Height of Star Pyramid given Ridge Length Calculator

✖Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.ⓘ Ridge Length of Star Pyramid [l_e(Ridge)]			+10% -10%
✖Pentagonal Edge Length of Base of Star Pyramid is the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed.ⓘ Pentagonal Edge Length of Base of Star Pyramid [l_e(Pentagon)]			+10% -10%

✖Height of Star Pyramid is the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid.ⓘ Height of Star Pyramid given Ridge Length [h]

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Formula

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Height of Star Pyramid given Ridge Length

Formula

`"h" = sqrt(("l"_{"e(Ridge)"})^2-("l"_{"e(Pentagon)"}^2/100*(50+10*sqrt(5))))`

Example

`"7.240324m"=sqrt(("8m")^2-(("4m")^2/100*(50+10*sqrt(5))))`

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Height of Star Pyramid given Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Star Pyramid = sqrt((Ridge Length of Star Pyramid)^2-(Pentagonal Edge Length of Base of Star Pyramid^2/100*(50+10*sqrt(5))))
h = sqrt((l_e(Ridge))^2-(l_e(Pentagon)^2/100*(50+10*sqrt(5))))
This formula uses 1 Functions, 3 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

Height of Star Pyramid - (Measured in Meter) - Height of Star Pyramid is the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid.
Ridge Length of Star Pyramid - (Measured in Meter) - Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.
Pentagonal Edge Length of Base of Star Pyramid - (Measured in Meter) - Pentagonal Edge Length of Base of Star Pyramid is the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed.

STEP 1: Convert Input(s) to Base Unit

Ridge Length of Star Pyramid: 8 Meter --> 8 Meter No Conversion Required
Pentagonal Edge Length of Base of Star Pyramid: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt((l_e(Ridge))^2-(l_e(Pentagon)^2/100*(50+10*sqrt(5)))) --> sqrt((8)^2-(4^2/100*(50+10*sqrt(5))))

Evaluating ... ...

h = 7.24032397313824

STEP 3: Convert Result to Output's Unit

7.24032397313824 Meter --> No Conversion Required

FINAL ANSWER

7.24032397313824 ≈ 7.240324 Meter <-- Height of Star Pyramid

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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< 3 Height of Star Pyramid Calculators

Height of Star Pyramid given Ridge Length

Go Height of Star Pyramid = sqrt((Ridge Length of Star Pyramid)^2-(Pentagonal Edge Length of Base of Star Pyramid^2/100*(50+10*sqrt(5))))

Height of Star Pyramid given Lateral Edge Length

Go Height of Star Pyramid = sqrt(Lateral Edge Length of Star Pyramid^2-(Chord Length of Star Pyramid^2/100*(50+10*sqrt(5))))

Height of Star Pyramid given Volume

Go Height of Star Pyramid = (6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2)

Height of Star Pyramid given Ridge Length Formula

Height of Star Pyramid = sqrt((Ridge Length of Star Pyramid)^2-(Pentagonal Edge Length of Base of Star Pyramid^2/100*(50+10*sqrt(5))))
h = sqrt((l_e(Ridge))^2-(l_e(Pentagon)^2/100*(50+10*sqrt(5))))

What is a Star Pyramid?

A Star Pyramid is based on a regular pentagram and is concave. It is a pyramid with a pentagrammic base. It has 11 faces which include a pentagram base surface and 10 triangular surfaces. Also, It has 20 edges and 6 vertices.

How to Calculate Height of Star Pyramid given Ridge Length?

Height of Star Pyramid given Ridge Length calculator uses Height of Star Pyramid = sqrt((Ridge Length of Star Pyramid)^2-(Pentagonal Edge Length of Base of Star Pyramid^2/100*(50+10*sqrt(5)))) to calculate the Height of Star Pyramid, Height of Star Pyramid given Ridge Length formula is defined as the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid and is calculated using the ridge length and pentagonal edge length of base of the Star Pyramid. Height of Star Pyramid is denoted by h symbol.

How to calculate Height of Star Pyramid given Ridge Length using this online calculator? To use this online calculator for Height of Star Pyramid given Ridge Length, enter Ridge Length of Star Pyramid (l_e(Ridge)) & Pentagonal Edge Length of Base of Star Pyramid (l_e(Pentagon)) and hit the calculate button. Here is how the Height of Star Pyramid given Ridge Length calculation can be explained with given input values -> 7.240324 = sqrt((8)^2-(4^2/100*(50+10*sqrt(5)))).

FAQ

What is Height of Star Pyramid given Ridge Length?

Height of Star Pyramid given Ridge Length formula is defined as the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid and is calculated using the ridge length and pentagonal edge length of base of the Star Pyramid and is represented as h = sqrt((l_e(Ridge))^2-(l_e(Pentagon)^2/100*(50+10*sqrt(5)))) or Height of Star Pyramid = sqrt((Ridge Length of Star Pyramid)^2-(Pentagonal Edge Length of Base of Star Pyramid^2/100*(50+10*sqrt(5)))). Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid & Pentagonal Edge Length of Base of Star Pyramid is the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed.

How to calculate Height of Star Pyramid given Ridge Length?

Height of Star Pyramid given Ridge Length formula is defined as the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid and is calculated using the ridge length and pentagonal edge length of base of the Star Pyramid is calculated using Height of Star Pyramid = sqrt((Ridge Length of Star Pyramid)^2-(Pentagonal Edge Length of Base of Star Pyramid^2/100*(50+10*sqrt(5)))). To calculate Height of Star Pyramid given Ridge Length, you need Ridge Length of Star Pyramid (l_e(Ridge)) & Pentagonal Edge Length of Base of Star Pyramid (l_e(Pentagon)). With our tool, you need to enter the respective value for Ridge Length of Star Pyramid & Pentagonal Edge Length of Base of Star Pyramid 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 Height of Star Pyramid?

In this formula, Height of Star Pyramid uses Ridge Length of Star Pyramid & Pentagonal Edge Length of Base of Star Pyramid. We can use 2 other way(s) to calculate the same, which is/are as follows -

Height of Star Pyramid = sqrt(Lateral Edge Length of Star Pyramid^2-(Chord Length of Star Pyramid^2/100*(50+10*sqrt(5))))
Height of Star Pyramid = (6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2)

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