Spike Height of Polygram given Area Calculator

✖The Area of Polygram is the total quantity of plane enclosed by the boundary of Polygram shape.ⓘ Area of Polygram [A]			+10% -10%
✖The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the Polygram.ⓘ Number of Spikes in Polygram [N_Spikes]			+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 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 given Area [h_Spike]

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Spike Height of Polygram given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spike Height of Polygram = ((2*Area of Polygram)/(Number of Spikes in Polygram*Base Length of Polygram))-(Base Length of Polygram/(2*tan(pi/Number of Spikes in Polygram)))
h_Spike = ((2*A)/(N_Spikes*l_Base))-(l_Base/(2*tan(pi/N_Spikes)))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

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.
Area of Polygram - (Measured in Square Meter) - The Area of Polygram is the total quantity of plane enclosed by the boundary of Polygram shape.
Number of Spikes in Polygram - The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the Polygram.
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

Area of Polygram: 400 Square Meter --> 400 Square Meter No Conversion Required
Number of Spikes in Polygram: 10 --> No Conversion Required
Base Length of Polygram: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_Spike = ((2*A)/(N_Spikes*l_Base))-(l_Base/(2*tan(pi/N_Spikes))) --> ((2*400)/(10*6))-(6/(2*tan(pi/10)))

Evaluating ... ...

h_Spike = 4.10028272180757

STEP 3: Convert Result to Output's Unit

4.10028272180757 Meter --> No Conversion Required

FINAL ANSWER

4.10028272180757 ≈ 4.100283 Meter <-- Spike Height of Polygram

(Calculation completed in 00.004 seconds)

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< Spike Height of Polygram Calculators

Spike Height of Polygram given Area

LaTeX Go Spike Height of Polygram = ((2*Area of Polygram)/(Number of Spikes in Polygram*Base Length of Polygram))-(Base Length of Polygram/(2*tan(pi/Number of Spikes in Polygram)))

Spike Height of Polygram

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

Spike Height of Polygram given Area Formula

LaTeX Go

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 Spike Height of Polygram given Area?

Spike Height of Polygram given Area calculator uses Spike Height of Polygram = ((2*Area of Polygram)/(Number of Spikes in Polygram*Base Length of Polygram))-(Base Length of Polygram/(2*tan(pi/Number of Spikes in Polygram))) to calculate the Spike Height of Polygram, The Spike Height of Polygram given Area formula is defined assthe height of the isosceles triangles with respect to the unequal side, which are attached to the polygon of the Polygram as the spikes and calculated using the area of the Polygram. Spike Height of Polygram is denoted by h_Spike symbol.

How to calculate Spike Height of Polygram given Area using this online calculator? To use this online calculator for Spike Height of Polygram given Area, enter Area of Polygram (A), Number of Spikes in Polygram (N_Spikes) & Base Length of Polygram (l_Base) and hit the calculate button. Here is how the Spike Height of Polygram given Area calculation can be explained with given input values -> 4.100283 = ((2*400)/(10*6))-(6/(2*tan(pi/10))).

FAQ

What is Spike Height of Polygram given Area?

The Spike Height of Polygram given Area formula is defined assthe height of the isosceles triangles with respect to the unequal side, which are attached to the polygon of the Polygram as the spikes and calculated using the area of the Polygram and is represented as h_Spike = ((2*A)/(N_Spikes*l_Base))-(l_Base/(2*tan(pi/N_Spikes))) or Spike Height of Polygram = ((2*Area of Polygram)/(Number of Spikes in Polygram*Base Length of Polygram))-(Base Length of Polygram/(2*tan(pi/Number of Spikes in Polygram))). The Area of Polygram is the total quantity of plane enclosed by the boundary of Polygram shape, The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the 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.

How to calculate Spike Height of Polygram given Area?

The Spike Height of Polygram given Area formula is defined assthe height of the isosceles triangles with respect to the unequal side, which are attached to the polygon of the Polygram as the spikes and calculated using the area of the Polygram is calculated using Spike Height of Polygram = ((2*Area of Polygram)/(Number of Spikes in Polygram*Base Length of Polygram))-(Base Length of Polygram/(2*tan(pi/Number of Spikes in Polygram))). To calculate Spike Height of Polygram given Area, you need Area of Polygram (A), Number of Spikes in Polygram (N_Spikes) & Base Length of Polygram (l_Base). With our tool, you need to enter the respective value for Area of Polygram, Number of Spikes in 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 Spike Height of Polygram?

In this formula, Spike Height of Polygram uses Area of Polygram, Number of Spikes in Polygram & Base Length of Polygram. We can use 1 other way(s) to calculate the same, which is/are as follows -

Spike Height of Polygram = sqrt(((4*Edge Length of Polygram^2)-Base Length of Polygram^2)/4)

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