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Area of Astroid given Chord Length Formula

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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 {(\frac{l c}{2 \cdot \sin (\frac{π}{4})})}^{2}

A - Area of Astroid?l_c - Chord Length of Astroid?π - Archimedes' constant?

Area of Astroid given Chord Length Example

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

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

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

71.2749 = \frac{3}{8} \cdot 3.1416 \cdot {(\frac{11}{2 \cdot \sin (\frac{3.1416}{4})})}^{2}

71.2749m² = \frac{3}{8} \cdot 3.1416 \cdot {(\frac{11m}{2 \cdot \sin (\frac{3.1416}{4})})}^{2}

71.2749 = \frac{3}{8} \cdot 3.1416 \cdot {(\frac{11}{2 \cdot \sin (\frac{3.1416}{4})})}^{2}

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Area of Astroid given Chord Length Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{3}{8} \cdot π \cdot {(\frac{11m}{2 \cdot \sin (\frac{π}{4})})}^{2}

Next Step Substitute values of Constants

∴

A = \frac{3}{8} \cdot 3.1416 \cdot {(\frac{11m}{2 \cdot \sin (\frac{3.1416}{4})})}^{2}

Next Step Prepare to Evaluate

∴

A = \frac{3}{8} \cdot 3.1416 \cdot {(\frac{11}{2 \cdot \sin (\frac{3.1416}{4})})}^{2}

Next Step Evaluate

∴

A = 71.2748833283184m²

LAST Step Rounding Answer

∴

A = 71.2749m²

Area of Astroid given Chord Length Formula Elements

Variables

Constants

Functions

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

Chord Length of Astroid

A Chord Length of Astroid is a straight line segment whose endpoints both lie on a circular arc of an Astroid.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length 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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Area of Astroid

Go Area of Astroid

A = \frac{3}{8} \cdot π \cdot {r Fixed Circle}^{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 given Chord Length?

Area of Astroid given Chord Length evaluator uses Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2 to evaluate the Area of Astroid, The Area of Astroid given chord length formula is defined as the measure of the total area that the surface of the object occupies of an Astroid, calculated using the chord length of the Astroid. Area of Astroid is denoted by A symbol.

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

FAQs on Area of Astroid given Chord Length

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

The formula of Area of Astroid given Chord Length is expressed as Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2. Here is an example- 71.27488 = 3/8*pi*(11/(2*sin(pi/4)))^2.

How to calculate Area of Astroid given Chord Length?

With Chord Length of Astroid (l_c) we can find Area of Astroid given Chord Length using the formula - Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2. This formula also uses Archimedes' constant and Sine function(s).

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*Radius of Fixed Circle of Astroid^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 given Chord Length be negative?

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

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

Area of Astroid 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 Astroid given Chord Length can be measured.

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