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Space Diagonal of Dodecahedron given Face Area Formula

GoSpace Diagonal of Dodecahedron Formula

GoSpace Diagonal of Dodecahedron given Volume Formula

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

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot A Face}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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

Space Diagonal of Dodecahedron given Face Area Example

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

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

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

28.2646 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot 175}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

28.2646m = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot 175m²}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

28.2646 = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot 175}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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Space Diagonal of Dodecahedron given Face Area Solution

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

FIRST Step Consider the formula

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot A Face}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot 175m²}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{12 \cdot 175}{3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

d Space = 28.2645975327428m

LAST Step Rounding Answer

∴

d Space = 28.2646m

Space Diagonal of Dodecahedron given Face Area Formula Elements

Variables

Functions

Space Diagonal of Dodecahedron

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

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of Dodecahedron

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

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 Space Diagonal of Dodecahedron

Go Space Diagonal of Dodecahedron

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

Go Space Diagonal of Dodecahedron given Volume

d Space = \sqrt{3} \cdot \frac{1 + \sqrt{5}}{2} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{1}{3}}

Go Space Diagonal of Dodecahedron given Total Surface Area

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

Go Space Diagonal of Dodecahedron given Circumsphere Radius

d Space = 2 \cdot r c

How to Evaluate Space Diagonal of Dodecahedron given Face Area?

Space Diagonal of Dodecahedron given Face Area evaluator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5))))) to evaluate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Face Area formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using face area of Dodecahedron. Space Diagonal of Dodecahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Dodecahedron given Face Area

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

The formula of Space Diagonal of Dodecahedron given Face Area is expressed as Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5))))). Here is an example- 28.2646 = sqrt(3)*(1+sqrt(5))/2*sqrt((12*175)/(3*sqrt(25+(10*sqrt(5))))).

How to calculate Space Diagonal of Dodecahedron given Face Area?

With Face Area of Dodecahedron (A_Face) we can find Space Diagonal of Dodecahedron given Face Area using the formula - Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face 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 Space Diagonal of Dodecahedron?

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

Space Diagonal of Dodecahedron=sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
Space Diagonal of Dodecahedron=sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Space Diagonal of Dodecahedron=sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

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

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

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

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

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