Total Surface Area of Great Stellated Dodecahedron Calculator

✖Edge Length of Great Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron.ⓘ Edge Length of Great Stellated Dodecahedron [l_e]

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✖Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.ⓘ Total Surface Area of Great Stellated Dodecahedron [TSA]

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Formula

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Total Surface Area of Great Stellated Dodecahedron

Formula

`"TSA" = 15*sqrt(5+(2*sqrt(5)))*"l"_{"e"}^2`

Example

`"4616.525m²"=15*sqrt(5+(2*sqrt(5)))*("10m")^2`

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Total Surface Area of Great Stellated Dodecahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2
TSA = 15*sqrt(5+(2*sqrt(5)))*l_e^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

Total Surface Area of Great Stellated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.
Edge Length of Great Stellated Dodecahedron - (Measured in Meter) - Edge Length of Great Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Great Stellated Dodecahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 15*sqrt(5+(2*sqrt(5)))*l_e^2 --> 15*sqrt(5+(2*sqrt(5)))*10^2

Evaluating ... ...

TSA = 4616.52530576288

STEP 3: Convert Result to Output's Unit

4616.52530576288 Square Meter --> No Conversion Required

FINAL ANSWER

4616.52530576288 ≈ 4616.525 Square Meter <-- Total Surface Area of Great Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< 7 Surface Area of Great Stellated Dodecahedron Calculators

Total Surface Area of Great Stellated Dodecahedron given Surface to Volume Ratio

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^2

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2

Total Surface Area of Great Stellated Dodecahedron given Circumradius

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2

Total Surface Area of Great Stellated Dodecahedron given Volume

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(2/3)

Total Surface Area of Great Stellated Dodecahedron given Ridge Length

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^2

Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2

Total Surface Area of Great Stellated Dodecahedron

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2

Total Surface Area of Great Stellated Dodecahedron Formula

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2
TSA = 15*sqrt(5+(2*sqrt(5)))*l_e^2

What is Great Stellated Dodecahedron?

The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

How to Calculate Total Surface Area of Great Stellated Dodecahedron?

Total Surface Area of Great Stellated Dodecahedron calculator uses Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2 to calculate the Total Surface Area of Great Stellated Dodecahedron, Total Surface Area of Great Stellated Dodecahedron formula is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron. Total Surface Area of Great Stellated Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Stellated Dodecahedron using this online calculator? To use this online calculator for Total Surface Area of Great Stellated Dodecahedron, enter Edge Length of Great Stellated Dodecahedron (l_e) and hit the calculate button. Here is how the Total Surface Area of Great Stellated Dodecahedron calculation can be explained with given input values -> 4616.525 = 15*sqrt(5+(2*sqrt(5)))*10^2.

FAQ

What is Total Surface Area of Great Stellated Dodecahedron?

Total Surface Area of Great Stellated Dodecahedron formula is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron and is represented as TSA = 15*sqrt(5+(2*sqrt(5)))*l_e^2 or Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2. Edge Length of Great Stellated Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Stellated Dodecahedron.

How to calculate Total Surface Area of Great Stellated Dodecahedron?

Total Surface Area of Great Stellated Dodecahedron formula is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron is calculated using Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2. To calculate Total Surface Area of Great Stellated Dodecahedron, you need Edge Length of Great Stellated Dodecahedron (l_e). With our tool, you need to enter the respective value for Edge Length of Great Stellated 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 Great Stellated Dodecahedron?

In this formula, Total Surface Area of Great Stellated Dodecahedron uses Edge Length of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(2/3)
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^2

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