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Area of Hypocycloid Formula

GoArea of Hypocycloid given Chord Length 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 {r Large}^{2}

A - Area of Hypocycloid?N_Cusps - Number of Cusps of Hypocycloid?r_Large - Larger Radius of Hypocycloid?π - Archimedes' constant?

Area of Hypocycloid Example

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

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

Here is how the Area of Hypocycloid equation looks like.

150.7964 = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot 10^{2}

150.7964m² = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {10m}^{2}

150.7964 = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot 10^{2}

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2D Geometry » fx Area of Hypocycloid

Area of Hypocycloid Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = π \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {10m}^{2}

Next Step Substitute values of Constants

∴

A = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot {10m}^{2}

Next Step Prepare to Evaluate

∴

A = 3.1416 \cdot \frac{(5 - 1) \cdot (5 - 2)}{5^{2}} \cdot 10^{2}

Next Step Evaluate

∴

A = 150.79644737231m²

LAST Step Rounding Answer

∴

A = 150.7964m²

Area of Hypocycloid Formula Elements

Variables

Constants

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

Larger Radius of Hypocycloid

Larger Radius of Hypocycloid is the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed.

Symbol: r_Large

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Larger Radius 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

Other Formulas to find Area of Hypocycloid

Go Area of Hypocycloid given Chord Length

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}

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?

Area of Hypocycloid evaluator uses 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 to evaluate the Area of Hypocycloid, Area of Hypocycloid formula is defined as the total quantity of plane enclosed by the boundary of the Hypocycloid. Area of Hypocycloid is denoted by A symbol.

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

FAQs on Area of Hypocycloid

What is the formula to find Area of Hypocycloid?

The formula of Area of Hypocycloid 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)*Larger Radius of Hypocycloid^2. Here is an example- 150.7964 = pi*((5-1)*(5-2))/(5^2)*10^2.

How to calculate Area of Hypocycloid?

With Number of Cusps of Hypocycloid (N_Cusps) & Larger Radius of Hypocycloid (r_Large) we can find Area of Hypocycloid 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)*Larger Radius of Hypocycloid^2. This formula also uses Archimedes' constant .

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)*(Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps 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 be negative?

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

Which unit is used to measure Area of Hypocycloid?

Area of Hypocycloid 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 can be measured.

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Area of Hypocycloid Formula

​GoArea of Hypocycloid given Chord Length Formula

​GoArea of Hypocycloid given Perimeter Formula

Area of Hypocycloid Example

Area of Hypocycloid Solution

Area of Hypocycloid 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?

FAQs on Area of Hypocycloid

Variable Name

GoArea of Hypocycloid given Chord Length Formula

GoArea of Hypocycloid given Perimeter Formula