Area of Pentagram given Long and Short Chord Slice Calculator

✖The Long Chord Slice of Pentagram is the edge length of the entire star shape of the Pentagram or the equal side of the isosceles triangle which forms as the spike of the Pentagram.ⓘ Long Chord Slice of Pentagram [l_{Long Chord Slice}]			+10% -10%
✖The Short Chord Slice of Pentagram is the edge length of the regular pentagon which form inside the Pentagram when all the chords are drawn.ⓘ Short Chord Slice of Pentagram [l_{Short Chord Slice}]			+10% -10%

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

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Formula

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Area of Pentagram given Long and Short Chord Slice

Formula

`"A" = (sqrt(5*(5-(2*sqrt(5)))))/2*("l"_{"Long Chord Slice"}+"l"_{"Short Chord Slice"})^2`

Example

`"81.22992m²"=(sqrt(5*(5-(2*sqrt(5)))))/2*("6m"+"4m")^2`

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Area of Pentagram given Long and Short Chord Slice Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram+Short Chord Slice of Pentagram)^2
A = (sqrt(5*(5-(2*sqrt(5)))))/2*(l_{Long Chord Slice}+l_{Short Chord Slice})^2
This formula uses 1 Functions, 3 Variables

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.
Long Chord Slice of Pentagram - (Measured in Meter) - The Long Chord Slice of Pentagram is the edge length of the entire star shape of the Pentagram or the equal side of the isosceles triangle which forms as the spike of the Pentagram.
Short Chord Slice of Pentagram - (Measured in Meter) - The Short Chord Slice of Pentagram is the edge length of the regular pentagon which form inside the Pentagram when all the chords are drawn.

STEP 1: Convert Input(s) to Base Unit

Long Chord Slice of Pentagram: 6 Meter --> 6 Meter No Conversion Required
Short Chord Slice of Pentagram: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (sqrt(5*(5-(2*sqrt(5)))))/2*(l_{Long Chord Slice}+l_{Short Chord Slice})^2 --> (sqrt(5*(5-(2*sqrt(5)))))/2*(6+4)^2

Evaluating ... ...

A = 81.2299240582266

STEP 3: Convert Result to Output's Unit

81.2299240582266 Square Meter --> No Conversion Required

FINAL ANSWER

81.2299240582266 ≈ 81.22992 Square Meter <-- Area of Pentagram

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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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

Area of Pentagram given Long and Short Chord Slice Formula

Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram+Short Chord Slice of Pentagram)^2
A = (sqrt(5*(5-(2*sqrt(5)))))/2*(l_{Long Chord Slice}+l_{Short Chord Slice})^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 Long and Short Chord Slice?

Area of Pentagram given Long and Short Chord Slice calculator uses Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram+Short Chord Slice of Pentagram)^2 to calculate the Area of Pentagram, The Area of Pentagram given Long and Short Chord Slice formula is defined as the total quantity of plane enclosed by the boundary of the entire Pentagram shape and calculated by using a long chord slice and a short chord slice of the Pentagram. Area of Pentagram is denoted by A symbol.

How to calculate Area of Pentagram given Long and Short Chord Slice using this online calculator? To use this online calculator for Area of Pentagram given Long and Short Chord Slice, enter Long Chord Slice of Pentagram (l_{Long Chord Slice}) & Short Chord Slice of Pentagram (l_{Short Chord Slice}) and hit the calculate button. Here is how the Area of Pentagram given Long and Short Chord Slice calculation can be explained with given input values -> 81.22992 = (sqrt(5*(5-(2*sqrt(5)))))/2*(6+4)^2.

FAQ

What is Area of Pentagram given Long and Short Chord Slice?

The Area of Pentagram given Long and Short Chord Slice formula is defined as the total quantity of plane enclosed by the boundary of the entire Pentagram shape and calculated by using a long chord slice and a short chord slice of the Pentagram and is represented as A = (sqrt(5*(5-(2*sqrt(5)))))/2*(l_{Long Chord Slice}+l_{Short Chord Slice})^2 or Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram+Short Chord Slice of Pentagram)^2. The Long Chord Slice of Pentagram is the edge length of the entire star shape of the Pentagram or the equal side of the isosceles triangle which forms as the spike of the Pentagram & The Short Chord Slice of Pentagram is the edge length of the regular pentagon which form inside the Pentagram when all the chords are drawn.

How to calculate Area of Pentagram given Long and Short Chord Slice?

The Area of Pentagram given Long and Short Chord Slice formula is defined as the total quantity of plane enclosed by the boundary of the entire Pentagram shape and calculated by using a long chord slice and a short chord slice of the Pentagram is calculated using Area of Pentagram = (sqrt(5*(5-(2*sqrt(5)))))/2*(Long Chord Slice of Pentagram+Short Chord Slice of Pentagram)^2. To calculate Area of Pentagram given Long and Short Chord Slice, you need Long Chord Slice of Pentagram (l_{Long Chord Slice}) & Short Chord Slice of Pentagram (l_{Short Chord Slice}). With our tool, you need to enter the respective value for Long Chord Slice of Pentagram & Short Chord Slice 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 Long Chord Slice of Pentagram & Short Chord Slice of Pentagram. We can use 4 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*(Chord Length of Pentagram/[phi])^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

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