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Space Diagonal of Dodecahedron given Lateral Surface Area Formula

GoSpace Diagonal of Dodecahedron Formula

GoSpace Diagonal of Dodecahedron given Perimeter 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 = \frac{\sqrt{3} \cdot (1 + \sqrt{5})}{2} \cdot \sqrt{\frac{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

d_Space - Space Diagonal of Dodecahedron?LSA - Lateral Surface Area of Dodecahedron?

Space Diagonal of Dodecahedron given Lateral Surface Area Example

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

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

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

28.2646 = \frac{\sqrt{3} \cdot (1 + \sqrt{5})}{2} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

28.2646m = \frac{\sqrt{3} \cdot (1 + \sqrt{5})}{2} \cdot \sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

28.2646 = \frac{\sqrt{3} \cdot (1 + \sqrt{5})}{2} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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Space Diagonal of Dodecahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Space = \frac{\sqrt{3} \cdot (1 + \sqrt{5})}{2} \cdot \sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

d Space = \frac{\sqrt{3} \cdot (1 + \sqrt{5})}{2} \cdot \sqrt{\frac{2 \cdot 1750}{5 \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 Lateral Surface 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

Lateral Surface Area of Dodecahedron

Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral 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 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 Perimeter

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

Other formulas in Space Diagonal of Dodecahedron category

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}}}

Go Face Diagonal of Dodecahedron given Total Surface Area

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

How to Evaluate Space Diagonal of Dodecahedron given Lateral Surface Area?

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

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

FAQs on Space Diagonal of Dodecahedron given Lateral Surface Area

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

The formula of Space Diagonal of Dodecahedron given Lateral Surface Area is expressed as Space Diagonal of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))). Here is an example- 28.2646 = (sqrt(3)*(1+sqrt(5)))/2*sqrt((2*1750)/(5*sqrt(25+(10*sqrt(5))))).

How to calculate Space Diagonal of Dodecahedron given Lateral Surface Area?

With Lateral Surface Area of Dodecahedron (LSA) we can find Space Diagonal of Dodecahedron given Lateral Surface Area using the formula - Space Diagonal of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*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))*Perimeter of Dodecahedron/60

Can the Space Diagonal of Dodecahedron given Lateral Surface Area be negative?

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

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

Space Diagonal of Dodecahedron given Lateral Surface 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 Lateral Surface Area can be measured.

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