Edge Length of Polygram given Chord Length Calculator

✖The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip.ⓘ Chord Length of Polygram [l_c]			+10% -10%
✖The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.ⓘ Outer Angle of Polygram [∠_Outer]			+10% -10%

✖The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end.ⓘ Edge Length of Polygram given Chord Length [l_e]

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Formula

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Edge Length of Polygram given Chord Length

Formula

`"l"_{"e"} = "l"_{"c"}/sqrt(2*(1-cos("∠"_{"Outer"})))`

Example

`"4.883098m"="8m"/sqrt(2*(1-cos("110°")))`

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Edge Length of Polygram given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Polygram = Chord Length of Polygram/sqrt(2*(1-cos(Outer Angle of Polygram)))
l_e = l_c/sqrt(2*(1-cos(∠_Outer)))
This formula uses 2 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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 Polygram - (Measured in Meter) - The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end.
Chord Length of Polygram - (Measured in Meter) - The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip.
Outer Angle of Polygram - (Measured in Radian) - The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.

STEP 1: Convert Input(s) to Base Unit

Chord Length of Polygram: 8 Meter --> 8 Meter No Conversion Required
Outer Angle of Polygram: 110 Degree --> 1.9198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = l_c/sqrt(2*(1-cos(∠_Outer))) --> 8/sqrt(2*(1-cos(1.9198621771934)))

Evaluating ... ...

l_e = 4.88309835504644

STEP 3: Convert Result to Output's Unit

4.88309835504644 Meter --> No Conversion Required

FINAL ANSWER

4.88309835504644 ≈ 4.883098 Meter <-- Edge Length of Polygram

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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The National Institute of Engineering (NIE), Mysuru

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< 4 Edge Length of Polygram Calculators

Edge Length of Polygram given Chord Length

Go Edge Length of Polygram = Chord Length of Polygram/sqrt(2*(1-cos(Outer Angle of Polygram)))

Edge Length of Polygram given Base Length

Go Edge Length of Polygram = Base Length of Polygram/sqrt(2*(1-cos(Inner Angle of Polygram)))

Edge Length of Polygram given Spike Height

Go Edge Length of Polygram = sqrt(Spike Height of Polygram^2+Base Length of Polygram^2/4)

Edge Length of Polygram given Perimeter

Go Edge Length of Polygram = Perimeter of Polygram/(2*Number of Spikes in Polygram)

Edge Length of Polygram given Chord Length Formula

Edge Length of Polygram = Chord Length of Polygram/sqrt(2*(1-cos(Outer Angle of Polygram)))
l_e = l_c/sqrt(2*(1-cos(∠_Outer)))

What is Polygram ?

→ A Polygram is a regular n-sided polygon with identical isosceles triangles (also known as SPIKES) attached to each edge.
→ It looks like a n-pointed star.
→ For a n-pointed star, there will be n-spikes.
→ The Spike (Isosceles Triangle) is an important part of the polygram and it is defined using 4 parameters. They are :
1) The Base Length of the Triangle (a.k.a Base Length of the Polygram)
2) Length of the equal side of the triangle (a.k.a Edge Length of the Polygram)
3) Angle between the two equal sides of the isosceles triangle (a.k.a Inner Angle angle of the Polygram)
4) Height of the triangle (a.k.a Spike Height)

Apart from these there are other important parameters that define the Polygram. They are:
1) Outer Angle : The angle between two adjacent isosceles triangles.
2) Chord Length : The distance between two peaks of the adjacent Spikes of the Polygram.
3) Perimeter : The sum of lengths of all the edges of the polygram.
4) Area : The amount of space occupied by the polygram.

How to Calculate Edge Length of Polygram given Chord Length?

Edge Length of Polygram given Chord Length calculator uses Edge Length of Polygram = Chord Length of Polygram/sqrt(2*(1-cos(Outer Angle of Polygram))) to calculate the Edge Length of Polygram, The Edge Length of Polygram given Chord Length formula is defined as the length of the side (the length of equal sides) of the isosceles triangle attached to the n-sided polygon of the Polygram and calculated using its chord length. Edge Length of Polygram is denoted by l_e symbol.

How to calculate Edge Length of Polygram given Chord Length using this online calculator? To use this online calculator for Edge Length of Polygram given Chord Length, enter Chord Length of Polygram (l_c) & Outer Angle of Polygram (∠_Outer) and hit the calculate button. Here is how the Edge Length of Polygram given Chord Length calculation can be explained with given input values -> 4.883098 = 8/sqrt(2*(1-cos(1.9198621771934))).

FAQ

What is Edge Length of Polygram given Chord Length?

The Edge Length of Polygram given Chord Length formula is defined as the length of the side (the length of equal sides) of the isosceles triangle attached to the n-sided polygon of the Polygram and calculated using its chord length and is represented as l_e = l_c/sqrt(2*(1-cos(∠_Outer))) or Edge Length of Polygram = Chord Length of Polygram/sqrt(2*(1-cos(Outer Angle of Polygram))). The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip & The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.

How to calculate Edge Length of Polygram given Chord Length?

The Edge Length of Polygram given Chord Length formula is defined as the length of the side (the length of equal sides) of the isosceles triangle attached to the n-sided polygon of the Polygram and calculated using its chord length is calculated using Edge Length of Polygram = Chord Length of Polygram/sqrt(2*(1-cos(Outer Angle of Polygram))). To calculate Edge Length of Polygram given Chord Length, you need Chord Length of Polygram (l_c) & Outer Angle of Polygram (∠_Outer). With our tool, you need to enter the respective value for Chord Length of Polygram & Outer Angle of Polygram 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 Polygram?

In this formula, Edge Length of Polygram uses Chord Length of Polygram & Outer Angle of Polygram. We can use 3 other way(s) to calculate the same, which is/are as follows -

Edge Length of Polygram = Base Length of Polygram/sqrt(2*(1-cos(Inner Angle of Polygram)))
Edge Length of Polygram = Perimeter of Polygram/(2*Number of Spikes in Polygram)
Edge Length of Polygram = sqrt(Spike Height of Polygram^2+Base Length of Polygram^2/4)

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