Area of Astroid given Perimeter Calculator

✖Area of Astroid is defined as measure of the total area or region occupied by an Astroid within its four concave sides or boundaries.ⓘ Area of Astroid given Perimeter [A]

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Formula

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Area of Astroid given Perimeter

Formula

`"A" = 3/8*pi*("P"/6)^2`

Example

`"81.81231m²"=3/8*pi*("50m"/6)^2`

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Area of Astroid given Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2
A = 3/8*pi*(P/6)^2
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Area of Astroid - (Measured in Square Meter) - Area of Astroid is defined as measure of the total area or region occupied by an Astroid within its four concave sides or boundaries.
Perimeter of Astroid - (Measured in Meter) - The Perimeter of Astroid is a closed path that encompasses, surrounds, or outlines an Astroid.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Astroid: 50 Meter --> 50 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 3/8*pi*(P/6)^2 --> 3/8*pi*(50/6)^2

Evaluating ... ...

A = 81.8123086872342

STEP 3: Convert Result to Output's Unit

81.8123086872342 Square Meter --> No Conversion Required

FINAL ANSWER

81.8123086872342 ≈ 81.81231 Square Meter <-- Area of Astroid

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< 4 Area of Astroid Calculators

Area of Astroid given Chord Length

Go Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2

Area of Astroid given Radius of Rolling Circle

Go Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2

Area of Astroid

Go Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2

Area of Astroid given Perimeter

Go Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2

Area of Astroid given Perimeter Formula

Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2
A = 3/8*pi*(P/6)^2

What is an Astroid?

A 4-cusped Hypocycloid is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the Astroid can be obtained by plugging in n=a/b=4 or 4/3 into the equations for a general hypocycloid, giving parametric equations. The Astroid can also be formed as the envelope produced when a line segment is moved with each end on one of a pair of perpendicular axes (e.g., it is the curve enveloped by a ladder sliding against a wall or a garage door with the top corner moving along a vertical track; left figure above). The Astroid is therefore a glissette.

How to Calculate Area of Astroid given Perimeter?

Area of Astroid given Perimeter calculator uses Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2 to calculate the Area of Astroid, The Area of Astroid given perimeter formula is defined as the measure of the total area that the surface of the object occupies of an Astroid, calculated using the perimeter of it. Area of Astroid is denoted by A symbol.

How to calculate Area of Astroid given Perimeter using this online calculator? To use this online calculator for Area of Astroid given Perimeter, enter Perimeter of Astroid (P) and hit the calculate button. Here is how the Area of Astroid given Perimeter calculation can be explained with given input values -> 81.81231 = 3/8*pi*(50/6)^2.

FAQ

What is Area of Astroid given Perimeter?

The Area of Astroid given perimeter formula is defined as the measure of the total area that the surface of the object occupies of an Astroid, calculated using the perimeter of it and is represented as A = 3/8*pi*(P/6)^2 or Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2. The Perimeter of Astroid is a closed path that encompasses, surrounds, or outlines an Astroid.

How to calculate Area of Astroid given Perimeter?

The Area of Astroid given perimeter formula is defined as the measure of the total area that the surface of the object occupies of an Astroid, calculated using the perimeter of it is calculated using Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2. To calculate Area of Astroid given Perimeter, you need Perimeter of Astroid (P). With our tool, you need to enter the respective value for Perimeter of Astroid 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 Astroid?

In this formula, Area of Astroid uses Perimeter of Astroid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2
Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2
Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2

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