Area of Polygram Calculator

✖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 [h_Spike]			+10% -10%

✖The Area of Polygram is the total quantity of plane enclosed by the boundary of Polygram shape.ⓘ Area of Polygram [A]

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Formula

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Area of Polygram

Formula

`"A" = ("N"_{"Spikes"}*("l"_{"Base"}^2)/(4*tan(pi/"N"_{"Spikes"})))+("N"_{"Spikes"}*"h"_{"Spike"}*"l"_{"Base"}/2)`

Example

`"396.9915m²"=("10"*(("6m")^2)/(4*tan(pi/"10")))+("10"*"4m"*"6m"/2)`

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Area of Polygram Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Polygram = (Number of Spikes in Polygram*(Base Length of Polygram^2)/(4*tan(pi/Number of Spikes in Polygram)))+(Number of Spikes in Polygram*Spike Height of Polygram*Base Length of Polygram/2)
A = (N_Spikes*(l_Base^2)/(4*tan(pi/N_Spikes)))+(N_Spikes*h_Spike*l_Base/2)
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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Number of Spikes in Polygram: 10 --> No Conversion Required
Base Length of Polygram: 6 Meter --> 6 Meter No Conversion Required
Spike Height of Polygram: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (N_Spikes*(l_Base^2)/(4*tan(pi/N_Spikes)))+(N_Spikes*h_Spike*l_Base/2) --> (10*(6^2)/(4*tan(pi/10)))+(10*4*6/2)

Evaluating ... ...

A = 396.991518345773

STEP 3: Convert Result to Output's Unit

396.991518345773 Square Meter --> No Conversion Required

FINAL ANSWER

396.991518345773 ≈ 396.9915 Square Meter <-- Area of Polygram

(Calculation completed in 00.020 seconds)

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< 2 Area and Perimeter of Polygram Calculators

Area of Polygram

Go Area of Polygram = (Number of Spikes in Polygram*(Base Length of Polygram^2)/(4*tan(pi/Number of Spikes in Polygram)))+(Number of Spikes in Polygram*Spike Height of Polygram*Base Length of Polygram/2)

Perimeter of Polygram

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

Area of Polygram Formula

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 Area of Polygram?

Area of Polygram calculator uses Area of Polygram = (Number of Spikes in Polygram*(Base Length of Polygram^2)/(4*tan(pi/Number of Spikes in Polygram)))+(Number of Spikes in Polygram*Spike Height of Polygram*Base Length of Polygram/2) to calculate the Area of Polygram, The Area of Polygram formula is defined as the value of total quantity of plane enclosed by the Polygram. That is, the total area of the n isosceles triangles and area of the n-sided polygon. Area of Polygram is denoted by A symbol.

How to calculate Area of Polygram using this online calculator? To use this online calculator for Area of Polygram, enter Number of Spikes in Polygram (N_Spikes), Base Length of Polygram (l_Base) & Spike Height of Polygram (h_Spike) and hit the calculate button. Here is how the Area of Polygram calculation can be explained with given input values -> 396.9915 = (10*(6^2)/(4*tan(pi/10)))+(10*4*6/2).

FAQ

What is Area of Polygram?

The Area of Polygram formula is defined as the value of total quantity of plane enclosed by the Polygram. That is, the total area of the n isosceles triangles and area of the n-sided polygon and is represented as A = (N_Spikes*(l_Base^2)/(4*tan(pi/N_Spikes)))+(N_Spikes*h_Spike*l_Base/2) or Area of Polygram = (Number of Spikes in Polygram*(Base Length of Polygram^2)/(4*tan(pi/Number of Spikes in Polygram)))+(Number of Spikes in Polygram*Spike Height of Polygram*Base Length of Polygram/2). 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 & 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.

How to calculate Area of Polygram?

The Area of Polygram formula is defined as the value of total quantity of plane enclosed by the Polygram. That is, the total area of the n isosceles triangles and area of the n-sided polygon is calculated using Area of Polygram = (Number of Spikes in Polygram*(Base Length of Polygram^2)/(4*tan(pi/Number of Spikes in Polygram)))+(Number of Spikes in Polygram*Spike Height of Polygram*Base Length of Polygram/2). To calculate Area of Polygram, you need Number of Spikes in Polygram (N_Spikes), Base Length of Polygram (l_Base) & Spike Height of Polygram (h_Spike). With our tool, you need to enter the respective value for Number of Spikes in Polygram, Base Length of Polygram & Spike Height 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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