Inradius of Decagon 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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✖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 Circumradius [r_i]

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Inradius of Decagon given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5))
r_i = sqrt(5+(2*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

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.
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

r_i = sqrt(5+(2*sqrt(5)))/2*(2*r_c)/(1+sqrt(5)) --> sqrt(5+(2*sqrt(5)))/2*(2*16)/(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 00.004 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 Circumradius Formula

LaTeX Go

Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5))
r_i = sqrt(5+(2*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 Inradius of Decagon given Circumradius?

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

How to calculate Inradius of Decagon given Circumradius using this online calculator? To use this online calculator for Inradius of Decagon given Circumradius, enter Circumradius of Decagon (r_c) and hit the calculate button. Here is how the Inradius of Decagon given Circumradius calculation can be explained with given input values -> 15.2169 = sqrt(5+(2*sqrt(5)))/2*(2*16)/(1+sqrt(5)).

FAQ

What is Inradius of Decagon given Circumradius?

The Inradius of Decagon given Circumradius formula is defined as the length of the straight line from the center to any point on the incircle of the Decagon, calculated using circumradius and is represented as r_i = sqrt(5+(2*sqrt(5)))/2*(2*r_c)/(1+sqrt(5)) or Inradius of Decagon = sqrt(5+(2*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 Inradius of Decagon given Circumradius?

The Inradius of Decagon given Circumradius formula is defined as the length of the straight line from the center to any point on the incircle of the Decagon, calculated using circumradius is calculated using Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*(2*Circumradius of Decagon)/(1+sqrt(5)). To calculate Inradius of Decagon 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 Inradius of Decagon?

In this formula, Inradius of Decagon uses Circumradius 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 = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5))
Inradius of Decagon = Diagonal across Four Sides of Decagon/2

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