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Area of Hypocycloid given Chord Length Formula

GoArea of Hypocycloid Formula

GoArea of Hypocycloid given Perimeter Formula

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Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid. Check FAQs

A = π \cdot \frac{(N Cusps - 1) \cdot (N Cusps - 2)}{{N Cusps}^{2}} \cdot {(\frac{l c}{2 \cdot \sin (\frac{π}{N Cusps})})}^{2}

A - Area of Hypocycloid?N_Cusps - Number of Cusps of Hypocycloid?l_c - Chord Length of Hypocycloid?π - Archimedes' constant?

Area of Hypocycloid given Chord Length Example

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

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

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

157.129 = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {(\frac{12}{2 \cdot \sin (\frac{3.1416}{5})})}^{2}

157.129m² = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {(\frac{12m}{2 \cdot \sin (\frac{3.1416}{5})})}^{2}

157.129 = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {(\frac{12}{2 \cdot \sin (\frac{3.1416}{5})})}^{2}

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Area of Hypocycloid given Chord Length Solution

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

FIRST Step Consider the formula

A = π \cdot \frac{(N Cusps - 1) \cdot (N Cusps - 2)}{{N Cusps}^{2}} \cdot {(\frac{l c}{2 \cdot \sin (\frac{π}{N Cusps})})}^{2}

Next Step Substitute values of Variables

∴

A = π \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {(\frac{12m}{2 \cdot \sin (\frac{π}{5})})}^{2}

Next Step Substitute values of Constants

∴

A = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {(\frac{12m}{2 \cdot \sin (\frac{3.1416}{5})})}^{2}

Next Step Prepare to Evaluate

∴

A = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {(\frac{12}{2 \cdot \sin (\frac{3.1416}{5})})}^{2}

Next Step Evaluate

∴

A = 157.128961529017m²

LAST Step Rounding Answer

∴

A = 157.129m²

Area of Hypocycloid given Chord Length Formula Elements

Variables

Constants

Functions

Area of Hypocycloid

Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Hypocycloid

Number of Cusps of Hypocycloid

Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.

Symbol: N_Cusps

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Cusps of Hypocycloid

Chord Length of Hypocycloid

Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Hypocycloid

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 Hypocycloid

Go Area of Hypocycloid

A = π \cdot \frac{(N Cusps - 1) \cdot (N Cusps - 2)}{{N Cusps}^{2}} \cdot {r Large}^{2}

Go Area of Hypocycloid given Perimeter

A = \frac{π}{64} \cdot \frac{N Cusps - 2}{N Cusps - 1} \cdot P^{2}

Other formulas in Area and Number of Cusps of Hypocycloid category

Go Number of Cusps of Hypocycloid

N Cusps = \frac{r Large}{r Small}

How to Evaluate Area of Hypocycloid given Chord Length?

Area of Hypocycloid given Chord Length evaluator uses Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*(Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)))^2 to evaluate the Area of Hypocycloid, Area of Hypocycloid given Chord Length is defined as the total quantity of plane enclosed by the boundary of the Hypocycloid, and calculated using the chord length of the Hypocycloid. Area of Hypocycloid is denoted by A symbol.

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

FAQs on Area of Hypocycloid given Chord Length

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

The formula of Area of Hypocycloid given Chord Length is expressed as Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*(Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)))^2. Here is an example- 157.129 = pi*((5-1)*(5-2))/(5^2)*(12/(2*sin(pi/5)))^2.

How to calculate Area of Hypocycloid given Chord Length?

With Number of Cusps of Hypocycloid (N_Cusps) & Chord Length of Hypocycloid (l_c) we can find Area of Hypocycloid given Chord Length using the formula - Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*(Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)))^2. This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Area of Hypocycloid?

Here are the different ways to Calculate Area of Hypocycloid-

Area of Hypocycloid=pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2
Area of Hypocycloid=pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter of Hypocycloid^2

Can the Area of Hypocycloid given Chord Length be negative?

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

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

Area of Hypocycloid 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 Hypocycloid given Chord Length can be measured.

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Area of Hypocycloid given Chord Length Formula

​GoArea of Hypocycloid Formula

​GoArea of Hypocycloid given Perimeter Formula

Area of Hypocycloid given Chord Length Example

Area of Hypocycloid given Chord Length Solution

Area of Hypocycloid given Chord Length Formula Elements

Other Formulas to find Area of Hypocycloid

Other formulas in Area and Number of Cusps of Hypocycloid category

How to Evaluate Area of Hypocycloid given Chord Length?

FAQs on Area of Hypocycloid given Chord Length

Variable Name

GoArea of Hypocycloid Formula

GoArea of Hypocycloid given Perimeter Formula