Pentagonal Face Area of Icosidodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Midsphere Radius of Icosidodecahedron/(sqrt(5+(2*sqrt(5)))))^2
APentagon = sqrt(25+(10*sqrt(5)))*(rm/(sqrt(5+(2*sqrt(5)))))^2
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, 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.
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
APentagon = sqrt(25+(10*sqrt(5)))*(rm/(sqrt(5+(2*sqrt(5)))))^2 --> sqrt(25+(10*sqrt(5)))*(15/(sqrt(5+(2*sqrt(5)))))^2
Evaluating ... ...
APentagon = 163.472068801206
STEP 3: Convert Result to Output's Unit
163.472068801206 Square Meter --> No Conversion Required
FINAL ANSWER
163.472068801206 163.4721 Square Meter <-- Pentagonal Face Area of Icosidodecahedron
(Calculation completed in 00.003 seconds)

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Mumbai University (DJSCE), Mumbai
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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 Midsphere Radius Formula

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

Pentagonal Face Area of Icosidodecahedron given Midsphere Radius calculator uses Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Midsphere Radius of Icosidodecahedron/(sqrt(5+(2*sqrt(5)))))^2 to calculate the Pentagonal Face Area of Icosidodecahedron, Pentagonal Face Area of Icosidodecahedron given midsphere 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 midsphere radius of the Icosidodecahedron. Pentagonal Face Area of Icosidodecahedron is denoted by APentagon symbol.

How to calculate Pentagonal Face Area of Icosidodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Pentagonal Face Area of Icosidodecahedron given Midsphere Radius, enter Midsphere Radius of Icosidodecahedron (rm) and hit the calculate button. Here is how the Pentagonal Face Area of Icosidodecahedron given Midsphere Radius calculation can be explained with given input values -> 163.4721 = sqrt(25+(10*sqrt(5)))*(15/(sqrt(5+(2*sqrt(5)))))^2.

FAQ

What is Pentagonal Face Area of Icosidodecahedron given Midsphere Radius?
Pentagonal Face Area of Icosidodecahedron given midsphere 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 midsphere radius of the Icosidodecahedron and is represented as APentagon = sqrt(25+(10*sqrt(5)))*(rm/(sqrt(5+(2*sqrt(5)))))^2 or Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(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 Pentagonal Face Area of Icosidodecahedron given Midsphere Radius?
Pentagonal Face Area of Icosidodecahedron given midsphere 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 midsphere radius of the Icosidodecahedron is calculated using Pentagonal Face Area of Icosidodecahedron = sqrt(25+(10*sqrt(5)))*(Midsphere Radius of Icosidodecahedron/(sqrt(5+(2*sqrt(5)))))^2. To calculate Pentagonal Face Area of Icosidodecahedron given Midsphere Radius, you need Midsphere Radius of Icosidodecahedron (rm). 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 Pentagonal Face Area of Icosidodecahedron?
In this formula, Pentagonal Face Area of Icosidodecahedron uses Midsphere 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)))*(Circumsphere Radius of Icosidodecahedron/(1+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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