Face Area of Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
AFace = 1/4*sqrt(25+(10*sqrt(5)))*le^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
Face Area of Dodecahedron - (Measured in Square Meter) - The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.
Edge Length of Dodecahedron - (Measured in Meter) - Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Dodecahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AFace = 1/4*sqrt(25+(10*sqrt(5)))*le^2 --> 1/4*sqrt(25+(10*sqrt(5)))*10^2
Evaluating ... ...
AFace = 172.047740058897
STEP 3: Convert Result to Output's Unit
172.047740058897 Square Meter --> No Conversion Required
FINAL ANSWER
172.047740058897 172.0477 Square Meter <-- Face Area of Dodecahedron
(Calculation completed in 00.020 seconds)

Credits

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Mumbai University (DJSCE), Mumbai
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12 Face Area of Dodecahedron Calculators

Face Area of Dodecahedron given Surface to Volume Ratio
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
Face Area of Dodecahedron given Insphere Radius
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
Face Area of Dodecahedron given Circumsphere Radius
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Face Area of Dodecahedron given Space Diagonal
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Face Area of Dodecahedron given Midsphere Radius
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
Face Area of Dodecahedron given Volume
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Face Area of Dodecahedron given Face Diagonal
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
Face Area of Dodecahedron given Face Perimeter
Go Face Area of Dodecahedron = 1/100*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
Face Area of Dodecahedron given Perimeter
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
Face Area of Dodecahedron
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Face Area of Dodecahedron given Lateral Surface Area
Go Face Area of Dodecahedron = Lateral Surface Area of Dodecahedron/10
Face Area of Dodecahedron given Total Surface Area
Go Face Area of Dodecahedron = Total Surface Area of Dodecahedron/12

8 Area of Dodecahedron Calculators

Lateral Surface Area of Dodecahedron given Circumsphere Radius
Go Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Total Surface Area of Dodecahedron given Volume
Go Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Face Area of Dodecahedron given Midsphere Radius
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
Total Surface Area of Dodecahedron given Face Perimeter
Go Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
Lateral Surface Area of Dodecahedron
Go Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron
Go Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Face Area of Dodecahedron
Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Lateral Surface Area of Dodecahedron given Total Surface Area
Go Lateral Surface Area of Dodecahedron = 5/6*Total Surface Area of Dodecahedron

Face Area of Dodecahedron Formula

Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
AFace = 1/4*sqrt(25+(10*sqrt(5)))*le^2

What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Face Area of Dodecahedron?

Face Area of Dodecahedron calculator uses Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2 to calculate the Face Area of Dodecahedron, The Face Area of Dodecahedron formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron. Face Area of Dodecahedron is denoted by AFace symbol.

How to calculate Face Area of Dodecahedron using this online calculator? To use this online calculator for Face Area of Dodecahedron, enter Edge Length of Dodecahedron (le) and hit the calculate button. Here is how the Face Area of Dodecahedron calculation can be explained with given input values -> 172.0477 = 1/4*sqrt(25+(10*sqrt(5)))*10^2.

FAQ

What is Face Area of Dodecahedron?
The Face Area of Dodecahedron formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron and is represented as AFace = 1/4*sqrt(25+(10*sqrt(5)))*le^2 or Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2. Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.
How to calculate Face Area of Dodecahedron?
The Face Area of Dodecahedron formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron is calculated using Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2. To calculate Face Area of Dodecahedron, you need Edge Length of Dodecahedron (le). With our tool, you need to enter the respective value for Edge Length of Dodecahedron 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 Face Area of Dodecahedron?
In this formula, Face Area of Dodecahedron uses Edge Length of Dodecahedron. We can use 12 other way(s) to calculate the same, which is/are as follows -
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
  • Face Area of Dodecahedron = Total Surface Area of Dodecahedron/12
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
  • Face Area of Dodecahedron = 1/100*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
  • Face Area of Dodecahedron = Lateral Surface Area of Dodecahedron/10
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
  • Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
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