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Diagonal of Pentagon given Inradius Formula

GoDiagonal of Pentagon given Circumradius Formula

GoDiagonal of Pentagon Formula

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Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon. Check FAQs

d = 5 \cdot r i \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

d - Diagonal of Pentagon?r_i - Inradius of Pentagon?

Diagonal of Pentagon given Inradius Example

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Here is how the Diagonal of Pentagon given Inradius equation looks like with Values.

Here is how the Diagonal of Pentagon given Inradius equation looks like with Units.

Here is how the Diagonal of Pentagon given Inradius equation looks like.

16.458 = 5 \cdot 7 \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

16.458m = 5 \cdot 7m \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

16.458 = 5 \cdot 7 \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

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Diagonal of Pentagon given Inradius Solution

Follow our step by step solution on how to calculate Diagonal of Pentagon given Inradius?

FIRST Step Consider the formula

d = 5 \cdot r i \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

d = 5 \cdot 7m \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

d = 5 \cdot 7 \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Evaluate

∴

d = 16.4579870641892m

LAST Step Rounding Answer

∴

d = 16.458m

Diagonal of Pentagon given Inradius Formula Elements

Variables

Functions

Diagonal of Pentagon

Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Pentagon

Inradius of Pentagon

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

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 Diagonal of Pentagon

Go Diagonal of Pentagon given Circumradius

d = \frac{r c}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

Go Diagonal of Pentagon

d = (1 + \sqrt{5}) \cdot \frac{l e}{2}

Go Diagonal of Pentagon given Area

d = (1 + \sqrt{5}) \cdot \sqrt{\frac{A}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Diagonal of Pentagon given Perimeter

d = (1 + \sqrt{5}) \cdot \frac{P}{10}

How to Evaluate Diagonal of Pentagon given Inradius?

Diagonal of Pentagon given Inradius evaluator uses Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))) to evaluate the Diagonal of Pentagon, The Diagonal of Pentagon given Inradius formula is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using inradius. Diagonal of Pentagon is denoted by d symbol.

How to evaluate Diagonal of Pentagon given Inradius using this online evaluator? To use this online evaluator for Diagonal of Pentagon given Inradius, enter Inradius of Pentagon (r_i) and hit the calculate button.

FAQs on Diagonal of Pentagon given Inradius

What is the formula to find Diagonal of Pentagon given Inradius?

The formula of Diagonal of Pentagon given Inradius is expressed as Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))). Here is an example- 16.45799 = 5*7*(1+sqrt(5))/sqrt(25+(10*sqrt(5))).

How to calculate Diagonal of Pentagon given Inradius?

With Inradius of Pentagon (r_i) we can find Diagonal of Pentagon given Inradius using the formula - Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Diagonal of Pentagon?

Here are the different ways to Calculate Diagonal of Pentagon-

Diagonal of Pentagon=Circumradius of Pentagon/(sqrt((5-sqrt(5))/10))
Diagonal of Pentagon=(1+sqrt(5))*Edge Length of Pentagon/2
Diagonal of Pentagon=(1+sqrt(5))*sqrt(Area of Pentagon/sqrt(25+(10*sqrt(5))))

Can the Diagonal of Pentagon given Inradius be negative?

No, the Diagonal of Pentagon given Inradius, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Pentagon given Inradius?

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

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