Chord Length of Pentagram given Area and Short Chord Slice Calculator

✖The Area of Pentagram is the total quantity of plane enclosed by the boundary of the entire Pentagram shape.ⓘ Area of Pentagram [A]			+10% -10%
✖The Short Chord Slice of Pentagram is the edge length of the regular pentagon which form inside the Pentagram when all the chords are drawn.ⓘ Short Chord Slice of Pentagram [l_{Short Chord Slice}]			+10% -10%

✖The Chord Length of Pentagram is the diagonal length of regular pentagon from which the Pentagram is constructed using it's diagonals.ⓘ Chord Length of Pentagram given Area and Short Chord Slice [l_c]

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Formula

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Chord Length of Pentagram given Area and Short Chord Slice

Formula

`"l"_{"c"} = sqrt((2*"A")/sqrt(5*(5-2*sqrt(5))))+("l"_{"Short Chord Slice"}*"[phi]")`

Example

`"16.39614m"=sqrt((2*"80m²")/sqrt(5*(5-2*sqrt(5))))+("4m"*"[phi]")`

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Chord Length of Pentagram given Area and Short Chord Slice Solution

STEP 0: Pre-Calculation Summary

Formula Used

Chord Length of Pentagram = sqrt((2*Area of Pentagram)/sqrt(5*(5-2*sqrt(5))))+(Short Chord Slice of Pentagram*[phi])
l_c = sqrt((2*A)/sqrt(5*(5-2*sqrt(5))))+(l_{Short Chord Slice}*[phi])
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

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

Chord Length of Pentagram - (Measured in Meter) - The Chord Length of Pentagram is the diagonal length of regular pentagon from which the Pentagram is constructed using it's diagonals.
Area of Pentagram - (Measured in Square Meter) - The Area of Pentagram is the total quantity of plane enclosed by the boundary of the entire Pentagram shape.
Short Chord Slice of Pentagram - (Measured in Meter) - The Short Chord Slice of Pentagram is the edge length of the regular pentagon which form inside the Pentagram when all the chords are drawn.

STEP 1: Convert Input(s) to Base Unit

Area of Pentagram: 80 Square Meter --> 80 Square Meter No Conversion Required
Short Chord Slice of Pentagram: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = sqrt((2*A)/sqrt(5*(5-2*sqrt(5))))+(l_{Short Chord Slice}*[phi]) --> sqrt((2*80)/sqrt(5*(5-2*sqrt(5))))+(4*[phi])

Evaluating ... ...

l_c = 16.3961408516937

STEP 3: Convert Result to Output's Unit

16.3961408516937 Meter --> No Conversion Required

FINAL ANSWER

16.3961408516937 ≈ 16.39614 Meter <-- Chord Length of Pentagram

(Calculation completed in 00.008 seconds)

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Created by Nikhil

Mumbai University (DJSCE), Mumbai

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 9 Chord Length of Pentagram Calculators

Chord Length of Pentagram given Area and Short Chord Slice

Go Chord Length of Pentagram = sqrt((2*Area of Pentagram)/sqrt(5*(5-2*sqrt(5))))+(Short Chord Slice of Pentagram*[phi])

Chord Length of Pentagram given Area

Go Chord Length of Pentagram = ([phi]+1)/[phi]*sqrt((2*Area of Pentagram)/sqrt(5*(5-(2*sqrt(5)))))

Chord Length of Pentagram given Perimeter and Long Chord Slice

Go Chord Length of Pentagram = (Perimeter of Pentagram*[phi])/10+Long Chord Slice of Pentagram

Chord Length of Pentagram given Short Chord Slice

Go Chord Length of Pentagram = (2*Pentagonal Edge Length of Pentagram)-Short Chord Slice of Pentagram

Chord Length of Pentagram given Long Chord Slice

Go Chord Length of Pentagram = Pentagonal Edge Length of Pentagram+Long Chord Slice of Pentagram

Chord Length of Pentagram given Long Chord Slice and Short Chord Slice

Go Chord Length of Pentagram = (2*Long Chord Slice of Pentagram)+Short Chord Slice of Pentagram

Chord Length of Pentagram given Perimeter and Short Chord Slice

Go Chord Length of Pentagram = Perimeter of Pentagram/5+Short Chord Slice of Pentagram

Chord Length of Pentagram

Go Chord Length of Pentagram = [phi]*Pentagonal Edge Length of Pentagram

Chord Length of Pentagram given Perimeter

Go Chord Length of Pentagram = Perimeter of Pentagram/10*(1+[phi])

Chord Length of Pentagram given Area and Short Chord Slice Formula

Chord Length of Pentagram = sqrt((2*Area of Pentagram)/sqrt(5*(5-2*sqrt(5))))+(Short Chord Slice of Pentagram*[phi])
l_c = sqrt((2*A)/sqrt(5*(5-2*sqrt(5))))+(l_{Short Chord Slice}*[phi])

What is Pentagram?

