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Face Area of Dodecahedron given Space Diagonal Formula

GoFace Area of Dodecahedron Formula

GoFace Area of Dodecahedron given Circumsphere Radius Formula

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

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

A_Face - Face Area of Dodecahedron?d_Space - Space Diagonal of Dodecahedron?

Face Area of Dodecahedron given Space Diagonal Example

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

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

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

171.7388 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

171.7388m² = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

171.7388 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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Face Area of Dodecahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Substitute values of Variables

∴

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

A Face = 171.738829958917m²

LAST Step Rounding Answer

∴

A Face = 171.7388m²

Face Area of Dodecahedron given Space Diagonal Formula Elements

Variables

Functions

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

Space Diagonal of Dodecahedron

The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal 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 Area of Dodecahedron

Go Face Area of Dodecahedron

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

Go Face Area of Dodecahedron given Circumsphere Radius

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Go Face Area of Dodecahedron given Total Surface Area

A Face = \frac{TSA}{12}

Go Face Area of Dodecahedron given Face Diagonal

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

How to Evaluate Face Area of Dodecahedron given Space Diagonal?

Face Area of Dodecahedron given Space Diagonal evaluator uses Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2 to evaluate the Face Area of Dodecahedron, The Face Area of Dodecahedron given Space Diagonal formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using space diagonal of Dodecahedron. Face Area of Dodecahedron is denoted by A_Face symbol.

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

FAQs on Face Area of Dodecahedron given Space Diagonal

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

The formula of Face Area of Dodecahedron given Space Diagonal is expressed as Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. Here is an example- 171.7388 = 1/4*sqrt(25+(10*sqrt(5)))*((2*28)/(sqrt(3)*(1+sqrt(5))))^2.

How to calculate Face Area of Dodecahedron given Space Diagonal?

With Space Diagonal of Dodecahedron (d_Space) we can find Face Area of Dodecahedron given Space Diagonal using the formula - Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Face Area of Dodecahedron=1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Face Area of Dodecahedron=1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Face Area of Dodecahedron=Total Surface Area of Dodecahedron/12

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

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

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

Face Area of Dodecahedron given Space Diagonal is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Face Area of Dodecahedron given Space Diagonal can be measured.

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