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Area of Pentagram given Chord Length Formula

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GoArea of Pentagram given Long Chord Slice Formula

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

A = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{l c}{[phi]})}^{2}

A - Area of Pentagram?l_c - Chord Length of Pentagram?[phi] - Golden ratio?

Area of Pentagram given Chord Length Example

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Here is how the Area of Pentagram given Chord Length equation looks like with Values.

Here is how the Area of Pentagram given Chord Length equation looks like with Units.

Here is how the Area of Pentagram given Chord Length equation looks like.

79.4293 = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{16}{1.618})}^{2}

79.4293m² = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{16m}{1.618})}^{2}

79.4293 = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{16}{1.618})}^{2}

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Area of Pentagram given Chord Length Solution

Follow our step by step solution on how to calculate Area of Pentagram given Chord Length?

FIRST Step Consider the formula

A = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{l c}{[phi]})}^{2}

Next Step Substitute values of Variables

∴

A = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{16m}{[phi]})}^{2}

Next Step Substitute values of Constants

∴

A = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{16m}{1.618})}^{2}

Next Step Prepare to Evaluate

∴

A = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(\frac{16}{1.618})}^{2}

Next Step Evaluate

∴

A = 79.4292994218746m²

LAST Step Rounding Answer

∴

A = 79.4293m²

Area of Pentagram given Chord Length Formula Elements

Variables

Constants

Functions

Area of Pentagram

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

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Pentagram

Chord Length of Pentagram

The Chord Length of Pentagram is the diagonal length of regular pentagon from which the Pentagram is constructed using it's diagonals.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Pentagram

Golden ratio

The Golden ratio occurs when the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers.

Symbol: [phi]

Value: 1.61803398874989484820458683436563811

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.

Syntax: sqrt(Number)

Other Formulas to find Area of Pentagram

Go Area of Pentagram

A = \sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))} \cdot \frac{{l e(Pentagon)}^{2}}{2}

Go Area of Pentagram given Long Chord Slice

A = \frac{\sqrt{5 \cdot (5 - (2 \cdot \sqrt{5}))}}{2} \cdot {(l Long Chord Slice \cdot [phi])}^{2}

How to Evaluate Area of Pentagram given Chord Length?

Area of Pentagram given Chord Length evaluator uses Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2 to evaluate the Area of Pentagram, The Area of Pentagram given Chord Length formula is defined as the total quantity of plane enclosed by the boundary of the entire Pentagram shape, and calculated by using chord length of the Pentagram. Area of Pentagram is denoted by A symbol.

How to evaluate Area of Pentagram given Chord Length using this online evaluator? To use this online evaluator for Area of Pentagram given Chord Length, enter Chord Length of Pentagram (l_c) and hit the calculate button.

FAQs on Area of Pentagram given Chord Length

What is the formula to find Area of Pentagram given Chord Length?

The formula of Area of Pentagram given Chord Length is expressed as Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2. Here is an example- 79.4293 = sqrt(5*(5-(2*sqrt(5))))/2*(16/[phi])^2.

How to calculate Area of Pentagram given Chord Length?

With Chord Length of Pentagram (l_c) we can find Area of Pentagram given Chord Length using the formula - Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2. This formula also uses Golden ratio constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Area of Pentagram?

Here are the different ways to Calculate Area of Pentagram-

Area of Pentagram=sqrt(5*(5-(2*sqrt(5))))*Pentagonal Edge Length of Pentagram^2/2
Area of Pentagram=(sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram*[phi])^2

Can the Area of Pentagram given Chord Length be negative?

No, the Area of Pentagram given Chord Length, measured in Area cannot be negative.

Which unit is used to measure Area of Pentagram given Chord Length?

Area of Pentagram given Chord Length 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 Pentagram given Chord Length can be measured.

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