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Face Diagonal of Dodecahedron given Lateral Surface Area Formula

GoFace Diagonal of Dodecahedron Formula

GoFace Diagonal of Dodecahedron given Volume 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{2 \cdot LSA}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

d_Face - Face Diagonal of Dodecahedron?LSA - Lateral Surface Area of Dodecahedron?

Face Diagonal of Dodecahedron given Lateral Surface Area Example

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

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

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

16.3186 = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

16.3186m = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2 \cdot 1750m²}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

16.3186 = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2 \cdot 1750}{5 \cdot \sqrt{25 + (10 \cdot \sqrt{5})}}}

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Face Diagonal of Dodecahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

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

Next Step Prepare to Evaluate

∴

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{2 \cdot 1750}{5 \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 Lateral 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

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 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 Volume

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

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})}}}

Go Face Diagonal of Dodecahedron given Face Area

d Face = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{\frac{4 \cdot A Face}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

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

Face Diagonal of Dodecahedron given Lateral Surface Area evaluator uses Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))) to evaluate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Lateral 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 lateral surface area of Dodecahedron. Face Diagonal of Dodecahedron is denoted by d_Face symbol.

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

FAQs on Face Diagonal of Dodecahedron given Lateral Surface Area

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

The formula of Face Diagonal of Dodecahedron given Lateral Surface Area is expressed as Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5))))). Here is an example- 16.31857 = (1+sqrt(5))/2*sqrt((2*1750)/(5*sqrt(25+(10*sqrt(5))))).

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

With Lateral Surface Area of Dodecahedron (LSA) we can find Face Diagonal of Dodecahedron given Lateral Surface Area using the formula - Face Diagonal of Dodecahedron = (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 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))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Face Diagonal of Dodecahedron=(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))

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

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

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

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

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