Area of Pentagram given Chord Length Calculator

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

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✖The Area of Pentagram is the total quantity of plane enclosed by the boundary of the entire Pentagram shape.ⓘ Area of Pentagram given Chord Length [A]

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Formula

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Area of Pentagram given Chord Length

Formula

`"A" = sqrt(5*(5-(2*sqrt(5))))/2*("l"_{"c"}/"[phi]")^2`

Example

`"79.4293m²"=sqrt(5*(5-(2*sqrt(5))))/2*("16m"/"[phi]")^2`

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Area of Pentagram given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2
A = sqrt(5*(5-(2*sqrt(5))))/2*(l_c/[phi])^2
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

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

Area of Pentagram - (Measured in Square Meter) - The Area of Pentagram is the total quantity of plane enclosed by the boundary of the entire Pentagram shape.
Chord Length of Pentagram - (Measured in Meter) - The Chord Length of Pentagram is the diagonal length of regular pentagon from which the Pentagram is constructed using it's diagonals.

STEP 1: Convert Input(s) to Base Unit

Chord Length of Pentagram: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = sqrt(5*(5-(2*sqrt(5))))/2*(l_c/[phi])^2 --> sqrt(5*(5-(2*sqrt(5))))/2*(16/[phi])^2

Evaluating ... ...

A = 79.4292994218746

STEP 3: Convert Result to Output's Unit

79.4292994218746 Square Meter --> No Conversion Required

FINAL ANSWER

79.4292994218746 ≈ 79.4293 Square Meter <-- Area of Pentagram

(Calculation completed in 00.020 seconds)

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< 5 Area of Pentagram Calculators

Area of Pentagram given Long and Short Chord Slice

Go Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram+Short Chord Slice of Pentagram)^2

Area of Pentagram given Long Chord Slice and Chord Length

Go Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Chord Length of Pentagram-Long Chord Slice of Pentagram)^2

Area of Pentagram given Long Chord Slice

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

Area of Pentagram given Chord Length

Go Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2

Area of Pentagram

Go Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))*Pentagonal Edge Length of Pentagram^2/2

< 3 Area of Pentagram Calculators

Area of Pentagram given Long Chord Slice

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

Area of Pentagram given Chord Length

Go Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2

Area of Pentagram

Go Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))*Pentagonal Edge Length of Pentagram^2/2

Area of Pentagram given Chord Length Formula

Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2
A = sqrt(5*(5-(2*sqrt(5))))/2*(l_c/[phi])^2

What is Pentagram?

A Pentagram is constructed from the diagonals of a pentagon. The Pentagram is the most simple regular star polygon. The chord slices of a regular Pentagram are in the golden ratio φ 1.6180.

How to Calculate Area of Pentagram given Chord Length?

Area of Pentagram given Chord Length calculator uses Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2 to calculate 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 calculate Area of Pentagram given Chord Length using this online calculator? To use this online calculator for Area of Pentagram given Chord Length, enter Chord Length of Pentagram (l_c) and hit the calculate button. Here is how the Area of Pentagram given Chord Length calculation can be explained with given input values -> 79.4293 = sqrt(5*(5-(2*sqrt(5))))/2*(16/[phi])^2.

FAQ

What is Area of Pentagram given Chord Length?

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 and is represented as A = sqrt(5*(5-(2*sqrt(5))))/2*(l_c/[phi])^2 or Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2. The Chord Length of Pentagram is the diagonal length of regular pentagon from which the Pentagram is constructed using it's diagonals.

How to calculate Area of Pentagram given Chord Length?

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 is calculated using Area of Pentagram = sqrt(5*(5-(2*sqrt(5))))/2*(Chord Length of Pentagram/[phi])^2. To calculate Area of Pentagram given Chord Length, you need Chord Length of Pentagram (l_c). With our tool, you need to enter the respective value for Chord Length of Pentagram 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 Area of Pentagram?

In this formula, Area of Pentagram uses Chord Length of Pentagram. We can use 6 other way(s) to calculate the same, which is/are as follows -

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
Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Chord Length of Pentagram-Long Chord Slice of Pentagram)^2
Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram+Short Chord Slice of Pentagram)^2
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

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