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Lateral Surface Area of Dodecahedron given Space 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 Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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

Lateral Surface Area of Dodecahedron given Space Diagonal Example

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

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

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

1717.3883 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

1717.3883m² = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

1717.3883 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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Lateral Surface Area of Dodecahedron given Space Diagonal Solution

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

FIRST Step Consider the formula

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Space}{\sqrt{3} \cdot (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 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

LSA = 1717.38829958917m²

LAST Step Rounding Answer

∴

LSA = 1717.3883m²

Lateral Surface Area of Dodecahedron given Space 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

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

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 Space Diagonal?

Lateral Surface Area of Dodecahedron given Space Diagonal evaluator uses Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2 to evaluate the Lateral Surface Area of Dodecahedron, The Lateral Surface Area of Dodecahedron given Space 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 space diagonal of Dodecahedron. Lateral Surface Area of Dodecahedron is denoted by LSA symbol.

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

FAQs on Lateral Surface Area of Dodecahedron given Space Diagonal

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

The formula of Lateral Surface Area of Dodecahedron given Space Diagonal is expressed as Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. Here is an example- 1717.388 = 5/2*sqrt(25+(10*sqrt(5)))*((2*28)/(sqrt(3)*(1+sqrt(5))))^2.

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

With Space Diagonal of Dodecahedron (d_Space) we can find Lateral Surface Area of Dodecahedron given Space Diagonal using the formula - Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(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 Space Diagonal be negative?

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

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

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

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