Edge Length of Polygram given Base Length Calculator

✖The Base Length of Polygram is the length of the unequal side of the isosceles triangle which forms as the spikes of the Polygram or the side length of the polygon of Polygram.ⓘ Base Length of Polygram [l_Base]			+10% -10%
✖The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.ⓘ Inner Angle of Polygram [∠_Inner]			+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 Base Length [l_e]

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Edge Length of Polygram given Base Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Polygram = Base Length of Polygram/sqrt(2*(1-cos(Inner Angle of Polygram)))
l_e = l_Base/sqrt(2*(1-cos(∠_Inner)))
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.
Base Length of Polygram - (Measured in Meter) - The Base Length of Polygram is the length of the unequal side of the isosceles triangle which forms as the spikes of the Polygram or the side length of the polygon of Polygram.
Inner Angle of Polygram - (Measured in Radian) - The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.

STEP 1: Convert Input(s) to Base Unit

Base Length of Polygram: 6 Meter --> 6 Meter No Conversion Required
Inner Angle of Polygram: 74 Degree --> 1.29154364647556 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = l_Base/sqrt(2*(1-cos(∠_Inner))) --> 6/sqrt(2*(1-cos(1.29154364647556)))

Evaluating ... ...

l_e = 4.98492042336826

STEP 3: Convert Result to Output's Unit

4.98492042336826 Meter --> No Conversion Required

FINAL ANSWER

4.98492042336826 ≈ 4.98492 Meter <-- Edge Length of Polygram

(Calculation completed in 00.004 seconds)

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< Edge Length of Polygram Calculators

Edge Length of Polygram given Chord Length

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

Edge Length of Polygram given Base Length

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

Edge Length of Polygram given Spike Height

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

Edge Length of Polygram given Perimeter

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

Edge Length of Polygram given Base Length Formula

LaTeX Go

Edge Length of Polygram = Base Length of Polygram/sqrt(2*(1-cos(Inner Angle of Polygram)))
l_e = l_Base/sqrt(2*(1-cos(∠_Inner)))

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 (Base Length of the Polygram)
2) Length of the equal side of the triangle (Edge Length of the Polygram)
3) Angle between the two equal sides of the isosceles triangle (Inner Angle angle of the Polygram)
4) Height of the triangle (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 Base Length?

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

How to calculate Edge Length of Polygram given Base Length using this online calculator? To use this online calculator for Edge Length of Polygram given Base Length, enter Base Length of Polygram (l_Base) & Inner Angle of Polygram (∠_Inner) and hit the calculate button. Here is how the Edge Length of Polygram given Base Length calculation can be explained with given input values -> 4.98492 = 6/sqrt(2*(1-cos(1.29154364647556))).

FAQ

What is Edge Length of Polygram given Base Length?

The Edge Length of Polygram given Base Length formula is defined as the length of the equal sides of the isosceles triangle attached to the n-sided polygon of the Polygram and calculated using the base length of the Polygram and is represented as l_e = l_Base/sqrt(2*(1-cos(∠_Inner))) or Edge Length of Polygram = Base Length of Polygram/sqrt(2*(1-cos(Inner Angle of Polygram))). The Base Length of Polygram is the length of the unequal side of the isosceles triangle which forms as the spikes of the Polygram or the side length of the polygon of Polygram & The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.

How to calculate Edge Length of Polygram given Base Length?

The Edge Length of Polygram given Base Length formula is defined as the length of the equal sides of the isosceles triangle attached to the n-sided polygon of the Polygram and calculated using the base length of the Polygram is calculated using Edge Length of Polygram = Base Length of Polygram/sqrt(2*(1-cos(Inner Angle of Polygram))). To calculate Edge Length of Polygram given Base Length, you need Base Length of Polygram (l_Base) & Inner Angle of Polygram (∠_Inner). With our tool, you need to enter the respective value for Base Length of Polygram & Inner 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 Base Length of Polygram & Inner Angle of Polygram. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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