Total Surface Area of Triangular Cupola given Height Calculator

✖Height of Triangular Cupola is the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola.ⓘ Height of Triangular Cupola [h]

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✖Total Surface Area of Triangular Cupola is the total amount of 2D space occupied by all the faces of the Triangular Cupola.ⓘ Total Surface Area of Triangular Cupola given Height [TSA]

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Formula

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Total Surface Area of Triangular Cupola given Height

Formula

`"TSA" = (3+(5*sqrt(3))/2)*"h"^(2)/(1-(1/4*cosec(pi/3)^(2)))`

Example

`"703.6922m²"=(3+(5*sqrt(3))/2)*("8m")^(2)/(1-(1/4*cosec(pi/3)^(2)))`

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Total Surface Area of Triangular Cupola given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Height of Triangular Cupola^(2)/(1-(1/4*cosec(pi/3)^(2)))
TSA = (3+(5*sqrt(3))/2)*h^(2)/(1-(1/4*cosec(pi/3)^(2)))
This formula uses 1 Constants, 3 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
cosec - The cosecant function is a trigonometric function that is the reciprocal of the sine function., cosec(Angle)
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 Triangular Cupola - (Measured in Square Meter) - Total Surface Area of Triangular Cupola is the total amount of 2D space occupied by all the faces of the Triangular Cupola.
Height of Triangular Cupola - (Measured in Meter) - Height of Triangular Cupola is the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola.

STEP 1: Convert Input(s) to Base Unit

Height of Triangular Cupola: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (3+(5*sqrt(3))/2)*h^(2)/(1-(1/4*cosec(pi/3)^(2))) --> (3+(5*sqrt(3))/2)*8^(2)/(1-(1/4*cosec(pi/3)^(2)))

Evaluating ... ...

TSA = 703.692193816531

STEP 3: Convert Result to Output's Unit

703.692193816531 Square Meter --> No Conversion Required

FINAL ANSWER

703.692193816531 ≈ 703.6922 Square Meter <-- Total Surface Area of Triangular Cupola

(Calculation completed in 00.020 seconds)

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< 4 Total Surface Area of Triangular Cupola Calculators

Total Surface Area of Triangular Cupola given Surface to Volume Ratio

Go Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(2)

Total Surface Area of Triangular Cupola given Height

Go Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Height of Triangular Cupola^(2)/(1-(1/4*cosec(pi/3)^(2)))

Total Surface Area of Triangular Cupola given Volume

Go Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*((3*sqrt(2)*Volume of Triangular Cupola)/5)^(2/3)

Total Surface Area of Triangular Cupola

Go Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Edge Length of Triangular Cupola^(2)

Total Surface Area of Triangular Cupola given Height Formula

Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Height of Triangular Cupola^(2)/(1-(1/4*cosec(pi/3)^(2)))
TSA = (3+(5*sqrt(3))/2)*h^(2)/(1-(1/4*cosec(pi/3)^(2)))

What is a Triangular Cupola?

A cupola is a polyhedron with two opposite polygons, of which one has twice as many vertices as the other and with alternating triangles and quadrangles as side faces. When all faces of the cupola are regular, then the cupola itself is regular and is a Johnson solid. There are three regular cupolae, the triangular, the square, and the pentagonal cupola. A Triangular Cupola has 8 faces, 15 edges, and 9 vertices. Its top surface is an equilateral triangle and its base surface is a regular hexagon.

How to Calculate Total Surface Area of Triangular Cupola given Height?

Total Surface Area of Triangular Cupola given Height calculator uses Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Height of Triangular Cupola^(2)/(1-(1/4*cosec(pi/3)^(2))) to calculate the Total Surface Area of Triangular Cupola, The Total Surface Area of Triangular Cupola given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Triangular Cupola and is calculated using the height of the Triangular Cupola. Total Surface Area of Triangular Cupola is denoted by TSA symbol.

How to calculate Total Surface Area of Triangular Cupola given Height using this online calculator? To use this online calculator for Total Surface Area of Triangular Cupola given Height, enter Height of Triangular Cupola (h) and hit the calculate button. Here is how the Total Surface Area of Triangular Cupola given Height calculation can be explained with given input values -> 703.6922 = (3+(5*sqrt(3))/2)*8^(2)/(1-(1/4*cosec(pi/3)^(2))).

FAQ

What is Total Surface Area of Triangular Cupola given Height?

The Total Surface Area of Triangular Cupola given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Triangular Cupola and is calculated using the height of the Triangular Cupola and is represented as TSA = (3+(5*sqrt(3))/2)*h^(2)/(1-(1/4*cosec(pi/3)^(2))) or Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Height of Triangular Cupola^(2)/(1-(1/4*cosec(pi/3)^(2))). Height of Triangular Cupola is the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola.

How to calculate Total Surface Area of Triangular Cupola given Height?

The Total Surface Area of Triangular Cupola given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Triangular Cupola and is calculated using the height of the Triangular Cupola is calculated using Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Height of Triangular Cupola^(2)/(1-(1/4*cosec(pi/3)^(2))). To calculate Total Surface Area of Triangular Cupola given Height, you need Height of Triangular Cupola (h). With our tool, you need to enter the respective value for Height of Triangular Cupola 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 Triangular Cupola?

In this formula, Total Surface Area of Triangular Cupola uses Height of Triangular Cupola. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*Edge Length of Triangular Cupola^(2)
Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*((3*sqrt(2)*Volume of Triangular Cupola)/5)^(2/3)
Total Surface Area of Triangular Cupola = (3+(5*sqrt(3))/2)*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(2)

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