Lateral Surface Area of Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
LSA = 5/2*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
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.
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
LSA = 5/2*sqrt(25+(10*sqrt(5)))*le^2 --> 5/2*sqrt(25+(10*sqrt(5)))*10^2
Evaluating ... ...
LSA = 1720.47740058897
STEP 3: Convert Result to Output's Unit
1720.47740058897 Square Meter --> No Conversion Required
FINAL ANSWER
1720.47740058897 1720.477 Square Meter <-- Lateral Surface Area of Dodecahedron
(Calculation completed in 00.004 seconds)

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Created by Nikhil
Mumbai University (DJSCE), Mumbai
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Lateral Surface Area of Dodecahedron Calculators

Lateral Surface Area of Dodecahedron given Volume
​ LaTeX ​ Go 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 Perimeter
​ LaTeX ​ Go Lateral Surface Area of Dodecahedron = sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2/10
Lateral Surface Area of Dodecahedron
​ LaTeX ​ Go Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Lateral Surface Area of Dodecahedron given Face Area
​ LaTeX ​ Go Lateral Surface Area of Dodecahedron = 10*Face Area of Dodecahedron

Area of Dodecahedron Calculators

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

Lateral Surface Area of Dodecahedron Formula

​LaTeX ​Go
Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
LSA = 5/2*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 Lateral Surface Area of Dodecahedron?

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

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

FAQ

What is Lateral Surface Area of Dodecahedron?
The Lateral Surface Area of Dodecahedron 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 is represented as LSA = 5/2*sqrt(25+(10*sqrt(5)))*le^2 or Lateral Surface Area of Dodecahedron = 5/2*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 Lateral Surface Area of Dodecahedron?
The Lateral Surface Area of Dodecahedron 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 is calculated using Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2. To calculate Lateral 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 Lateral Surface Area of Dodecahedron?
In this formula, Lateral Surface Area of Dodecahedron uses Edge Length of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • 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)
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