Edge Length 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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✖Edge Length of Triangular Cupola is the length of any edge of the Triangular Cupola.ⓘ Edge Length of Triangular Cupola given Height [l_e]

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Edge Length of Triangular Cupola given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Triangular Cupola = Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2)))
l_e = h/sqrt(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

Edge Length of Triangular Cupola - (Measured in Meter) - Edge Length of Triangular Cupola is the length of any edge 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

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

Evaluating ... ...

l_e = 9.79795897113271

STEP 3: Convert Result to Output's Unit

9.79795897113271 Meter --> No Conversion Required

FINAL ANSWER

9.79795897113271 ≈ 9.797959 Meter <-- Edge Length of Triangular Cupola

(Calculation completed in 00.004 seconds)

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< Edge Length of Triangular Cupola Calculators

Edge Length of Triangular Cupola given Height

LaTeX Go Edge Length of Triangular Cupola = Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2)))

Edge Length of Triangular Cupola given Surface to Volume Ratio

LaTeX Go Edge Length of Triangular Cupola = ((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola)

Edge Length of Triangular Cupola given Total Surface Area

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

Edge Length of Triangular Cupola given Volume

LaTeX Go Edge Length of Triangular Cupola = ((3*sqrt(2)*Volume of Triangular Cupola)/5)^(1/3)

Edge Length of Triangular Cupola given Height Formula

LaTeX Go

Edge Length of Triangular Cupola = Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2)))
l_e = h/sqrt(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 Edge Length of Triangular Cupola given Height?

Edge Length of Triangular Cupola given Height calculator uses Edge Length of Triangular Cupola = Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2))) to calculate the Edge Length of Triangular Cupola, The Edge Length of Triangular Cupola given Height formula is defined as the length of any edge of the Triangular Cupola and is calculated using the height of the Triangular Cupola. Edge Length of Triangular Cupola is denoted by l_e symbol.

How to calculate Edge Length of Triangular Cupola given Height using this online calculator? To use this online calculator for Edge Length of Triangular Cupola given Height, enter Height of Triangular Cupola (h) and hit the calculate button. Here is how the Edge Length of Triangular Cupola given Height calculation can be explained with given input values -> 9.797959 = 8/sqrt(1-(1/4*cosec(pi/3)^(2))).

FAQ

What is Edge Length of Triangular Cupola given Height?

The Edge Length of Triangular Cupola given Height formula is defined as the length of any edge of the Triangular Cupola and is calculated using the height of the Triangular Cupola and is represented as l_e = h/sqrt(1-(1/4*cosec(pi/3)^(2))) or Edge Length of Triangular Cupola = Height of Triangular Cupola/sqrt(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 Edge Length of Triangular Cupola given Height?

The Edge Length of Triangular Cupola given Height formula is defined as the length of any edge of the Triangular Cupola and is calculated using the height of the Triangular Cupola is calculated using Edge Length of Triangular Cupola = Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2))). To calculate Edge Length 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 Edge Length of Triangular Cupola?

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

Edge Length of Triangular Cupola = sqrt(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))
Edge Length of Triangular Cupola = ((3*sqrt(2)*Volume of Triangular Cupola)/5)^(1/3)
Edge Length of Triangular Cupola = ((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola)

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