Total Surface Area of Icosidodecahedron given Midsphere Radius Calculator

✖Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Icosidodecahedron [r_m]

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✖Total Surface Area of Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Icosidodecahedron.ⓘ Total Surface Area of Icosidodecahedron given Midsphere Radius [TSA]

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Formula

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Total Surface Area of Icosidodecahedron given Midsphere Radius

Formula

`"TSA" = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*"r"_{"m"})/(sqrt(5+(2*sqrt(5)))))^2`

Example

`"2784.523m²"=((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*"15m")/(sqrt(5+(2*sqrt(5)))))^2`

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Total Surface Area of Icosidodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5)))))^2
TSA = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/(sqrt(5+(2*sqrt(5)))))^2
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

Total Surface Area of Icosidodecahedron - (Measured in Square Meter) - Total Surface Area of Icosidodecahedron is the total quantity of plane enclosed by the entire surface of the Icosidodecahedron.
Midsphere Radius of Icosidodecahedron - (Measured in Meter) - Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Icosidodecahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/(sqrt(5+(2*sqrt(5)))))^2 --> ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*15)/(sqrt(5+(2*sqrt(5)))))^2

Evaluating ... ...

TSA = 2784.52343650107

STEP 3: Convert Result to Output's Unit

2784.52343650107 Square Meter --> No Conversion Required

FINAL ANSWER

2784.52343650107 ≈ 2784.523 Square Meter <-- Total Surface Area of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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< 12 Total Surface Area of Icosidodecahedron Calculators

Total Surface Area of Icosidodecahedron given Surface to Volume Ratio

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5)))))^2

Total Surface Area of Icosidodecahedron given Pentagonal Face Height

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Pentagonal Face Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5))))^2

Total Surface Area of Icosidodecahedron given Pentagonal Face Area

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*(4*Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5)))

Total Surface Area of Icosidodecahedron given Midsphere Radius

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5)))))^2

Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Pentagonal Face Diagonal of Icosidodecahedron)/(1+sqrt(5)))^2

Total Surface Area of Icosidodecahedron given Circumsphere Radius

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^2

Total Surface Area of Icosidodecahedron given Volume

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(2/3)

Total Surface Area of Icosidodecahedron given Triangular Face Area

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*(4*Triangular Face Area of Icosidodecahedron)/sqrt(3)

Total Surface Area of Icosidodecahedron given Pentagonal Face Perimeter

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Pentagonal Face Perimeter of Icosidodecahedron^2/25

Total Surface Area of Icosidodecahedron given Triangular Face Perimeter

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Triangular Face Perimeter of Icosidodecahedron^2/9

Total Surface Area of Icosidodecahedron given Triangular Face Height

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*4/3*Triangular Face Height of Icosidodecahedron^2

Total Surface Area of Icosidodecahedron

Go Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Edge Length of Icosidodecahedron^2

Total Surface Area of Icosidodecahedron given Midsphere Radius Formula

What is an Icosidodecahedron?

In geometry, an Icosidodecahedron is a closed and convex polyhedron with 20 (icosi) triangular faces and 12 (dodeca) pentagonal faces. An Icosidodecahedron has 30 identical vertices, with 2 triangles and 2 pentagons meeting at each. And 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

How to Calculate Total Surface Area of Icosidodecahedron given Midsphere Radius?

Total Surface Area of Icosidodecahedron given Midsphere Radius calculator uses Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5)))))^2 to calculate the Total Surface Area of Icosidodecahedron, Total Surface Area of Icosidodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosidodecahedron, and calculated using the midsphere radius of the Icosidodecahedron. Total Surface Area of Icosidodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosidodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Icosidodecahedron given Midsphere Radius, enter Midsphere Radius of Icosidodecahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Icosidodecahedron given Midsphere Radius calculation can be explained with given input values -> 2784.523 = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*15)/(sqrt(5+(2*sqrt(5)))))^2.

FAQ

What is Total Surface Area of Icosidodecahedron given Midsphere Radius?

Total Surface Area of Icosidodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosidodecahedron, and calculated using the midsphere radius of the Icosidodecahedron and is represented as TSA = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*r_m)/(sqrt(5+(2*sqrt(5)))))^2 or Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5)))))^2. Midsphere Radius of Icosidodecahedron is the radius of the sphere for which all the edges of the Icosidodecahedron become a tangent line on that sphere.

How to calculate Total Surface Area of Icosidodecahedron given Midsphere Radius?

Total Surface Area of Icosidodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosidodecahedron, and calculated using the midsphere radius of the Icosidodecahedron is calculated using Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5)))))^2. To calculate Total Surface Area of Icosidodecahedron given Midsphere Radius, you need Midsphere Radius of Icosidodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Icosidodecahedron 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 Total Surface Area of Icosidodecahedron?

In this formula, Total Surface Area of Icosidodecahedron uses Midsphere Radius of Icosidodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Edge Length of Icosidodecahedron^2
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(2/3)
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((6*((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))/(Surface to Volume Ratio of Icosidodecahedron*(45+(17*sqrt(5)))))^2
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*(4*Triangular Face Area of Icosidodecahedron)/sqrt(3)
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Triangular Face Perimeter of Icosidodecahedron^2/9
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*4/3*Triangular Face Height of Icosidodecahedron^2
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Pentagonal Face Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5))))^2
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Pentagonal Face Diagonal of Icosidodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*(4*Pentagonal Face Area of Icosidodecahedron)/sqrt(25+(10*sqrt(5)))
Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Pentagonal Face Perimeter of Icosidodecahedron^2/25

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