Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length Calculator

✖Lateral Surface Area of Icosahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron.ⓘ Lateral Surface Area of Icosahedron [LSA]			+10% -10%
✖Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.ⓘ Edge Length of Icosahedron [l_e]			+10% -10%

✖Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.ⓘ Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length [TSA]

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Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2
TSA = LSA+sqrt(3)/2*l_e^2
This formula uses 1 Functions, 3 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 Icosahedron - (Measured in Square Meter) - Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.
Lateral Surface Area of Icosahedron - (Measured in Square Meter) - Lateral Surface Area of Icosahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron.
Edge Length of Icosahedron - (Measured in Meter) - Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Lateral Surface Area of Icosahedron: 780 Square Meter --> 780 Square Meter No Conversion Required
Edge Length of Icosahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = LSA+sqrt(3)/2*l_e^2 --> 780+sqrt(3)/2*10^2

Evaluating ... ...

TSA = 866.602540378444

STEP 3: Convert Result to Output's Unit

866.602540378444 Square Meter --> No Conversion Required

FINAL ANSWER

866.602540378444 ≈ 866.6025 Square Meter <-- Total Surface Area of Icosahedron

(Calculation completed in 00.020 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Total Surface Area of Icosahedron Calculators

Total Surface Area of Icosahedron given Circumsphere Radius

LaTeX Go Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2

Total Surface Area of Icosahedron given Midsphere Radius

LaTeX Go Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2

Total Surface Area of Icosahedron given Volume

LaTeX Go Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(2/3)

Total Surface Area of Icosahedron

LaTeX Go Total Surface Area of Icosahedron = 5*sqrt(3)*Edge Length of Icosahedron^2

< Surface Area of Icosahedron Calculators

Face Area of Icosahedron given Circumsphere Radius

LaTeX Go Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2

Lateral Surface Area of Icosahedron

LaTeX Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*Edge Length of Icosahedron^2

Face Area of Icosahedron

LaTeX Go Face Area of Icosahedron = sqrt(3)/4*Edge Length of Icosahedron^2

Face Area of Icosahedron given Total Surface Area

LaTeX Go Face Area of Icosahedron = Total Surface Area of Icosahedron/20

Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length Formula

LaTeX Go

Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2
TSA = LSA+sqrt(3)/2*l_e^2

What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

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 Icosahedron given Lateral Surface Area and Edge Length?

Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length calculator uses Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2 to calculate the Total Surface Area of Icosahedron, The Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the lateral surface area and edge length of the Icosahedron. Total Surface Area of Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length using this online calculator? To use this online calculator for Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length, enter Lateral Surface Area of Icosahedron (LSA) & Edge Length of Icosahedron (l_e) and hit the calculate button. Here is how the Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length calculation can be explained with given input values -> 866.6025 = 780+sqrt(3)/2*10^2.

FAQ

What is Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length?

The Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the lateral surface area and edge length of the Icosahedron and is represented as TSA = LSA+sqrt(3)/2*l_e^2 or Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2. Lateral Surface Area of Icosahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron & Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.

How to calculate Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length?

The Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the lateral surface area and edge length of the Icosahedron is calculated using Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2. To calculate Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length, you need Lateral Surface Area of Icosahedron (LSA) & Edge Length of Icosahedron (l_e). With our tool, you need to enter the respective value for Lateral Surface Area of Icosahedron & Edge Length of Icosahedron 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 Icosahedron?

In this formula, Total Surface Area of Icosahedron uses Lateral Surface Area of Icosahedron & Edge Length of Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(2/3)
Total Surface Area of Icosahedron = 5*sqrt(3)*Edge Length of Icosahedron^2

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