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Lateral Surface Area of Dodecahedron given Face Diagonal Formula

GoLateral Surface Area of Dodecahedron Formula

GoLateral Surface Area of Dodecahedron given Face Area Formula

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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. Check FAQs

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

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

Lateral Surface Area of Dodecahedron given Face Diagonal Example

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

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

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

1682.3396 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

1682.3396m² = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{2}

1682.3396 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

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Lateral Surface Area of Dodecahedron given Face Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{2}

Next Step Prepare to Evaluate

∴

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

Next Step Evaluate

∴

LSA = 1682.33955878123m²

LAST Step Rounding Answer

∴

LSA = 1682.3396m²

Lateral Surface Area of Dodecahedron given Face Diagonal Formula Elements

Variables

Functions

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

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

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 Lateral Surface Area of Dodecahedron

Go Lateral Surface Area of Dodecahedron

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {l e}^{2}

Go Lateral Surface Area of Dodecahedron given Face Area

LSA = 10 \cdot A Face

Go Lateral Surface Area of Dodecahedron given Face Perimeter

LSA = \sqrt{25 + (10 \cdot \sqrt{5})} \cdot \frac{{P Face}^{2}}{10}

Go Lateral Surface Area of Dodecahedron given Volume

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{2}{3}}

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

Lateral Surface Area of Dodecahedron given Face Diagonal evaluator uses Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2 to evaluate the Lateral Surface Area of Dodecahedron, The Lateral Surface Area of Dodecahedron given Face Diagonal formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron, and calculated using face diagonal of Dodecahedron. Lateral Surface Area of Dodecahedron is denoted by LSA symbol.

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

FAQs on Lateral Surface Area of Dodecahedron given Face Diagonal

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

The formula of Lateral Surface Area of Dodecahedron given Face Diagonal is expressed as Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2. Here is an example- 1682.34 = 5/2*sqrt(25+(10*sqrt(5)))*((2*16)/(1+sqrt(5)))^2.

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

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

What are the other ways to Calculate Lateral Surface Area of Dodecahedron?

Here are the different ways to Calculate Lateral Surface Area of Dodecahedron-

Lateral Surface Area of Dodecahedron=5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Lateral Surface Area of Dodecahedron=10*Face Area of Dodecahedron
Lateral Surface Area of Dodecahedron=sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2/10

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

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

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

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

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