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Lateral Surface Area of Icosahedron given Circumsphere Radius Formula

GoLateral Surface Area of Icosahedron given Total Surface Area Formula

GoLateral Surface Area of Icosahedron given Face Perimeter Formula

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

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

LSA - Lateral Surface Area of Icosahedron?r_c - Circumsphere Radius of Icosahedron?

Lateral Surface Area of Icosahedron given Circumsphere Radius Example

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

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

Here is how the Lateral Surface Area of Icosahedron given Circumsphere Radius equation looks like.

697.9841 = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

697.9841m² = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

697.9841 = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

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Lateral Surface Area of Icosahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Substitute values of Variables

∴

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Prepare to Evaluate

∴

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Evaluate

∴

LSA = 697.98406684067m²

LAST Step Rounding Answer

∴

LSA = 697.9841m²

Lateral Surface Area of Icosahedron given Circumsphere Radius Formula Elements

Variables

Functions

Lateral Surface Area of Icosahedron

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

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of Icosahedron

Circumsphere Radius of Icosahedron

Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Icosahedron

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 Icosahedron

Go Lateral Surface Area of Icosahedron given Total Surface Area

LSA = \frac{9}{10} \cdot TSA

Go Lateral Surface Area of Icosahedron given Face Perimeter

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{P Face}{3})}^{2}

Go Lateral Surface Area of Icosahedron given Face Area

LSA = 18 \cdot A Face

Go Lateral Surface Area of Icosahedron

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {l e}^{2}

How to Evaluate Lateral Surface Area of Icosahedron given Circumsphere Radius?

Lateral Surface Area of Icosahedron given Circumsphere Radius evaluator uses Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2 to evaluate the Lateral Surface Area of Icosahedron, The Lateral Surface Area of Icosahedron given Circumsphere 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 Icosahedron and is calculated using the circumsphere radius of the Icosahedron. Lateral Surface Area of Icosahedron is denoted by LSA symbol.

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

FAQs on Lateral Surface Area of Icosahedron given Circumsphere Radius

What is the formula to find Lateral Surface Area of Icosahedron given Circumsphere Radius?

The formula of Lateral Surface Area of Icosahedron given Circumsphere Radius is expressed as Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. Here is an example- 697.9841 = 9*sqrt(3)/2*((4*9)/(sqrt(10+(2*sqrt(5)))))^2.

How to calculate Lateral Surface Area of Icosahedron given Circumsphere Radius?

With Circumsphere Radius of Icosahedron (r_c) we can find Lateral Surface Area of Icosahedron given Circumsphere Radius using the formula - Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Lateral Surface Area of Icosahedron=9/10*Total Surface Area of Icosahedron
Lateral Surface Area of Icosahedron=9*sqrt(3)/2*(Face Perimeter of Icosahedron/3)^2
Lateral Surface Area of Icosahedron=18*Face Area of Icosahedron

Can the Lateral Surface Area of Icosahedron given Circumsphere Radius be negative?

No, the Lateral Surface Area of Icosahedron given Circumsphere Radius, measured in Area cannot be negative.

Which unit is used to measure Lateral Surface Area of Icosahedron given Circumsphere Radius?

Lateral Surface Area of Icosahedron given Circumsphere 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 Icosahedron given Circumsphere Radius can be measured.

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