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Face Area of Dodecahedron given Circumsphere Radius Formula

GoFace Area of Dodecahedron Formula

GoFace Area of Dodecahedron given Total Surface Area 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{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

A_Face - Face Area of Dodecahedron?r_c - Circumsphere Radius of Dodecahedron?

Face Area of Dodecahedron given Circumsphere Radius Example

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

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

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

171.7388 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

171.7388m² = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

171.7388 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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Face Area of Dodecahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14m}{\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{4 \cdot 14}{\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 Circumsphere Radius 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

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius 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 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}

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 Circumsphere Radius?

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

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

FAQs on Face Area of Dodecahedron given Circumsphere Radius

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

The formula of Face Area of Dodecahedron given Circumsphere Radius is expressed as Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. Here is an example- 171.7388 = 1/4*sqrt(25+(10*sqrt(5)))*((4*14)/(sqrt(3)*(1+sqrt(5))))^2.

How to calculate Face Area of Dodecahedron given Circumsphere Radius?

With Circumsphere Radius of Dodecahedron (r_c) we can find Face Area of Dodecahedron given Circumsphere Radius using the formula - Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius 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=Total Surface Area of Dodecahedron/12
Face Area of Dodecahedron=1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2

Can the Face Area of Dodecahedron given Circumsphere Radius be negative?

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

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

Face Area of Dodecahedron given Circumsphere Radius 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 Circumsphere Radius can be measured.

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