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Face Area of Icosahedron given Space Diagonal Formula

GoFace Area of Icosahedron Formula

GoFace Area of Icosahedron given Midsphere Radius 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{2 \cdot d Space}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

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

Face Area of Icosahedron given Space Diagonal Example

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

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

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

43.2051 = \frac{\sqrt{3}}{4} \cdot {(\frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

43.2051m² = \frac{\sqrt{3}}{4} \cdot {(\frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

43.2051 = \frac{\sqrt{3}}{4} \cdot {(\frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

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Face Area of Icosahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A Face = \frac{\sqrt{3}}{4} \cdot {(\frac{2 \cdot 19m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Prepare to Evaluate

∴

A Face = \frac{\sqrt{3}}{4} \cdot {(\frac{2 \cdot 19}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Evaluate

∴

A Face = 43.2051179920237m²

LAST Step Rounding Answer

∴

A Face = 43.2051m²

Face Area of Icosahedron given Space Diagonal 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

Space Diagonal of Icosahedron

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

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal 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 Midsphere Radius

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

Go Face Area of Icosahedron given Insphere Radius

A Face = \frac{\sqrt{3}}{4} \cdot {(\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Go Face Area of Icosahedron given Circumsphere Radius

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

How to Evaluate Face Area of Icosahedron given Space Diagonal?

Face Area of Icosahedron given Space Diagonal evaluator uses Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2 to evaluate the Face Area of Icosahedron, The Face Area of Icosahedron given Space Diagonal 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 space diagonal of the Icosahedron. Face Area of Icosahedron is denoted by A_Face symbol.

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

FAQs on Face Area of Icosahedron given Space Diagonal

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

The formula of Face Area of Icosahedron given Space Diagonal is expressed as Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. Here is an example- 43.20512 = sqrt(3)/4*((2*19)/(sqrt(10+(2*sqrt(5)))))^2.

How to calculate Face Area of Icosahedron given Space Diagonal?

With Space Diagonal of Icosahedron (d_Space) we can find Face Area of Icosahedron given Space Diagonal using the formula - Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal 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=sqrt(3)/4*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
Face Area of Icosahedron=sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2

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

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

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

Face Area of Icosahedron 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 Icosahedron given Space Diagonal can be measured.

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