A Pentagram is constructed from the diagonals of a pentagon. The Pentagram is the most simple regular star polygon. The chord slices of a regular Pentagram are in the golden ratio φ 1.6180.

How to Calculate Chord Length of Pentagram given Area and Short Chord Slice?

Chord Length of Pentagram given Area and Short Chord Slice calculator uses Chord Length of Pentagram = sqrt((2*Area of Pentagram)/sqrt(5*(5-2*sqrt(5))))+(Short Chord Slice of Pentagram*[phi]) to calculate the Chord Length of Pentagram, The Chord Length of Pentagram given Area and Short Chord Slice formula is defined as the diagonal length of a regular pentagon from which the Pentagram is constructed using its diagonals, and calculated using the area and short chord slice of the Pentagram. Chord Length of Pentagram is denoted by l_c symbol.

How to calculate Chord Length of Pentagram given Area and Short Chord Slice using this online calculator? To use this online calculator for Chord Length of Pentagram given Area and Short Chord Slice, enter Area of Pentagram (A) & Short Chord Slice of Pentagram (l_{Short Chord Slice}) and hit the calculate button. Here is how the Chord Length of Pentagram given Area and Short Chord Slice calculation can be explained with given input values -> 16.39614 = sqrt((2*80)/sqrt(5*(5-2*sqrt(5))))+(4*[phi]).

FAQ

What is Chord Length of Pentagram given Area and Short Chord Slice?

The Chord Length of Pentagram given Area and Short Chord Slice formula is defined as the diagonal length of a regular pentagon from which the Pentagram is constructed using its diagonals, and calculated using the area and short chord slice of the Pentagram and is represented as l_c = sqrt((2*A)/sqrt(5*(5-2*sqrt(5))))+(l_{Short Chord Slice}*[phi]) or Chord Length of Pentagram = sqrt((2*Area of Pentagram)/sqrt(5*(5-2*sqrt(5))))+(Short Chord Slice of Pentagram*[phi]). The Area of Pentagram is the total quantity of plane enclosed by the boundary of the entire Pentagram shape & The Short Chord Slice of Pentagram is the edge length of the regular pentagon which form inside the Pentagram when all the chords are drawn.

How to calculate Chord Length of Pentagram given Area and Short Chord Slice?

The Chord Length of Pentagram given Area and Short Chord Slice formula is defined as the diagonal length of a regular pentagon from which the Pentagram is constructed using its diagonals, and calculated using the area and short chord slice of the Pentagram is calculated using Chord Length of Pentagram = sqrt((2*Area of Pentagram)/sqrt(5*(5-2*sqrt(5))))+(Short Chord Slice of Pentagram*[phi]). To calculate Chord Length of Pentagram given Area and Short Chord Slice, you need Area of Pentagram (A) & Short Chord Slice of Pentagram (l_{Short Chord Slice}). With our tool, you need to enter the respective value for Area of Pentagram & Short Chord Slice of Pentagram 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 Chord Length of Pentagram?

In this formula, Chord Length of Pentagram uses Area of Pentagram & Short Chord Slice of Pentagram. We can use 8 other way(s) to calculate the same, which is/are as follows -

Chord Length of Pentagram = [phi]*Pentagonal Edge Length of Pentagram
Chord Length of Pentagram = Pentagonal Edge Length of Pentagram+Long Chord Slice of Pentagram
Chord Length of Pentagram = Perimeter of Pentagram/10*(1+[phi])
Chord Length of Pentagram = ([phi]+1)/[phi]*sqrt((2*Area of Pentagram)/sqrt(5*(5-(2*sqrt(5)))))
Chord Length of Pentagram = (Perimeter of Pentagram*[phi])/10+Long Chord Slice of Pentagram
Chord Length of Pentagram = Perimeter of Pentagram/5+Short Chord Slice of Pentagram
Chord Length of Pentagram = (2*Long Chord Slice of Pentagram)+Short Chord Slice of Pentagram
Chord Length of Pentagram = (2*Pentagonal Edge Length of Pentagram)-Short Chord Slice of Pentagram

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