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Face Area of Dodecahedron given Face 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 Face}{1 + \sqrt{5}})}^{2}

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

Face Area of Dodecahedron given Face Diagonal Example

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

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

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

168.234 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

168.234m² = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{2}

168.234 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

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Face Area of Dodecahedron given Face Diagonal Solution

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

FIRST Step Consider the formula

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Face}{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 16m}{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 16}{1 + \sqrt{5}})}^{2}

Next Step Evaluate

∴

A Face = 168.233955878123m²

LAST Step Rounding Answer

∴

A Face = 168.234m²

Face Area of Dodecahedron given Face 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

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

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 Perimeter

A Face = \frac{1}{100} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {P Face}^{2}

How to Evaluate Face Area of Dodecahedron given Face Diagonal?

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

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

FAQs on Face Area of Dodecahedron given Face Diagonal

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

The formula of Face Area of Dodecahedron given Face Diagonal is expressed as Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2. Here is an example- 168.234 = 1/4*sqrt(25+(10*sqrt(5)))*((2*16)/(1+sqrt(5)))^2.

How to calculate Face Area of Dodecahedron given Face Diagonal?

With Face Diagonal of Dodecahedron (d_Face) we can find Face Area of Dodecahedron given Face Diagonal using the formula - Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(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 Face Diagonal be negative?

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

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

Face Area of Dodecahedron given Face 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 Face Diagonal can be measured.

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