## Lateral Surface Area of Dodecahedron given Face Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
LSA = 5/2*sqrt(25+(10*sqrt(5)))*((2*dFace)/(1+sqrt(5)))^2
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
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.
Face Diagonal of Dodecahedron - (Measured in Meter) - The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Face Diagonal of Dodecahedron: 16 Meter --> 16 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
LSA = 5/2*sqrt(25+(10*sqrt(5)))*((2*dFace)/(1+sqrt(5)))^2 --> 5/2*sqrt(25+(10*sqrt(5)))*((2*16)/(1+sqrt(5)))^2
Evaluating ... ...
LSA = 1682.33955878123
STEP 3: Convert Result to Output's Unit
1682.33955878123 Square Meter --> No Conversion Required
1682.33955878123 1682.34 Square Meter <-- Lateral Surface Area of Dodecahedron
(Calculation completed in 00.003 seconds)
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## < 12 Lateral Surface Area of Dodecahedron Calculators

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

## Lateral Surface Area of Dodecahedron given Face Diagonal Formula

Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
LSA = 5/2*sqrt(25+(10*sqrt(5)))*((2*dFace)/(1+sqrt(5)))^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 Lateral Surface Area of Dodecahedron given Face Diagonal?

Lateral Surface Area of Dodecahedron given Face Diagonal calculator uses Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2 to calculate the Lateral Surface Area of Dodecahedron, The Lateral Surface Area of Dodecahedron given Face Diagonal formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron, and calculated using face diagonal of Dodecahedron. Lateral Surface Area of Dodecahedron is denoted by LSA symbol.

How to calculate Lateral Surface Area of Dodecahedron given Face Diagonal using this online calculator? To use this online calculator for Lateral Surface Area of Dodecahedron given Face Diagonal, enter Face Diagonal of Dodecahedron (dFace) and hit the calculate button. Here is how the Lateral Surface Area of Dodecahedron given Face Diagonal calculation can be explained with given input values -> 1682.34 = 5/2*sqrt(25+(10*sqrt(5)))*((2*16)/(1+sqrt(5)))^2.

### FAQ

What is Lateral Surface Area of Dodecahedron given Face Diagonal?
The Lateral Surface Area of Dodecahedron given Face Diagonal formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron, and calculated using face diagonal of Dodecahedron and is represented as LSA = 5/2*sqrt(25+(10*sqrt(5)))*((2*dFace)/(1+sqrt(5)))^2 or Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2. The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.
How to calculate Lateral Surface Area of Dodecahedron given Face Diagonal?
The Lateral Surface Area of Dodecahedron given Face Diagonal formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron, and calculated using face diagonal of Dodecahedron is calculated using Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2. To calculate Lateral Surface Area of Dodecahedron given Face Diagonal, you need Face Diagonal of Dodecahedron (dFace). With our tool, you need to enter the respective value for Face Diagonal 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 Lateral Surface Area of Dodecahedron?
In this formula, Lateral Surface Area of Dodecahedron uses Face Diagonal of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
• Lateral Surface Area of Dodecahedron = 10*Face Area of Dodecahedron
• Lateral Surface Area of Dodecahedron = sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2/10
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((12*sqrt((25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
• Lateral Surface Area of Dodecahedron = 5/6*Total Surface Area of Dodecahedron
• Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2 Let Others Know