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Inradius of Decagon given Diagonal across Five Sides Formula

GoInradius of Decagon Formula

GoInradius of Decagon given Diagonal across Four Sides Formula

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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. Check FAQs

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{d 5}{1 + \sqrt{5}}

r_i - Inradius of Decagon?d₅ - Diagonal across Five Sides of Decagon?

Inradius of Decagon given Diagonal across Five Sides Example

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Here is how the Inradius of Decagon given Diagonal across Five Sides equation looks like with Values.

Here is how the Inradius of Decagon given Diagonal across Five Sides equation looks like with Units.

Here is how the Inradius of Decagon given Diagonal across Five Sides equation looks like.

15.2169 = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{32}{1 + \sqrt{5}}

15.2169m = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{32m}{1 + \sqrt{5}}

15.2169 = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{32}{1 + \sqrt{5}}

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2D Geometry » fx Inradius of Decagon given Diagonal across Five Sides

Inradius of Decagon given Diagonal across Five Sides Solution

Follow our step by step solution on how to calculate Inradius of Decagon given Diagonal across Five Sides?

FIRST Step Consider the formula

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{d 5}{1 + \sqrt{5}}

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{32m}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{32}{1 + \sqrt{5}}

Next Step Evaluate

∴

r i = 15.2169042607225m

LAST Step Rounding Answer

∴

r i = 15.2169m

Inradius of Decagon given Diagonal across Five Sides Formula Elements

Variables

Functions

Inradius of Decagon

Inradius of Decagon is the length of the straight line from the center to any point on the incircle of the Decagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Decagon

Diagonal across Five Sides of Decagon

Diagonal across Five Sides of Decagon is a straight line joining two opposite sides which is across five sides of the Decagon.

Symbol: d₅

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Five Sides of Decagon

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.

Syntax: sqrt(Number)

Other Formulas to find Inradius of Decagon

Go Inradius of Decagon

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot S

Go Inradius of Decagon given Diagonal across Four Sides

r i = \frac{d 4}{2}

Go Inradius of Decagon given Diagonal across Three Sides

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot d 3}{\sqrt{14 + (6 \cdot \sqrt{5})}}

Go Inradius of Decagon given Diagonal across Two Sides

r i = \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{2} \cdot \frac{2 \cdot d 2}{\sqrt{10 + (2 \cdot \sqrt{5})}}

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

Inradius of Decagon given Diagonal across Five Sides evaluator uses Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5)) to evaluate 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 evaluate Inradius of Decagon given Diagonal across Five Sides using this online evaluator? To use this online evaluator for Inradius of Decagon given Diagonal across Five Sides, enter Diagonal across Five Sides of Decagon (d₅) and hit the calculate button.

FAQs on Inradius of Decagon given Diagonal across Five Sides

What is the formula to find Inradius of Decagon given Diagonal across Five Sides?

The formula of Inradius of Decagon given Diagonal across Five Sides is expressed as Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5)). Here is an example- 15.2169 = sqrt(5+(2*sqrt(5)))/2*32/(1+sqrt(5)).

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

With Diagonal across Five Sides of Decagon (d₅) we can find Inradius of Decagon given Diagonal across Five Sides using the formula - Inradius of Decagon = sqrt(5+(2*sqrt(5)))/2*Diagonal across Five Sides of Decagon/(1+sqrt(5)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Decagon?

Here are the different ways to Calculate Inradius of Decagon-

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)))

Can the Inradius of Decagon given Diagonal across Five Sides be negative?

No, the Inradius of Decagon given Diagonal across Five Sides, measured in Length cannot be negative.

Which unit is used to measure Inradius of Decagon given Diagonal across Five Sides?

Inradius of Decagon given Diagonal across Five Sides is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Decagon given Diagonal across Five Sides can be measured.

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