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Area of Hypocycloid given Perimeter Formula

GoArea of Hypocycloid Formula

GoArea of Hypocycloid given Chord Length Formula

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

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

A - Area of Hypocycloid?N_Cusps - Number of Cusps of Hypocycloid?P - Perimeter of Hypocycloid?π - Archimedes' constant?

Area of Hypocycloid given Perimeter Example

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

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

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

155.5457 = \frac{3.1416}{64} \cdot \frac{5 - 2}{5 - 1} \cdot 65^{2}

155.5457m² = \frac{3.1416}{64} \cdot \frac{5 - 2}{5 - 1} \cdot {65m}^{2}

155.5457 = \frac{3.1416}{64} \cdot \frac{5 - 2}{5 - 1} \cdot 65^{2}

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Area of Hypocycloid given Perimeter Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{π}{64} \cdot \frac{5 - 2}{5 - 1} \cdot {65m}^{2}

Next Step Substitute values of Constants

∴

A = \frac{3.1416}{64} \cdot \frac{5 - 2}{5 - 1} \cdot {65m}^{2}

Next Step Prepare to Evaluate

∴

A = \frac{3.1416}{64} \cdot \frac{5 - 2}{5 - 1} \cdot 65^{2}

Next Step Evaluate

∴

A = 155.545651891604m²

LAST Step Rounding Answer

∴

A = 155.5457m²

Area of Hypocycloid given Perimeter 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

Perimeter of Hypocycloid

Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter 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

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

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}

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 Perimeter?

Area of Hypocycloid given Perimeter evaluator uses Area of Hypocycloid = pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter of Hypocycloid^2 to evaluate the Area of Hypocycloid, Area of Hypocycloid given Perimeter formula is defined as the total quantity of plane enclosed by the boundary of the Hypocycloid, and calculated using the perimeter of the Hypocycloid. Area of Hypocycloid is denoted by A symbol.

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

FAQs on Area of Hypocycloid given Perimeter

What is the formula to find Area of Hypocycloid given Perimeter?

The formula of Area of Hypocycloid given Perimeter is expressed as Area of Hypocycloid = pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter of Hypocycloid^2. Here is an example- 155.5457 = pi/64*(5-2)/(5-1)*65^2.

How to calculate Area of Hypocycloid given Perimeter?

With Number of Cusps of Hypocycloid (N_Cusps) & Perimeter of Hypocycloid (P) we can find Area of Hypocycloid given Perimeter using the formula - Area of Hypocycloid = pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter 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)*Larger Radius of Hypocycloid^2
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

Can the Area of Hypocycloid given Perimeter be negative?

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

Which unit is used to measure Area of Hypocycloid given Perimeter?

Area of Hypocycloid given Perimeter 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 Perimeter can be measured.

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Area of Hypocycloid given Perimeter Formula

​GoArea of Hypocycloid Formula

​GoArea of Hypocycloid given Chord Length Formula

Area of Hypocycloid given Perimeter Example

Area of Hypocycloid given Perimeter Solution

Area of Hypocycloid given Perimeter 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 Perimeter?

FAQs on Area of Hypocycloid given Perimeter

Variable Name

GoArea of Hypocycloid Formula

GoArea of Hypocycloid given Chord Length Formula