## Total Surface Area of Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
TSA = 3*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
Total Surface Area of Dodecahedron - (Measured in Square Meter) - Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the 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
TSA = 3*sqrt(25+(10*sqrt(5)))*le^2 --> 3*sqrt(25+(10*sqrt(5)))*10^2
Evaluating ... ...
TSA = 2064.57288070676
STEP 3: Convert Result to Output's Unit
2064.57288070676 Square Meter --> No Conversion Required
2064.57288070676 2064.573 Square Meter <-- Total Surface Area of Dodecahedron
(Calculation completed in 00.004 seconds)
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Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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## < 12 Total Surface Area of Dodecahedron Calculators

Total Surface Area of Dodecahedron given Surface to Volume Ratio
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
Total Surface Area of Dodecahedron given Insphere Radius
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
Total Surface Area of Dodecahedron given Circumsphere Radius
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Total Surface Area of Dodecahedron given Space Diagonal
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Total Surface Area of Dodecahedron given Midsphere Radius
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
Total Surface Area of Dodecahedron given Volume
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Total Surface Area of Dodecahedron given Face Diagonal
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Dodecahedron given Face Perimeter
Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
Total Surface Area of Dodecahedron given Perimeter
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
Total Surface Area of Dodecahedron
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron given Lateral Surface Area
Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron
Total Surface Area of Dodecahedron given Face Area
Total Surface Area of Dodecahedron = 12*Face Area of Dodecahedron

## < 8 Area of Dodecahedron Calculators

Lateral Surface Area of Dodecahedron given Circumsphere Radius
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
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
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
Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
Lateral Surface Area of Dodecahedron
Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Face Area of Dodecahedron
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
Lateral Surface Area of Dodecahedron = 5/6*Total Surface Area of Dodecahedron

## Total Surface Area of Dodecahedron Formula

Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
TSA = 3*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 Total Surface Area of Dodecahedron?

Total Surface Area of Dodecahedron calculator uses Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2 to calculate the Total Surface Area of Dodecahedron, Total Surface Area of Dodecahedron formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron. Total Surface Area of Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Dodecahedron using this online calculator? To use this online calculator for Total Surface Area of Dodecahedron, enter Edge Length of Dodecahedron (le) and hit the calculate button. Here is how the Total Surface Area of Dodecahedron calculation can be explained with given input values -> 2064.573 = 3*sqrt(25+(10*sqrt(5)))*10^2.

### FAQ

What is Total Surface Area of Dodecahedron?
Total Surface Area of Dodecahedron formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron and is represented as TSA = 3*sqrt(25+(10*sqrt(5)))*le^2 or Total Surface Area of Dodecahedron = 3*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 Total Surface Area of Dodecahedron?
Total Surface Area of Dodecahedron formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron is calculated using Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2. To calculate Total Surface 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 Total Surface Area of Dodecahedron?
In this formula, Total Surface Area of Dodecahedron uses Edge Length of Dodecahedron. We can use 13 other way(s) to calculate the same, which is/are as follows -
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Total Surface Area of Dodecahedron = 12*Face Area of Dodecahedron
• Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
• Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
• Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
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