Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height Calculator

✖Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.ⓘ Pyramidal Height of Great Stellated Dodecahedron [h_Pyramid]

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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 given Pyramidal Height [TSA]

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Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
TSA = 15*sqrt(5+(2*sqrt(5)))*((6*h_Pyramid)/(sqrt(3)*(3+sqrt(5))))^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.
Pyramidal Height of Great Stellated Dodecahedron - (Measured in Meter) - Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pyramidal Height of Great Stellated Dodecahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 15*sqrt(5+(2*sqrt(5)))*((6*h_Pyramid)/(sqrt(3)*(3+sqrt(5))))^2 --> 15*sqrt(5+(2*sqrt(5)))*((6*15)/(sqrt(3)*(3+sqrt(5))))^2

Evaluating ... ...

TSA = 4546.4082628683

STEP 3: Convert Result to Output's Unit

4546.4082628683 Square Meter --> No Conversion Required

FINAL ANSWER

4546.4082628683 ≈ 4546.408 Square Meter <-- Total Surface Area of Great Stellated Dodecahedron

(Calculation completed in 00.020 seconds)

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< Surface Area of Great Stellated Dodecahedron Calculators

Total Surface Area of Great Stellated Dodecahedron given Circumradius

LaTeX 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 Ridge Length

LaTeX 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

LaTeX 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

LaTeX 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 given Pyramidal Height Formula

LaTeX Go

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 given Pyramidal Height?

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height calculator uses 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 to calculate the Total Surface Area of Great Stellated Dodecahedron, Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height formula is defined as the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its pyramidal height. Total Surface Area of Great Stellated Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height using this online calculator? To use this online calculator for Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height, enter Pyramidal Height of Great Stellated Dodecahedron (h_Pyramid) and hit the calculate button. Here is how the Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height calculation can be explained with given input values -> 4546.408 = 15*sqrt(5+(2*sqrt(5)))*((6*15)/(sqrt(3)*(3+sqrt(5))))^2.

FAQ

What is Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height?

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height formula is defined as the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its pyramidal height and is represented as TSA = 15*sqrt(5+(2*sqrt(5)))*((6*h_Pyramid)/(sqrt(3)*(3+sqrt(5))))^2 or 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. Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.

How to calculate Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height?

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height formula is defined as the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its pyramidal height is calculated using 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. To calculate Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height, you need Pyramidal Height of Great Stellated Dodecahedron (h_Pyramid). With our tool, you need to enter the respective value for Pyramidal Height 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 Pyramidal Height of Great Stellated Dodecahedron. We can use 3 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)))*Edge Length of Great Stellated Dodecahedron^2
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

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