Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal Calculator

✖Pentagonal Face Diagonal of Icosidodecahedron is the distance between any pair of non adjacent vertices of any of the pentagonal faces of the Icosidodecahedron.ⓘ Pentagonal Face Diagonal of Icosidodecahedron [d_Pentagon]

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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 Pentagonal Face Diagonal [TSA]

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Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Pentagonal Face Diagonal of Icosidodecahedron - (Measured in Meter) - Pentagonal Face Diagonal of Icosidodecahedron is the distance between any pair of non adjacent vertices of any of the pentagonal faces of the Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagonal Face Diagonal of Icosidodecahedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*d_Pentagon)/(1+sqrt(5)))^2 --> ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*16)/(1+sqrt(5)))^2

Evaluating ... ...

TSA = 2865.63567949697

STEP 3: Convert Result to Output's Unit

2865.63567949697 Square Meter --> No Conversion Required

FINAL ANSWER

2865.63567949697 ≈ 2865.636 Square Meter <-- Total Surface Area of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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Mumbai University (DJSCE), Mumbai

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< Total Surface Area of Icosidodecahedron Calculators

Total Surface Area of Icosidodecahedron given Midsphere Radius

LaTeX 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 Circumsphere Radius

LaTeX 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

LaTeX 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

LaTeX 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 Pentagonal Face Diagonal Formula

LaTeX Go

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 Pentagonal Face Diagonal?

Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal calculator uses Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Pentagonal Face Diagonal of Icosidodecahedron)/(1+sqrt(5)))^2 to calculate the Total Surface Area of Icosidodecahedron, Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal formula is defined as the total quantity of plane enclosed on the entire surface of the Icosidodecahedron, and calculated using the pentagonal face diagonal of the Icosidodecahedron. Total Surface Area of Icosidodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal using this online calculator? To use this online calculator for Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal, enter Pentagonal Face Diagonal of Icosidodecahedron (d_Pentagon) and hit the calculate button. Here is how the Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal calculation can be explained with given input values -> 2865.636 = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*16)/(1+sqrt(5)))^2.

FAQ

What is Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal?

Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal formula is defined as the total quantity of plane enclosed on the entire surface of the Icosidodecahedron, and calculated using the pentagonal face diagonal of the Icosidodecahedron and is represented as TSA = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*d_Pentagon)/(1+sqrt(5)))^2 or Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Pentagonal Face Diagonal of Icosidodecahedron)/(1+sqrt(5)))^2. Pentagonal Face Diagonal of Icosidodecahedron is the distance between any pair of non adjacent vertices of any of the pentagonal faces of the Icosidodecahedron.

How to calculate Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal?

Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal formula is defined as the total quantity of plane enclosed on the entire surface of the Icosidodecahedron, and calculated using the pentagonal face diagonal of the Icosidodecahedron is calculated using Total Surface Area of Icosidodecahedron = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Pentagonal Face Diagonal of Icosidodecahedron)/(1+sqrt(5)))^2. To calculate Total Surface Area of Icosidodecahedron given Pentagonal Face Diagonal, you need Pentagonal Face Diagonal of Icosidodecahedron (d_Pentagon). With our tool, you need to enter the respective value for Pentagonal Face Diagonal 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 Pentagonal Face Diagonal of Icosidodecahedron. We can use 3 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

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