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Area of Astroid Formula

GoArea of Astroid given Chord Length Formula

GoArea of Astroid given Perimeter Formula

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Area of Astroid is defined as measure of the total area or region occupied by an Astroid within its four concave sides or boundaries. Check FAQs

A = \frac{3}{8} \cdot π \cdot {r Fixed Circle}^{2}

A - Area of Astroid?r_{Fixed Circle} - Radius of Fixed Circle of Astroid?π - Archimedes' constant?

Area of Astroid Example

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

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

Here is how the Area of Astroid equation looks like.

75.3982 = \frac{3}{8} \cdot 3.1416 \cdot 8^{2}

75.3982m² = \frac{3}{8} \cdot 3.1416 \cdot {8m}^{2}

75.3982 = \frac{3}{8} \cdot 3.1416 \cdot 8^{2}

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Area of Astroid Solution

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

FIRST Step Consider the formula

A = \frac{3}{8} \cdot π \cdot {r Fixed Circle}^{2}

Next Step Substitute values of Variables

∴

A = \frac{3}{8} \cdot π \cdot {8m}^{2}

Next Step Substitute values of Constants

∴

A = \frac{3}{8} \cdot 3.1416 \cdot {8m}^{2}

Next Step Prepare to Evaluate

∴

A = \frac{3}{8} \cdot 3.1416 \cdot 8^{2}

Next Step Evaluate

∴

A = 75.398223686155m²

LAST Step Rounding Answer

∴

A = 75.3982m²

Area of Astroid Formula Elements

Variables

Constants

Area of Astroid

Area of Astroid is defined as measure of the total area or region occupied by an Astroid within its four concave sides or boundaries.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Astroid

Radius of Fixed Circle of Astroid

The Radius of Fixed Circle of Astroid is the distance from the center of the fixed circle to any point on its circumference.

Symbol: r_{Fixed Circle}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Fixed Circle of Astroid

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

Other Formulas to find Area of Astroid

Go Area of Astroid given Chord Length

A = \frac{3}{8} \cdot π \cdot {(\frac{l c}{2 \cdot \sin (\frac{π}{4})})}^{2}

Go Area of Astroid given Perimeter

A = \frac{3}{8} \cdot π \cdot {(\frac{P}{6})}^{2}

Go Area of Astroid given Radius of Rolling Circle

A = \frac{3}{8} \cdot π \cdot {(4 \cdot r Rolling circle)}^{2}

How to Evaluate Area of Astroid?

Area of Astroid evaluator uses Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2 to evaluate the Area of Astroid, The Area of Astroid formula is defined as a measure of the total area that the surface of the object occupies of a concave pentagon. Area of Astroid is denoted by A symbol.

How to evaluate Area of Astroid using this online evaluator? To use this online evaluator for Area of Astroid, enter Radius of Fixed Circle of Astroid (r_{Fixed Circle}) and hit the calculate button.

FAQs on Area of Astroid

What is the formula to find Area of Astroid?

The formula of Area of Astroid is expressed as Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2. Here is an example- 75.39822 = 3/8*pi*8^2.

How to calculate Area of Astroid?

With Radius of Fixed Circle of Astroid (r_{Fixed Circle}) we can find Area of Astroid using the formula - Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2. This formula also uses Archimedes' constant .

What are the other ways to Calculate Area of Astroid?

Here are the different ways to Calculate Area of Astroid-

Area of Astroid=3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2
Area of Astroid=3/8*pi*(Perimeter of Astroid/6)^2
Area of Astroid=3/8*pi*(4*Radius of Rolling Circle of Astroid)^2

Can the Area of Astroid be negative?

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

Which unit is used to measure Area of Astroid?

Area of Astroid 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 Astroid can be measured.

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