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Area of Polygram Formula

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The Area of Polygram is the total quantity of plane enclosed by the boundary of Polygram shape. Check FAQs

A = (N Spikes \cdot \frac{{l Base}^{2}}{4 \cdot \tan (\frac{π}{N Spikes})}) + (N Spikes \cdot h Spike \cdot \frac{l Base}{2})

A - Area of Polygram?N_Spikes - Number of Spikes in Polygram?l_Base - Base Length of Polygram?h_Spike - Spike Height of Polygram?π - Archimedes' constant?

Area of Polygram Example

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Here is how the Area of Polygram equation looks like with Values.

Here is how the Area of Polygram equation looks like with Units.

Here is how the Area of Polygram equation looks like.

396.9915 = (10 \cdot \frac{6^{2}}{4 \cdot \tan (\frac{3.1416}{10})}) + (10 \cdot 4 \cdot \frac{6}{2})

396.9915m² = (10 \cdot \frac{{6m}^{2}}{4 \cdot \tan (\frac{3.1416}{10})}) + (10 \cdot 4m \cdot \frac{6m}{2})

396.9915 = (10 \cdot \frac{6^{2}}{4 \cdot \tan (\frac{3.1416}{10})}) + (10 \cdot 4 \cdot \frac{6}{2})

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Area of Polygram Solution

Follow our step by step solution on how to calculate Area of Polygram?

FIRST Step Consider the formula

A = (N Spikes \cdot \frac{{l Base}^{2}}{4 \cdot \tan (\frac{π}{N Spikes})}) + (N Spikes \cdot h Spike \cdot \frac{l Base}{2})

Next Step Substitute values of Variables

∴

A = (10 \cdot \frac{{6m}^{2}}{4 \cdot \tan (\frac{π}{10})}) + (10 \cdot 4m \cdot \frac{6m}{2})

Next Step Substitute values of Constants

∴

A = (10 \cdot \frac{{6m}^{2}}{4 \cdot \tan (\frac{3.1416}{10})}) + (10 \cdot 4m \cdot \frac{6m}{2})

Next Step Prepare to Evaluate

∴

A = (10 \cdot \frac{6^{2}}{4 \cdot \tan (\frac{3.1416}{10})}) + (10 \cdot 4 \cdot \frac{6}{2})

Next Step Evaluate

∴

A = 396.991518345773m²

LAST Step Rounding Answer

∴

A = 396.9915m²

Area of Polygram Formula Elements

Variables

Constants

Functions

Area of Polygram

The Area of Polygram is the total quantity of plane enclosed by the boundary of Polygram shape.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Polygram

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.

Symbol: N_Spikes

Measurement: NAUnit: Unitless

Note: Value should be greater than 2.

Formulas to find Number of Spikes in Polygram

Base Length 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.

Symbol: l_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Length of Polygram

Spike Height 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.

Symbol: h_Spike

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Spike Height of Polygram

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: tan(Angle)

Other formulas in Area and Perimeter of Polygram category

Go Perimeter of Polygram

P = 2 \cdot N Spikes \cdot l e

How to Evaluate Area of Polygram?

Area of Polygram evaluator 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 evaluate 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 evaluate Area of Polygram using this online evaluator? To use this online evaluator 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.

FAQs on Area of Polygram

What is the formula to find Area of Polygram?

The formula of Area of Polygram is expressed as 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). Here is an example- 396.9915 = (10*(6^2)/(4*tan(pi/10)))+(10*4*6/2).

How to calculate Area of Polygram?

With Number of Spikes in Polygram (N_Spikes), Base Length of Polygram (l_Base) & Spike Height of Polygram (h_Spike) we can find Area of Polygram using the formula - 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). This formula also uses Archimedes' constant and Tangent (tan) function(s).

Can the Area of Polygram be negative?

No, the Area of Polygram, measured in Area cannot be negative.

Which unit is used to measure Area of Polygram?

Area of Polygram is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Polygram can be measured.

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Area of Polygram Formula

Area of Polygram Example

Area of Polygram Solution

Area of Polygram Formula Elements

Other formulas in Area and Perimeter of Polygram category

How to Evaluate Area of Polygram?

FAQs on Area of Polygram

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