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Face Diagonal of Dodecahedron given Total Surface Area Formula

GoFace Diagonal of Dodecahedron Formula

GoFace Diagonal of Dodecahedron given Insphere Radius Formula

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The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron. Check FAQs

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

d_Face - Face Diagonal of Dodecahedron?TSA - Total Surface Area of Dodecahedron?

Face Diagonal of Dodecahedron given Total Surface Area Example

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

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

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

16.3186 = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

16.3186m = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2100m²}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

16.3186 = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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Face Diagonal of Dodecahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{TSA}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2100m²}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2100}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

d Face = 16.3185729940655m

LAST Step Rounding Answer

∴

d Face = 16.3186m

Face Diagonal of Dodecahedron given Total Surface Area Formula Elements

Variables

Functions

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

Total Surface Area of Dodecahedron

Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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 Diagonal of Dodecahedron

Go Face Diagonal of Dodecahedron

d Face = (\frac{1 + \sqrt{5}}{2}) \cdot l e

Go Face Diagonal of Dodecahedron given Insphere Radius

d Face = (1 + \sqrt{5}) \cdot \frac{r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}}

Other formulas in Face Diagonal of Dodecahedron category

Go Space Diagonal of Dodecahedron

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{l e}{2}

Go Space Diagonal of Dodecahedron given Lateral Surface Area

d Space = \frac{\sqrt{3} \cdot (1 + \sqrt{5})}{2} \cdot \sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Space Diagonal of Dodecahedron given Perimeter

d Space = \sqrt{3} \cdot (1 + \sqrt{5}) \cdot \frac{P}{60}

How to Evaluate Face Diagonal of Dodecahedron given Total Surface Area?

Face Diagonal of Dodecahedron given Total Surface Area evaluator uses Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))) to evaluate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Total Surface Area formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using total surface area of Dodecahedron. Face Diagonal of Dodecahedron is denoted by d_Face symbol.

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

FAQs on Face Diagonal of Dodecahedron given Total Surface Area

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

The formula of Face Diagonal of Dodecahedron given Total Surface Area is expressed as Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))). Here is an example- 16.31857 = (1+sqrt(5))/2*sqrt(2100/(3*sqrt(25+(10*sqrt(5))))).

How to calculate Face Diagonal of Dodecahedron given Total Surface Area?

With Total Surface Area of Dodecahedron (TSA) we can find Face Diagonal of Dodecahedron given Total Surface Area using the formula - Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Face Diagonal of Dodecahedron?

Here are the different ways to Calculate Face Diagonal of Dodecahedron-

Face Diagonal of Dodecahedron=((1+sqrt(5))/2)*Edge Length of Dodecahedron
Face Diagonal of Dodecahedron=(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)

Can the Face Diagonal of Dodecahedron given Total Surface Area be negative?

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

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

Face Diagonal of Dodecahedron given Total Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Face Diagonal of Dodecahedron given Total Surface Area can be measured.

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