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Lateral Surface Area of Icosahedron given Insphere 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{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

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

Lateral Surface Area of Icosahedron given Insphere Radius Example

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

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

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

668.6516 = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

668.6516m² = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

668.6516 = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

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Lateral Surface Area of Icosahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Substitute values of Variables

∴

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

LSA = 668.651627798135m²

LAST Step Rounding Answer

∴

LSA = 668.6516m²

Lateral Surface Area of Icosahedron given Insphere 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

Insphere Radius of Icosahedron

Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron 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 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 Insphere Radius?

Lateral Surface Area of Icosahedron given Insphere Radius evaluator uses Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2 to evaluate the Lateral Surface Area of Icosahedron, The Lateral Surface Area of Icosahedron 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 Icosahedron and is calculated using the insphere radius of the Icosahedron. Lateral Surface Area of Icosahedron is denoted by LSA symbol.

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

FAQs on Lateral Surface Area of Icosahedron given Insphere Radius

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

The formula of Lateral Surface Area of Icosahedron given Insphere Radius is expressed as Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. Here is an example- 668.6516 = 9*sqrt(3)/2*((12*7)/(sqrt(3)*(3+sqrt(5))))^2.

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

With Insphere Radius of Icosahedron (r_i) we can find Lateral Surface Area of Icosahedron given Insphere Radius using the formula - Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+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 Insphere Radius be negative?

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

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

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

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