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Lateral Surface Area of Dodecahedron given Insphere Radius 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 r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

LSA - Lateral Surface Area of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Lateral Surface Area of Dodecahedron given Insphere Radius Example

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

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

Here is how the Lateral Surface Area of Dodecahedron given Insphere Radius equation looks like.

1678.963 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

1678.963m² = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

1678.963 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

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Lateral Surface Area of Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Substitute values of Variables

∴

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Prepare to Evaluate

∴

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Evaluate

∴

LSA = 1678.96303612594m²

LAST Step Rounding Answer

∴

LSA = 1678.963m²

Lateral Surface Area of Dodecahedron given Insphere Radius 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

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius 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 Insphere Radius?

Lateral Surface Area of Dodecahedron given Insphere Radius evaluator uses Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2 to evaluate the Lateral Surface Area of Dodecahedron, The Lateral Surface Area of Dodecahedron given Insphere Radius 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 insphere radius of Dodecahedron. Lateral Surface Area of Dodecahedron is denoted by LSA symbol.

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

FAQs on Lateral Surface Area of Dodecahedron given Insphere Radius

What is the formula to find Lateral Surface Area of Dodecahedron given Insphere Radius?

The formula of Lateral Surface Area of Dodecahedron given Insphere Radius is expressed as Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2. Here is an example- 1678.963 = 5/2*sqrt(25+(10*sqrt(5)))*((2*11)/(sqrt((25+(11*sqrt(5)))/10)))^2.

How to calculate Lateral Surface Area of Dodecahedron given Insphere Radius?

With Insphere Radius of Dodecahedron (r_i) we can find Lateral Surface Area of Dodecahedron given Insphere Radius using the formula - Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^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 Insphere Radius be negative?

No, the Lateral Surface Area of Dodecahedron given Insphere Radius, measured in Area cannot be negative.

Which unit is used to measure Lateral Surface Area of Dodecahedron given Insphere Radius?

Lateral Surface Area of Dodecahedron given Insphere Radius 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 Insphere Radius can be measured.

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