Circumradius 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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