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Face Area of Dodecahedron given Insphere Radius 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 r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

A_Face - Face Area of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Face Area of Dodecahedron given Insphere Radius Example

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

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

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

167.8963 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

167.8963m² = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

167.8963 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

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Face Area of Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Substitute values of Variables

∴

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Prepare to Evaluate

∴

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Evaluate

∴

A Face = 167.896303612594m²

LAST Step Rounding Answer

∴

A Face = 167.8963m²

Face Area of Dodecahedron given Insphere 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

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere 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 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 Insphere Radius?

Face Area of Dodecahedron given Insphere Radius evaluator uses Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2 to evaluate the Face Area of Dodecahedron, The Face Area of Dodecahedron given Insphere Radius formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using insphere radius of Dodecahedron. Face Area of Dodecahedron is denoted by A_Face symbol.

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

FAQs on Face Area of Dodecahedron given Insphere Radius

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

The formula of Face Area of Dodecahedron given Insphere Radius is expressed as Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2. Here is an example- 167.8963 = 1/4*sqrt(25+(10*sqrt(5)))*((2*11)/(sqrt((25+(11*sqrt(5)))/10)))^2.

How to calculate Face Area of Dodecahedron given Insphere Radius?

With Insphere Radius of Dodecahedron (r_i) we can find Face Area of Dodecahedron given Insphere Radius using the formula - Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^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 Insphere Radius be negative?

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

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

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

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