Diagonal of Decagon across Four Sides given Circumradius Calculator

✖Diagonal across Four Sides of Decagon is a straight line joining two non-adjacent sides which is across four sides of the Decagon.ⓘ Diagonal of Decagon across Four Sides given Circumradius [d₄]

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Formula

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Diagonal of Decagon across Four Sides given Circumradius

Formula

`"d"_{"4"} = sqrt(5+(2*sqrt(5)))*(2*"r"_{"c"})/(1+sqrt(5))`

Example

`"30.43381m"=sqrt(5+(2*sqrt(5)))*(2*"16m")/(1+sqrt(5))`

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Diagonal of Decagon across Four Sides given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Circumradius of Decagon)/(1+sqrt(5))
d₄ = sqrt(5+(2*sqrt(5)))*(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 Four Sides of Decagon - (Measured in Meter) - Diagonal across Four Sides of Decagon is a straight line joining two non-adjacent sides which is across four 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

d₄ = sqrt(5+(2*sqrt(5)))*(2*r_c)/(1+sqrt(5)) --> sqrt(5+(2*sqrt(5)))*(2*16)/(1+sqrt(5))

Evaluating ... ...

d₄ = 30.4338085214449

STEP 3: Convert Result to Output's Unit

30.4338085214449 Meter --> No Conversion Required

FINAL ANSWER

30.4338085214449 ≈ 30.43381 Meter <-- Diagonal across Four Sides of Decagon

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 10+ Diagonal of Decagon across Four Sides Calculators

Diagonal of Decagon across Four Sides given Area

Go Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*sqrt((2*Area of Decagon)/(5*sqrt(5+(2*sqrt(5)))))

Diagonal of Decagon across Four Sides given Diagonal across Three Sides

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

Diagonal of Decagon across Four Sides given Diagonal across Two Sides

Go Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(2*sqrt(5)))

Diagonal of Decagon across Four Sides given Diagonal across Five Sides

Go Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Diagonal across Five Sides of Decagon/(1+sqrt(5))

Diagonal of Decagon across Four Sides given Circumradius

Go Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Circumradius of Decagon)/(1+sqrt(5))

Diagonal of Decagon across Four Sides given Width

Go Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Width of Decagon/(1+sqrt(5))

Diagonal of Decagon across Four Sides given Perimeter

Go Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Perimeter of Decagon/10

Diagonal of Decagon across Four Sides

Go Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Side of Decagon

Diagonal of Decagon across Four Sides given Inradius

Go Diagonal across Four Sides of Decagon = (2*Inradius of Decagon)

Diagonal of Decagon across Four Sides given Height

Go Diagonal across Four Sides of Decagon = 1*Height of Decagon

Diagonal of Decagon across Four Sides given Circumradius Formula

Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Circumradius of Decagon)/(1+sqrt(5))
d₄ = sqrt(5+(2*sqrt(5)))*(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 Four Sides given Circumradius?

Diagonal of Decagon across Four Sides given Circumradius calculator uses Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Circumradius of Decagon)/(1+sqrt(5)) to calculate the Diagonal across Four Sides of Decagon, The Diagonal of Decagon across Four Sides given Circumradius formula is defined as the straight line joining two non-adjacent vertices across the four sides of the Decagon, calculated using circumradius. Diagonal across Four Sides of Decagon is denoted by d₄ symbol.

How to calculate Diagonal of Decagon across Four Sides given Circumradius using this online calculator? To use this online calculator for Diagonal of Decagon across Four Sides given Circumradius, enter Circumradius of Decagon (r_c) and hit the calculate button. Here is how the Diagonal of Decagon across Four Sides given Circumradius calculation can be explained with given input values -> 30.43381 = sqrt(5+(2*sqrt(5)))*(2*16)/(1+sqrt(5)).

FAQ

What is Diagonal of Decagon across Four Sides given Circumradius?

The Diagonal of Decagon across Four Sides given Circumradius formula is defined as the straight line joining two non-adjacent vertices across the four sides of the Decagon, calculated using circumradius and is represented as d₄ = sqrt(5+(2*sqrt(5)))*(2*r_c)/(1+sqrt(5)) or Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(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 Four Sides given Circumradius?

The Diagonal of Decagon across Four Sides given Circumradius formula is defined as the straight line joining two non-adjacent vertices across the four sides of the Decagon, calculated using circumradius is calculated using Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Circumradius of Decagon)/(1+sqrt(5)). To calculate Diagonal of Decagon across Four 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 Four Sides of Decagon?

In this formula, Diagonal across Four Sides of Decagon uses Circumradius of Decagon. We can use 9 other way(s) to calculate the same, which is/are as follows -

Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Side of Decagon
Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Diagonal across Five Sides of Decagon/(1+sqrt(5))
Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Diagonal across Three Sides of Decagon)/sqrt(14+(6*sqrt(5)))
Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*(2*Diagonal across Two Sides of Decagon)/sqrt(10+(2*sqrt(5)))
Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Perimeter of Decagon/10
Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*sqrt((2*Area of Decagon)/(5*sqrt(5+(2*sqrt(5)))))
Diagonal across Four Sides of Decagon = 1*Height of Decagon
Diagonal across Four Sides of Decagon = (2*Inradius of Decagon)
Diagonal across Four Sides of Decagon = sqrt(5+(2*sqrt(5)))*Width of Decagon/(1+sqrt(5))

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