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Face Diagonal of Dodecahedron given Face Area Formula

GoFace Diagonal of Dodecahedron Formula

GoFace Diagonal of Dodecahedron given Volume Formula

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The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron. Check FAQs

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

d_Face - Face Diagonal of Dodecahedron?A_Face - Face Area of Dodecahedron?

Face Diagonal of Dodecahedron given Face Area Example

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Here is how the Face Diagonal of Dodecahedron given Face Area equation looks like with Values.

Here is how the Face Diagonal of Dodecahedron given Face Area equation looks like with Units.

Here is how the Face Diagonal of Dodecahedron given Face Area equation looks like.

16.3186 = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

16.3186m = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

16.3186 = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

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Face Diagonal of Dodecahedron given Face Area Solution

Follow our step by step solution on how to calculate Face Diagonal of Dodecahedron given Face Area?

FIRST Step Consider the formula

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot 175m²}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot 175}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

d Face = 16.3185729940655m

LAST Step Rounding Answer

∴

d Face = 16.3186m

Face Diagonal of Dodecahedron given Face Area Formula Elements

Variables

Functions

Face Diagonal of Dodecahedron

The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.

Symbol: d_Face

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Face Diagonal of Dodecahedron

Face Area of Dodecahedron

The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area of Dodecahedron

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 Face Diagonal of Dodecahedron

Go Face Diagonal of Dodecahedron

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

Go Face Diagonal of Dodecahedron given Volume

d Face = \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Face Diagonal of Dodecahedron given Total Surface Area

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Face Diagonal of Dodecahedron given Circumsphere Radius

d Face = \frac{2}{\sqrt{3}} \cdot r c

How to Evaluate Face Diagonal of Dodecahedron given Face Area?

Face Diagonal of Dodecahedron given Face Area evaluator uses Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5))))) to evaluate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Face Area formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using face area of Dodecahedron. Face Diagonal of Dodecahedron is denoted by d_Face symbol.

How to evaluate Face Diagonal of Dodecahedron given Face Area using this online evaluator? To use this online evaluator for Face Diagonal of Dodecahedron given Face Area, enter Face Area of Dodecahedron (A_Face) and hit the calculate button.

FAQs on Face Diagonal of Dodecahedron given Face Area

What is the formula to find Face Diagonal of Dodecahedron given Face Area?

The formula of Face Diagonal of Dodecahedron given Face Area is expressed as Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5))))). Here is an example- 16.31857 = (1+sqrt(5))/2*sqrt((4*175)/(sqrt(25+(10*sqrt(5))))).

How to calculate Face Diagonal of Dodecahedron given Face Area?

With Face Area of Dodecahedron (A_Face) we can find Face Diagonal of Dodecahedron given Face Area using the formula - Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Face Diagonal of Dodecahedron?

Here are the different ways to Calculate Face Diagonal of Dodecahedron-

Face Diagonal of Dodecahedron=((1+sqrt(5))/2)*Edge Length of Dodecahedron
Face Diagonal of Dodecahedron=(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Face Diagonal of Dodecahedron=(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

Can the Face Diagonal of Dodecahedron given Face Area be negative?

No, the Face Diagonal of Dodecahedron given Face Area, measured in Length cannot be negative.

Which unit is used to measure Face Diagonal of Dodecahedron given Face Area?

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

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