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Edge length of Pentagonal Cupola given height Solution

STEP 0: Pre-Calculation Summary
Formula Used
side = Height/(sqrt(1-(1/4)*cosec(pi/Number of vertices on top surface)))
S = h/(sqrt(1-(1/4)*cosec(pi/NVertices_TopSurface)))
This formula uses 2 Constants, 4 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
cos - Trigonometric cosine function, cos(Angle)
sec - Trigonometric secant function, sec(Angle)
cosec - Trigonometric cosecant function, cosec(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Height - Height is the distance between the lowest and highest points of a person standing upright. (Measured in Meter)
Number of vertices on top surface- Number of vertices on top surface is the total number of vertices of the given 3D object.
STEP 1: Convert Input(s) to Base Unit
Height: 12 Meter --> 12 Meter No Conversion Required
Number of vertices on top surface: 5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
S = h/(sqrt(1-(1/4)*cosec(pi/NVertices_TopSurface))) --> 12/(sqrt(1-(1/4)*cosec(pi/5)))
Evaluating ... ...
S = 15.829611144581
STEP 3: Convert Result to Output's Unit
15.829611144581 Meter --> No Conversion Required
FINAL ANSWER
15.829611144581 Meter <-- Side
(Calculation completed in 00.018 seconds)

4 Edge length of Pentagonal Cupola Calculators

Edge length of Pentagonal Cupola given surface to volume ratio
side = ((1/4)*(20+(5*sqrt(3))+sqrt(5*(145+62*sqrt(5)))))/((1/6)*(5+(4*sqrt(5)))*Surface to Volume Ratio) Go
Edge length of Pentagonal Cupola given surface area
side = sqrt(Surface Area/((1/4)*(20+(5*sqrt(3))+sqrt(5*(145+62*sqrt(5)))))) Go
Edge length of Pentagonal Cupola given height
side = Height/(sqrt(1-(1/4)*cosec(pi/Number of vertices on top surface))) Go
Edge length of Pentagonal Cupola given volume
side = (Volume/((1/6)*(5+(4*sqrt(5)))))^(1/3) Go

Edge length of Pentagonal Cupola given height Formula

side = Height/(sqrt(1-(1/4)*cosec(pi/Number of vertices on top surface)))
S = h/(sqrt(1-(1/4)*cosec(pi/NVertices_TopSurface)))

What is a 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 (J3), the square (J4) and the pentagonal (J5) cupola.

How to Calculate Edge length of Pentagonal Cupola given height?

Edge length of Pentagonal Cupola given height calculator uses side = Height/(sqrt(1-(1/4)*cosec(pi/Number of vertices on top surface))) to calculate the Side, The Edge length of Pentagonal Cupola given height formula is defined as straight line joining two adjacent vertices of cupola , Where, a = cupola edge. Side and is denoted by S symbol.

How to calculate Edge length of Pentagonal Cupola given height using this online calculator? To use this online calculator for Edge length of Pentagonal Cupola given height, enter Height (h) & Number of vertices on top surface (NVertices_TopSurface) and hit the calculate button. Here is how the Edge length of Pentagonal Cupola given height calculation can be explained with given input values -> 15.82961 = 12/(sqrt(1-(1/4)*cosec(pi/5))).

FAQ

What is Edge length of Pentagonal Cupola given height?
The Edge length of Pentagonal Cupola given height formula is defined as straight line joining two adjacent vertices of cupola , Where, a = cupola edge and is represented as S = h/(sqrt(1-(1/4)*cosec(pi/NVertices_TopSurface))) or side = Height/(sqrt(1-(1/4)*cosec(pi/Number of vertices on top surface))). Height is the distance between the lowest and highest points of a person standing upright & Number of vertices on top surface is the total number of vertices of the given 3D object.
How to calculate Edge length of Pentagonal Cupola given height?
The Edge length of Pentagonal Cupola given height formula is defined as straight line joining two adjacent vertices of cupola , Where, a = cupola edge is calculated using side = Height/(sqrt(1-(1/4)*cosec(pi/Number of vertices on top surface))). To calculate Edge length of Pentagonal Cupola given height, you need Height (h) & Number of vertices on top surface (NVertices_TopSurface). With our tool, you need to enter the respective value for Height & Number of vertices on top surface 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 Side?
In this formula, Side uses Height & Number of vertices on top surface. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • side = Height/(sqrt(1-(1/4)*cosec(pi/Number of vertices on top surface)))
  • side = sqrt(Surface Area/((1/4)*(20+(5*sqrt(3))+sqrt(5*(145+62*sqrt(5))))))
  • side = (Volume/((1/6)*(5+(4*sqrt(5)))))^(1/3)
  • side = ((1/4)*(20+(5*sqrt(3))+sqrt(5*(145+62*sqrt(5)))))/((1/6)*(5+(4*sqrt(5)))*Surface to Volume Ratio)
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