Area of Hypocycloid given Chord Length Calculator

✖Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.ⓘ Number of Cusps of Hypocycloid [N_Cusps]			+10% -10%
✖Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.ⓘ Chord Length of Hypocycloid [l_c]			+10% -10%

✖Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.ⓘ Area of Hypocycloid given Chord Length [A]

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Formula

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Area of Hypocycloid given Chord Length

Formula

`"A" = pi*(("N"_{"Cusps"}-1)*("N"_{"Cusps"}-2))/("N"_{"Cusps"}^2)*("l"_{"c"}/(2*sin(pi/"N"_{"Cusps"})))^2`

Example

`"157.129m²"=pi*(("5"-1)*("5"-2))/(("5")^2)*("12m"/(2*sin(pi/"5")))^2`

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Area of Hypocycloid given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
A = pi*((N_Cusps-1)*(N_Cusps-2))/(N_Cusps^2)*(l_c/(2*sin(pi/N_Cusps)))^2
This formula uses 1 Constants, 1 Functions, 3 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 Hypocycloid - (Measured in Square Meter) - Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the 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.
Chord Length of Hypocycloid - (Measured in Meter) - Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.

STEP 1: Convert Input(s) to Base Unit

Number of Cusps of Hypocycloid: 5 --> No Conversion Required
Chord Length of Hypocycloid: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = pi*((N_Cusps-1)*(N_Cusps-2))/(N_Cusps^2)*(l_c/(2*sin(pi/N_Cusps)))^2 --> pi*((5-1)*(5-2))/(5^2)*(12/(2*sin(pi/5)))^2

Evaluating ... ...

A = 157.128961529017

STEP 3: Convert Result to Output's Unit

157.128961529017 Square Meter --> No Conversion Required

FINAL ANSWER

157.128961529017 ≈ 157.129 Square Meter <-- Area of Hypocycloid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Hypocycloid » Area and Number of Cusps of Hypocycloid » Area of Hypocycloid given Chord Length

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< 4 Area and Number of Cusps of Hypocycloid Calculators

Area of Hypocycloid given Chord Length

Go 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

Go 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 given Perimeter

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

Number of Cusps of Hypocycloid

Go Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid

Area of Hypocycloid given Chord Length Formula

What is a Hypocycloid?

In geometry, a Hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the Hypocycloid becomes more like the cycloid created by rolling a circle on a line.
Any Hypocycloid with an integral value of k, and thus k cusps, can move snugly inside another Hypocycloid with k+1 cusps, such that the points of the smaller Hypocycloid will always be in contact with the larger. This motion looks like 'rolling', though it is not technically rolling in the sense of classical mechanics, since it involves slipping.

How to Calculate Area of Hypocycloid given Chord Length?

Area of Hypocycloid given Chord Length calculator 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 calculate 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 calculate Area of Hypocycloid given Chord Length using this online calculator? To use this online calculator 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. Here is how the Area of Hypocycloid given Chord Length calculation can be explained with given input values -> 157.129 = pi*((5-1)*(5-2))/(5^2)*(12/(2*sin(pi/5)))^2.

FAQ

What is Area of Hypocycloid given Chord Length?

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 and is represented as A = pi*((N_Cusps-1)*(N_Cusps-2))/(N_Cusps^2)*(l_c/(2*sin(pi/N_Cusps)))^2 or 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. Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid & Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.

How to calculate Area of Hypocycloid given Chord Length?

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 is calculated using 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 calculate Area of Hypocycloid given Chord Length, you need Number of Cusps of Hypocycloid (N_Cusps) & Chord Length of Hypocycloid (l_c). With our tool, you need to enter the respective value for Number of Cusps of Hypocycloid & Chord Length of Hypocycloid 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 Hypocycloid?

In this formula, Area of Hypocycloid uses Number of Cusps of Hypocycloid & Chord Length of Hypocycloid. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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