Total Surface Area of Dodecahedron given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron
TSA = 6/5*LSA
This formula uses 2 Variables
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.
Lateral Surface Area of Dodecahedron - (Measured in Square Meter) - Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Lateral Surface Area of Dodecahedron: 1750 Square Meter --> 1750 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = 6/5*LSA --> 6/5*1750
Evaluating ... ...
TSA = 2100
STEP 3: Convert Result to Output's Unit
2100 Square Meter --> No Conversion Required
FINAL ANSWER
2100 Square Meter <-- Total Surface Area of Dodecahedron
(Calculation completed in 00.020 seconds)

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Total Surface Area of Dodecahedron Calculators

Total Surface Area of Dodecahedron given Circumsphere Radius
​ LaTeX ​ Go 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 Volume
​ LaTeX ​ Go 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
​ LaTeX ​ Go 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
​ LaTeX ​ Go 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 Formula

​LaTeX ​Go
Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron
TSA = 6/5*LSA

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 given Lateral Surface Area?

Total Surface Area of Dodecahedron given Lateral Surface Area calculator uses Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron to calculate the Total Surface Area of Dodecahedron, The Total Surface Area of Dodecahedron given Lateral Surface Area formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using lateral surface area of Dodecahedron. Total Surface Area of Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Dodecahedron given Lateral Surface Area using this online calculator? To use this online calculator for Total Surface Area of Dodecahedron given Lateral Surface Area, enter Lateral Surface Area of Dodecahedron (LSA) and hit the calculate button. Here is how the Total Surface Area of Dodecahedron given Lateral Surface Area calculation can be explained with given input values -> 2100 = 6/5*1750.

FAQ

What is Total Surface Area of Dodecahedron given Lateral Surface Area?
The Total Surface Area of Dodecahedron given Lateral Surface Area formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using lateral surface area of Dodecahedron and is represented as TSA = 6/5*LSA or Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron. Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.
How to calculate Total Surface Area of Dodecahedron given Lateral Surface Area?
The Total Surface Area of Dodecahedron given Lateral Surface Area formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using lateral surface area of Dodecahedron is calculated using Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron. To calculate Total Surface Area of Dodecahedron given Lateral Surface Area, you need Lateral Surface Area of Dodecahedron (LSA). With our tool, you need to enter the respective value for Lateral Surface Area 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 Lateral Surface Area of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^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*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
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