Long Ridge Length of Great Icosahedron given Total Surface Area Calculator

✖Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.ⓘ Total Surface Area of Great Icosahedron [TSA]

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✖Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.ⓘ Long Ridge Length of Great Icosahedron given Total Surface Area [l_Ridge(Long)]

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Formula

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Long Ridge Length of Great Icosahedron given Total Surface Area

Formula

`"l"_{"Ridge(Long)"} = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt("TSA"/(3*sqrt(3)*(5+(4*sqrt(5)))))`

Example

`"16.50565m"=(sqrt(2)*(5+(3*sqrt(5))))/10*sqrt("7200m²"/(3*sqrt(3)*(5+(4*sqrt(5)))))`

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Long Ridge Length of Great Icosahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5)))))
l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(TSA/(3*sqrt(3)*(5+(4*sqrt(5)))))
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Long Ridge Length of Great Icosahedron - (Measured in Meter) - Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.
Total Surface Area of Great Icosahedron - (Measured in Square Meter) - Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Great Icosahedron: 7200 Square Meter --> 7200 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(TSA/(3*sqrt(3)*(5+(4*sqrt(5))))) --> (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(7200/(3*sqrt(3)*(5+(4*sqrt(5)))))

Evaluating ... ...

l_Ridge(Long) = 16.505651148174

STEP 3: Convert Result to Output's Unit

16.505651148174 Meter --> No Conversion Required

FINAL ANSWER

16.505651148174 ≈ 16.50565 Meter <-- Long Ridge Length of Great Icosahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 7 Long Ridge Length of Great Icosahedron Calculators

Long Ridge Length of Great Icosahedron given Surface to Volume Ratio

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron)

Long Ridge Length of Great Icosahedron given Total Surface Area

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5)))))

Long Ridge Length of Great Icosahedron given Circumsphere Radius

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5))))

Long Ridge Length of Great Icosahedron given Volume

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)

Long Ridge Length of Great Icosahedron given Mid Ridge Length

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5))

Long Ridge Length of Great Icosahedron given Short Ridge Length

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)

Long Ridge Length of Great Icosahedron

Go Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*Edge Length of Great Icosahedron

Long Ridge Length of Great Icosahedron given Total Surface Area Formula

What is Great Icosahedron?

The Great Icosahedron can be constructed from an icosahedron with unit edge lengths by taking the 20 sets of vertices that are mutually spaced by a distance phi, the golden ratio. The solid therefore consists of 20 equilateral triangles. The symmetry of their arrangement is such that the resulting solid contains 12 pentagrams.

How to Calculate Long Ridge Length of Great Icosahedron given Total Surface Area?

Long Ridge Length of Great Icosahedron given Total Surface Area calculator uses Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))) to calculate the Long Ridge Length of Great Icosahedron, Long Ridge Length of Great Icosahedron given Total Surface Area formula is defined as the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of the Great Icosahedron is attached, calculated using total surface area. Long Ridge Length of Great Icosahedron is denoted by l_Ridge(Long) symbol.

How to calculate Long Ridge Length of Great Icosahedron given Total Surface Area using this online calculator? To use this online calculator for Long Ridge Length of Great Icosahedron given Total Surface Area, enter Total Surface Area of Great Icosahedron (TSA) and hit the calculate button. Here is how the Long Ridge Length of Great Icosahedron given Total Surface Area calculation can be explained with given input values -> 16.50565 = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(7200/(3*sqrt(3)*(5+(4*sqrt(5))))).

FAQ

What is Long Ridge Length of Great Icosahedron given Total Surface Area?

Long Ridge Length of Great Icosahedron given Total Surface Area formula is defined as the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of the Great Icosahedron is attached, calculated using total surface area and is represented as l_Ridge(Long) = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(TSA/(3*sqrt(3)*(5+(4*sqrt(5))))) or Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))). Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.

How to calculate Long Ridge Length of Great Icosahedron given Total Surface Area?

Long Ridge Length of Great Icosahedron given Total Surface Area formula is defined as the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of the Great Icosahedron is attached, calculated using total surface area is calculated using Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*sqrt(Total Surface Area of Great Icosahedron/(3*sqrt(3)*(5+(4*sqrt(5))))). To calculate Long Ridge Length of Great Icosahedron given Total Surface Area, you need Total Surface Area of Great Icosahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Great Icosahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Long Ridge Length of Great Icosahedron?

In this formula, Long Ridge Length of Great Icosahedron uses Total Surface Area of Great Icosahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*Edge Length of Great Icosahedron
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5))
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(5*Short Ridge Length of Great Icosahedron)/sqrt(10)
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5))))
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(1/3)
Long Ridge Length of Great Icosahedron = (sqrt(2)*(5+(3*sqrt(5))))/10*(3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron)

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