Total Surface Area of Icosidodecahedron given Pentagonal Face Height Calculator

✖Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.ⓘ Pentagonal Face Height of Icosidodecahedron [h_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 Height [TSA]

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Total Surface Area of Icosidodecahedron given Pentagonal Face Height 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 Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5))))^2
TSA = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*h_Pentagon)/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.
Pentagonal Face Height of Icosidodecahedron - (Measured in Meter) - Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagonal Face Height 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*h_Pentagon)/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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Created by Nikhil

Mumbai University (DJSCE), Mumbai

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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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 Height 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 Height?

Total Surface Area of Icosidodecahedron given Pentagonal Face Height calculator uses 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 to calculate the Total Surface Area of Icosidodecahedron, Total Surface Area of Icosidodecahedron given Pentagonal Face Height formula is defined as the total quantity of plane enclosed on the entire surface of the Icosidodecahedron, and calculated using the pentagonal face height of the Icosidodecahedron. Total Surface Area of Icosidodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosidodecahedron given Pentagonal Face Height using this online calculator? To use this online calculator for Total Surface Area of Icosidodecahedron given Pentagonal Face Height, enter Pentagonal Face Height of Icosidodecahedron (h_Pentagon) and hit the calculate button. Here is how the Total Surface Area of Icosidodecahedron given Pentagonal Face Height 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 Pentagonal Face Height?

Total Surface Area of Icosidodecahedron given Pentagonal Face Height formula is defined as the total quantity of plane enclosed on the entire surface of the Icosidodecahedron, and calculated using the pentagonal face height of the Icosidodecahedron and is represented as TSA = ((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*h_Pentagon)/sqrt(5+(2*sqrt(5))))^2 or 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. Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.

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

Total Surface Area of Icosidodecahedron given Pentagonal Face Height formula is defined as the total quantity of plane enclosed on the entire surface of the Icosidodecahedron, and calculated using the pentagonal face height of the Icosidodecahedron is calculated using 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. To calculate Total Surface Area of Icosidodecahedron given Pentagonal Face Height, you need Pentagonal Face Height of Icosidodecahedron (h_Pentagon). With our tool, you need to enter the respective value for Pentagonal Face Height 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 Height 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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