Chord Length of Polygram Calculator

✖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 [l_e]			+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 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]

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Formula

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Chord Length of Polygram

Formula

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

Example

`"8.19152m"=sqrt(2*("5m")^2*(1-cos("110°")))`

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Chord Length of Polygram Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Edge Length of Polygram: 5 Meter --> 5 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_c = sqrt(2*l_e^2*(1-cos(∠_Outer))) --> sqrt(2*5^2*(1-cos(1.9198621771934)))

Evaluating ... ...

l_c = 8.19152044288888

STEP 3: Convert Result to Output's Unit

8.19152044288888 Meter --> No Conversion Required

FINAL ANSWER

8.19152044288888 ≈ 8.19152 Meter <-- Chord Length of Polygram

(Calculation completed in 00.004 seconds)

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< 1 Chord Length of Polygram Calculators

Chord Length of Polygram

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

Chord Length of Polygram Formula

Chord Length of Polygram = sqrt(2*Edge Length of Polygram^2*(1-cos(Outer Angle of Polygram)))
l_c = sqrt(2*l_e^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 an n-pointed star. For an 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 Chord Length of Polygram?

Chord Length of Polygram calculator uses Chord Length of Polygram = sqrt(2*Edge Length of Polygram^2*(1-cos(Outer Angle of Polygram))) to calculate the Chord Length of Polygram, The Chord Length of Polygram formula is defined as the distance between peaks of two adjacent spikes or two adjacent isosceles triangles that are attached to the polygon of the whole Polygram. Chord Length of Polygram is denoted by l_c symbol.

How to calculate Chord Length of Polygram using this online calculator? To use this online calculator for Chord Length of Polygram, enter Edge Length of Polygram (l_e) & Outer Angle of Polygram (∠_Outer) and hit the calculate button. Here is how the Chord Length of Polygram calculation can be explained with given input values -> 8.19152 = sqrt(2*5^2*(1-cos(1.9198621771934))).

FAQ

What is Chord Length of Polygram?

The Chord Length of Polygram formula is defined as the distance between peaks of two adjacent spikes or two adjacent isosceles triangles that are attached to the polygon of the whole Polygram and is represented as l_c = sqrt(2*l_e^2*(1-cos(∠_Outer))) or Chord Length of Polygram = sqrt(2*Edge Length of Polygram^2*(1-cos(Outer Angle of Polygram))). The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end & The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.

How to calculate Chord Length of Polygram?

The Chord Length of Polygram formula is defined as the distance between peaks of two adjacent spikes or two adjacent isosceles triangles that are attached to the polygon of the whole Polygram is calculated using Chord Length of Polygram = sqrt(2*Edge Length of Polygram^2*(1-cos(Outer Angle of Polygram))). To calculate Chord Length of Polygram, you need Edge Length of Polygram (l_e) & Outer Angle of Polygram (∠_Outer). With our tool, you need to enter the respective value for Edge 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.

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