Inradius of Decagon given Diagonal across Five Sides Calculator

✖Diagonal across Five Sides of Decagon is a straight line joining two opposite sides which is across five sides of the Decagon.ⓘ Diagonal across Five Sides of Decagon [d₅]

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✖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 given Diagonal across Five Sides [r_i]

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Inradius of Decagon given Diagonal across Five Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5))
r_i = sqrt(5+(2*sqrt(5)))/2*d₅/(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

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.
Diagonal across Five Sides of Decagon - (Measured in Meter) - Diagonal across Five Sides of Decagon is a straight line joining two opposite sides which is across five sides of the Decagon.

STEP 1: Convert Input(s) to Base Unit

Diagonal across Five Sides of Decagon: 32 Meter --> 32 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = sqrt(5+(2*sqrt(5)))/2*d₅/(1+sqrt(5)) --> sqrt(5+(2*sqrt(5)))/2*32/(1+sqrt(5))

Evaluating ... ...

r_i = 15.2169042607225

STEP 3: Convert Result to Output's Unit

15.2169042607225 Meter --> No Conversion Required

FINAL ANSWER

15.2169042607225 ≈ 15.2169 Meter <-- Inradius of Decagon

(Calculation completed in 00.007 seconds)

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< Inradius of Decagon Calculators

Inradius of Decagon given Diagonal across Three Sides

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

Inradius of Decagon given Diagonal across Five Sides

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

Inradius of Decagon

LaTeX Go Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Side of Decagon

Inradius of Decagon given Diagonal across Four Sides

LaTeX Go Inradius of Decagon = Diagonal across Four Sides of Decagon/2

Inradius of Decagon given Diagonal across Five Sides Formula

LaTeX Go

Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5))
r_i = sqrt(5+(2*sqrt(5)))/2*d₅/(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 Inradius of Decagon given Diagonal across Five Sides?

Inradius of Decagon given Diagonal across Five Sides calculator uses Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5)) to calculate the Inradius of Decagon, The Inradius of Decagon given Diagonal across Five Sides formula is defined as the length of the straight line from the center to any point on the incircle of the Decagon, calculated using a diagonal across five sides. Inradius of Decagon is denoted by r_i symbol.

How to calculate Inradius of Decagon given Diagonal across Five Sides using this online calculator? To use this online calculator for Inradius of Decagon given Diagonal across Five Sides, enter Diagonal across Five Sides of Decagon (d₅) and hit the calculate button. Here is how the Inradius of Decagon given Diagonal across Five Sides calculation can be explained with given input values -> 15.2169 = sqrt(5+(2*sqrt(5)))/2*32/(1+sqrt(5)).

FAQ

What is Inradius of Decagon given Diagonal across Five Sides?

The Inradius of Decagon given Diagonal across Five Sides formula is defined as the length of the straight line from the center to any point on the incircle of the Decagon, calculated using a diagonal across five sides and is represented as r_i = sqrt(5+(2*sqrt(5)))/2*d₅/(1+sqrt(5)) or Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5)). Diagonal across Five Sides of Decagon is a straight line joining two opposite sides which is across five sides of the Decagon.

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

The Inradius of Decagon given Diagonal across Five Sides formula is defined as the length of the straight line from the center to any point on the incircle of the Decagon, calculated using a diagonal across five sides is calculated using Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5)). To calculate Inradius of Decagon given Diagonal across Five Sides, you need Diagonal across Five Sides of Decagon (d₅). With our tool, you need to enter the respective value for Diagonal across Five Sides 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 Inradius of Decagon?

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

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

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