## Lateral Surface Area of Dodecahedron given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lateral Surface Area of Dodecahedron = 5/2*(Perimeter of Dodecahedron/30)^2*sqrt(25+10*sqrt(5))
LSA = 5/2*(P/30)^2*sqrt(25+10*sqrt(5))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre 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.
Perimeter of Dodecahedron - (Measured in Meter) - Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Perimeter of Dodecahedron: 300 Meter --> 300 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
LSA = 5/2*(P/30)^2*sqrt(25+10*sqrt(5)) --> 5/2*(300/30)^2*sqrt(25+10*sqrt(5))
Evaluating ... ...
LSA = 1720.47740058897
STEP 3: Convert Result to Output's Unit
1720.47740058897 Square Meter --> No Conversion Required
1720.47740058897 Square Meter <-- Lateral Surface Area of Dodecahedron
(Calculation completed in 00.003 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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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)*((12*sqrt((25+10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+7*sqrt(5))))^2*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Insphere Radius
Lateral Surface Area of Dodecahedron = (5/2)*((2*Insphere Radius of Dodecahedron)/(sqrt((25+11*sqrt(5))/10)))^2*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Circumsphere Radius
Lateral Surface Area of Dodecahedron = (5/2)*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Space Diagonal
Lateral Surface Area of Dodecahedron = (5/2)*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Midsphere Radius
Lateral Surface Area of Dodecahedron = (5/2)*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Face Diagonal
Lateral Surface Area of Dodecahedron = (5/2)*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Volume
Lateral Surface Area of Dodecahedron = (5/2)*((4*Volume of Dodecahedron)/(15+7*sqrt(5)))^(2/3)*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Face Perimeter
Lateral Surface Area of Dodecahedron = Face Perimeter of Dodecahedron^2/10*(sqrt(25+10*sqrt(5)))
Lateral Surface Area of Dodecahedron given Perimeter
Lateral Surface Area of Dodecahedron = 5/2*(Perimeter of Dodecahedron/30)^2*sqrt(25+10*sqrt(5))
Lateral Surface Area of Dodecahedron
Lateral Surface Area of Dodecahedron = (5/2)*Edge Length of Dodecahedron^2*sqrt(25+10*sqrt(5))
Lateral Surface Area of Dodecahedron given Total Surface Area
Lateral Surface Area of Dodecahedron = 5*Total Surface Area of Dodecahedron/6
Lateral Surface Area of Dodecahedron given Face Area
Lateral Surface Area of Dodecahedron = 10*Face Area of Dodecahedron

## Lateral Surface Area of Dodecahedron given Perimeter Formula

Lateral Surface Area of Dodecahedron = 5/2*(Perimeter of Dodecahedron/30)^2*sqrt(25+10*sqrt(5))
LSA = 5/2*(P/30)^2*sqrt(25+10*sqrt(5))

## 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 Perimeter?

Lateral Surface Area of Dodecahedron given Perimeter calculator uses Lateral Surface Area of Dodecahedron = 5/2*(Perimeter of Dodecahedron/30)^2*sqrt(25+10*sqrt(5)) to calculate the Lateral Surface Area of Dodecahedron, The Lateral Surface Area of Dodecahedron given Perimeter 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 the perimeter of the Dodecahedron. Lateral Surface Area of Dodecahedron is denoted by LSA symbol.

How to calculate Lateral Surface Area of Dodecahedron given Perimeter using this online calculator? To use this online calculator for Lateral Surface Area of Dodecahedron given Perimeter, enter Perimeter of Dodecahedron (P) and hit the calculate button. Here is how the Lateral Surface Area of Dodecahedron given Perimeter calculation can be explained with given input values -> 1720.477 = 5/2*(300/30)^2*sqrt(25+10*sqrt(5)).

### FAQ

What is Lateral Surface Area of Dodecahedron given Perimeter?
The Lateral Surface Area of Dodecahedron given Perimeter 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 the perimeter of the Dodecahedron and is represented as LSA = 5/2*(P/30)^2*sqrt(25+10*sqrt(5)) or Lateral Surface Area of Dodecahedron = 5/2*(Perimeter of Dodecahedron/30)^2*sqrt(25+10*sqrt(5)). Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
How to calculate Lateral Surface Area of Dodecahedron given Perimeter?
The Lateral Surface Area of Dodecahedron given Perimeter 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 the perimeter of the Dodecahedron is calculated using Lateral Surface Area of Dodecahedron = 5/2*(Perimeter of Dodecahedron/30)^2*sqrt(25+10*sqrt(5)). To calculate Lateral Surface Area of Dodecahedron given Perimeter, you need Perimeter of Dodecahedron (P). With our tool, you need to enter the respective value for Perimeter 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 Perimeter 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)*Edge Length of Dodecahedron^2*sqrt(25+10*sqrt(5))
• Lateral Surface Area of Dodecahedron = 10*Face Area of Dodecahedron
• Lateral Surface Area of Dodecahedron = Face Perimeter of Dodecahedron^2/10*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = (5/2)*((4*Volume of Dodecahedron)/(15+7*sqrt(5)))^(2/3)*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = (5/2)*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = (5/2)*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = (5/2)*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = (5/2)*((2*Insphere Radius of Dodecahedron)/(sqrt((25+11*sqrt(5))/10)))^2*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = (5/2)*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = (5/2)*((12*sqrt((25+10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+7*sqrt(5))))^2*(sqrt(25+10*sqrt(5)))
• Lateral Surface Area of Dodecahedron = 5*Total Surface Area of Dodecahedron/6
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