Area of Astroid given Chord Length Calculator

✖A Chord Length of Astroid is a straight line segment whose endpoints both lie on a circular arc of an Astroid.ⓘ Chord Length of Astroid [l_c]

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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.ⓘ Area of Astroid given Chord Length [A]

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Area of Astroid given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2
A = 3/8*pi*(l_c/(2*sin(pi/4)))^2
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)

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.
Chord Length of Astroid - (Measured in Meter) - A Chord Length of Astroid is a straight line segment whose endpoints both lie on a circular arc of an Astroid.

STEP 1: Convert Input(s) to Base Unit

Chord Length of Astroid: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 3/8*pi*(l_c/(2*sin(pi/4)))^2 --> 3/8*pi*(11/(2*sin(pi/4)))^2

Evaluating ... ...

A = 71.2748833283184

STEP 3: Convert Result to Output's Unit

71.2748833283184 Square Meter --> No Conversion Required

FINAL ANSWER

71.2748833283184 ≈ 71.27488 Square Meter <-- Area of Astroid

(Calculation completed in 00.008 seconds)

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< Area of Astroid Calculators

Area of Astroid given Chord Length

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

Area of Astroid given Radius of Rolling Circle

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

Area of Astroid

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

Area of Astroid given Perimeter

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

Area of Astroid given Chord Length Formula

LaTeX Go

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

What is an Astroid?

A 4-cusped Hypocycloid which 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 Chord Length?

Area of Astroid given Chord Length calculator uses Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2 to calculate 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 calculate Area of Astroid given Chord Length using this online calculator? To use this online calculator for Area of Astroid given Chord Length, enter Chord Length of Astroid (l_c) and hit the calculate button. Here is how the Area of Astroid given Chord Length calculation can be explained with given input values -> 71.27488 = 3/8*pi*(11/(2*sin(pi/4)))^2.

FAQ

What is Area of Astroid given Chord Length?

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 and is represented as A = 3/8*pi*(l_c/(2*sin(pi/4)))^2 or Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2. A Chord Length of Astroid is a straight line segment whose endpoints both lie on a circular arc of an Astroid.

How to calculate Area of Astroid given Chord Length?

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 is calculated using Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2. To calculate Area of Astroid given Chord Length, you need Chord Length of Astroid (l_c). With our tool, you need to enter the respective value for Chord Length 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 Chord Length 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*(Perimeter of Astroid/6)^2
Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2

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