Edge Length of Polygram given Spike Height Calculator

✖The Spike Height of Polygram is the height of the isosceles triangles with respect to the unequal side, which are attached to the polygon of the Polygram as the spikes.ⓘ Spike Height of Polygram [h_Spike]			+10% -10%
✖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 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 Spike Height [l_e]

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Formula

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Edge Length of Polygram given Spike Height

Formula

`"l"_{"e"} = sqrt("h"_{"Spike"}^2+"l"_{"Base"}^2/4)`

Example

`"5m"=sqrt(("4m")^2+("6m")^2/4)`

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Edge Length of Polygram given Spike Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Spike Height of Polygram - (Measured in Meter) - The Spike Height of Polygram is the height of the isosceles triangles with respect to the unequal side, which are attached to the polygon of the Polygram as the spikes.
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.

STEP 1: Convert Input(s) to Base Unit

Spike Height of Polygram: 4 Meter --> 4 Meter No Conversion Required
Base Length of Polygram: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = sqrt(h_Spike^2+l_Base^2/4) --> sqrt(4^2+6^2/4)

Evaluating ... ...

l_e = 5

STEP 3: Convert Result to Output's Unit

5 Meter --> No Conversion Required

FINAL ANSWER

5 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 Spike Height Formula

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

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 Spike Height?

Edge Length of Polygram given Spike Height calculator uses Edge Length of Polygram = sqrt(Spike Height of Polygram^2+Base Length of Polygram^2/4) to calculate the Edge Length of Polygram, The Edge Length of Polygram given Spike Height 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 spike height. Edge Length of Polygram is denoted by l_e symbol.

How to calculate Edge Length of Polygram given Spike Height using this online calculator? To use this online calculator for Edge Length of Polygram given Spike Height, enter Spike Height of Polygram (h_Spike) & Base Length of Polygram (l_Base) and hit the calculate button. Here is how the Edge Length of Polygram given Spike Height calculation can be explained with given input values -> 5 = sqrt(4^2+6^2/4).

FAQ

What is Edge Length of Polygram given Spike Height?

The Edge Length of Polygram given Spike Height 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 spike height and is represented as l_e = sqrt(h_Spike^2+l_Base^2/4) or Edge Length of Polygram = sqrt(Spike Height of Polygram^2+Base Length of Polygram^2/4). The Spike Height of Polygram is the height of the isosceles triangles with respect to the unequal side, which are attached to the polygon of the Polygram as the spikes & 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.

How to calculate Edge Length of Polygram given Spike Height?

The Edge Length of Polygram given Spike Height 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 spike height is calculated using Edge Length of Polygram = sqrt(Spike Height of Polygram^2+Base Length of Polygram^2/4). To calculate Edge Length of Polygram given Spike Height, you need Spike Height of Polygram (h_Spike) & Base Length of Polygram (l_Base). With our tool, you need to enter the respective value for Spike Height of Polygram & Base Length 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 Spike Height of Polygram & Base Length 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 = Chord Length of Polygram/sqrt(2*(1-cos(Outer Angle of Polygram)))

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