Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Icosidodecahedron [r_c]

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✖Pentagonal Face Area of Icosidodecahedron is the total quantity of two dimensional space enclosed on any of the pentagonal faces of the Icosidodecahedron.ⓘ Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius [A_Pentagon]

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Formula

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Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius

Formula

`"A"_{"Pentagon"} = sqrt(25+(10*sqrt(5)))*("r"_{"c"}/(1+sqrt(5)))^2`

Example

`"168.234m²"=sqrt(25+(10*sqrt(5)))*("16m"/(1+sqrt(5)))^2`

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Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)))^2
A_Pentagon = sqrt(25+(10*sqrt(5)))*(r_c/(1+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

Pentagonal Face Area of Icosidodecahedron - (Measured in Square Meter) - Pentagonal Face Area of Icosidodecahedron is the total quantity of two dimensional space enclosed on any of the pentagonal faces of the Icosidodecahedron.
Circumsphere Radius of Icosidodecahedron - (Measured in Meter) - Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Icosidodecahedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Pentagon = sqrt(25+(10*sqrt(5)))*(r_c/(1+sqrt(5)))^2 --> sqrt(25+(10*sqrt(5)))*(16/(1+sqrt(5)))^2

Evaluating ... ...

A_Pentagon = 168.233955878123

STEP 3: Convert Result to Output's Unit

168.233955878123 Square Meter --> No Conversion Required

FINAL ANSWER

168.233955878123 ≈ 168.234 Square Meter <-- Pentagonal Face Area of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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< 7 Pentagonal Face Area of Icosidodecahedron Calculators

Pentagonal Face Area of Icosidodecahedron given Surface to Volume Ratio

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

Pentagonal Face Area of Icosidodecahedron given Total Surface Area

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

Pentagonal Face Area of Icosidodecahedron given Midsphere Radius

Go Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Midsphere Radius of Icosidodecahedron/(sqrt(5+(2*sqrt(5)))))^2

Pentagonal Face Area of Icosidodecahedron given Pentagonal Face Diagonal

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

Pentagonal Face Area of Icosidodecahedron given Volume

Go Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(2/3))/4

Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius

Go Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)))^2

Pentagonal Face Area of Icosidodecahedron

Go Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Edge Length of Icosidodecahedron^2)/4

Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius Formula

Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)))^2
A_Pentagon = sqrt(25+(10*sqrt(5)))*(r_c/(1+sqrt(5)))^2

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 Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius?

Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius calculator uses Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)))^2 to calculate the Pentagonal Face Area of Icosidodecahedron, Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius formula is defined as the total quantity of two dimensional space enclosed on any of the pentagonal faces of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron. Pentagonal Face Area of Icosidodecahedron is denoted by A_Pentagon symbol.

How to calculate Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius, enter Circumsphere Radius of Icosidodecahedron (r_c) and hit the calculate button. Here is how the Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius calculation can be explained with given input values -> 168.234 = sqrt(25+(10*sqrt(5)))*(16/(1+sqrt(5)))^2.

FAQ

What is Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius?

Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius formula is defined as the total quantity of two dimensional space enclosed on any of the pentagonal faces of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron and is represented as A_Pentagon = sqrt(25+(10*sqrt(5)))*(r_c/(1+sqrt(5)))^2 or Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)))^2. Circumsphere Radius of Icosidodecahedron is the radius of the sphere that contains the Icosidodecahedron in such a way that all the vertices are lying on the sphere.

How to calculate Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius?

Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius formula is defined as the total quantity of two dimensional space enclosed on any of the pentagonal faces of the Icosidodecahedron, and calculated using the circumsphere radius of the Icosidodecahedron is calculated using Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Circumsphere Radius of Icosidodecahedron/(1+sqrt(5)))^2. To calculate Pentagonal Face Area of Icosidodecahedron given Circumsphere Radius, you need Circumsphere Radius of Icosidodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere 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 Pentagonal Face Area of Icosidodecahedron?

In this formula, Pentagonal Face Area of Icosidodecahedron uses Circumsphere Radius of Icosidodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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