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Face Area of Icosahedron given Circumsphere Radius Formula

GoFace Area of Icosahedron Formula

GoFace Area of Icosahedron given Total Surface Area Formula

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

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

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

Face Area of Icosahedron given Circumsphere Radius Example

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

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

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

38.7769 = \frac{\sqrt{3}}{4} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

38.7769m² = \frac{\sqrt{3}}{4} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

38.7769 = \frac{\sqrt{3}}{4} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

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Face Area of Icosahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A Face = \frac{\sqrt{3}}{4} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Prepare to Evaluate

∴

A Face = \frac{\sqrt{3}}{4} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Evaluate

∴

A Face = 38.7768926022595m²

LAST Step Rounding Answer

∴

A Face = 38.7769m²

Face Area of Icosahedron given Circumsphere Radius Formula Elements

Variables

Functions

Face Area of Icosahedron

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

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area of Icosahedron

Circumsphere Radius of Icosahedron

Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron 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 Icosahedron

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 Icosahedron

Go Face Area of Icosahedron

A Face = \frac{\sqrt{3}}{4} \cdot {l e}^{2}

Go Face Area of Icosahedron given Total Surface Area

A Face = \frac{TSA}{20}

Other formulas in Face Area of Icosahedron category

Go Lateral Surface Area of Icosahedron

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {l e}^{2}

Go Lateral Surface Area of Icosahedron given Total Surface Area

LSA = \frac{9}{10} \cdot TSA

Go Lateral Surface Area of Icosahedron given Volume

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{\frac{12}{5} \cdot V}{3 + \sqrt{5}})}^{\frac{2}{3}}

Go Total Surface Area of Icosahedron

TSA = 5 \cdot \sqrt{3} \cdot {l e}^{2}

How to Evaluate Face Area of Icosahedron given Circumsphere Radius?

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

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

FAQs on Face Area of Icosahedron given Circumsphere Radius

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

The formula of Face Area of Icosahedron given Circumsphere Radius is expressed as Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. Here is an example- 38.77689 = sqrt(3)/4*((4*9)/(sqrt(10+(2*sqrt(5)))))^2.

How to calculate Face Area of Icosahedron given Circumsphere Radius?

With Circumsphere Radius of Icosahedron (r_c) we can find Face Area of Icosahedron given Circumsphere Radius using the formula - Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Face Area of Icosahedron=sqrt(3)/4*Edge Length of Icosahedron^2
Face Area of Icosahedron=Total Surface Area of Icosahedron/20

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

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

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

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

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