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Space Diagonal of Icosahedron given Lateral Surface Area Formula

GoSpace Diagonal of Icosahedron Formula

GoSpace Diagonal of Icosahedron given Total Surface Area Formula

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The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron. Check FAQs

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

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

Space Diagonal of Icosahedron given Lateral Surface Area Example

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

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

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

19.0282 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

19.0282m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

19.0282 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

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Space Diagonal of Icosahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

Next Step Prepare to Evaluate

∴

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

Next Step Evaluate

∴

d Space = 19.0281712785528m

LAST Step Rounding Answer

∴

d Space = 19.0282m

Space Diagonal of Icosahedron given Lateral Surface Area Formula Elements

Variables

Functions

Space Diagonal of Icosahedron

The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of Icosahedron

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

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 Space Diagonal of Icosahedron

Go Space Diagonal of Icosahedron

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot l e

Go Space Diagonal of Icosahedron given Total Surface Area

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}}

Go Space Diagonal of Icosahedron given Volume

d Space = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{2} \cdot {(\frac{\frac{12}{5} \cdot V}{3 + \sqrt{5}})}^{\frac{1}{3}}

How to Evaluate Space Diagonal of Icosahedron given Lateral Surface Area?

Space Diagonal of Icosahedron given Lateral Surface Area evaluator uses Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))) to evaluate the Space Diagonal of Icosahedron, The Space Diagonal of Icosahedron given Lateral Surface Area formula is defined as the line connecting two vertices that are not on the same face of the Icosahedron and is calculated using the lateral surface area of the Icosahedron. Space Diagonal of Icosahedron is denoted by d_Space symbol.

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

FAQs on Space Diagonal of Icosahedron given Lateral Surface Area

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

The formula of Space Diagonal of Icosahedron given Lateral Surface Area is expressed as Space Diagonal of Icosahedron = sqrt(10+(2*sqrt(5)))/2*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))). Here is an example- 19.02817 = sqrt(10+(2*sqrt(5)))/2*sqrt((2*780)/(9*sqrt(3))).

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

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

What are the other ways to Calculate Space Diagonal of Icosahedron?

Here are the different ways to Calculate Space Diagonal of Icosahedron-

Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))/2*Edge Length of Icosahedron
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))/2*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Space Diagonal of Icosahedron=sqrt(10+(2*sqrt(5)))/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(1/3)

Can the Space Diagonal of Icosahedron given Lateral Surface Area be negative?

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

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

Space Diagonal of Icosahedron given Lateral Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Space Diagonal of Icosahedron given Lateral Surface Area can be measured.

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