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Area of cycloid given perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
area = 3*pi*(Perimeter/((8+(2*pi))))^2
A = 3*pi*(P/((8+(2*pi))))^2
This formula uses 1 Constants, 1 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Perimeter - The perimeter of a figure is the total distance around the edge of the figure. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Perimeter: 20 Meter --> 20 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = 3*pi*(P/((8+(2*pi))))^2 --> 3*pi*(20/((8+(2*pi))))^2
Evaluating ... ...
A = 18.4791068810396
STEP 3: Convert Result to Output's Unit
18.4791068810396 Square Meter --> No Conversion Required
FINAL ANSWER
18.4791068810396 Square Meter <-- Area
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Diagonal of a Rectangle when breadth and perimeter are given
diagonal = sqrt((2*(Breadth)^2)-(Perimeter*Breadth)+((Perimeter)^2/4)) Go
Diagonal of a Rectangle when length and perimeter are given
diagonal = sqrt((2*(Length)^2)-(Perimeter*Length)+((Perimeter)^2/4)) Go
Area of a Rectangle when breadth and perimeter are given
area = (Perimeter*(Breadth/2))-(Breadth)^2 Go
Area of rectangle when perimeter and breadth are given
area = (Perimeter*Breadth-2*(Breadth)^2)/2 Go
Area of a Rectangle when length and perimeter are given
area = (Perimeter*(Length/2))-(Length)^2 Go
Area of rectangle when perimeter and length are given
area = (Perimeter*Length-2*(Length)^2)/2 Go
Length of rectangle when perimeter and breadth are given
length = (Perimeter-2*Breadth)/2 Go
Breadth of rectangle when perimeter and length are given
breadth = (Perimeter-2*Length)/2 Go
Diagonal of a Square when perimeter is given
diagonal = (Perimeter/4)*sqrt(2) Go
Side of a Kite when other side and perimeter are given
side_a = (Perimeter/2)-Side B Go
Area of a Square when perimeter is given
area = (1/16)*(Perimeter)^2 Go

11 Other formulas that calculate the same Output

Area of a Triangle when sides are given
area = sqrt((Side A+Side B+Side C)*(Side B+Side C-Side A)*(Side A-Side B+Side C)*(Side A+Side B-Side C))/4 Go
Area of a Rhombus when side and diagonals are given
area = (1/2)*(Diagonal A)*(sqrt(4*Side^2-(Diagonal A)^2)) Go
Area of a Rectangle when breadth and diagonal are given
area = Breadth*(sqrt((Diagonal)^2-(Breadth)^2)) Go
Area of a Rectangle when length and diagonal are given
area = Length*(sqrt((Diagonal)^2-(Length)^2)) Go
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Area of a Rhombus when diagonals are given
area = (Diagonal A*Diagonal B)/2 Go
Area of a Triangle when base and height are given
area = 1/2*Base*Height Go
Area of a Rectangle when length and breadth are given
area = Length*Breadth Go
Area of a Parallelogram when base and height are given
area = Base*Height Go
Area of a Square when diagonal is given
area = 1/2*(Diagonal)^2 Go
Area of a Square when side is given
area = (Side A)^2 Go

Area of cycloid given perimeter Formula

area = 3*pi*(Perimeter/((8+(2*pi))))^2
A = 3*pi*(P/((8+(2*pi))))^2

What is a cycloid?

In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve).

How to Calculate Area of cycloid given perimeter?

Area of cycloid given perimeter calculator uses area = 3*pi*(Perimeter/((8+(2*pi))))^2 to calculate the Area, The Area of cycloid given perimeter formula is defined as measure of the total area that the surface of the object occupies of a cycloid, where a = radius of cycloid, A = Area of cycloid. Area and is denoted by A symbol.

How to calculate Area of cycloid given perimeter using this online calculator? To use this online calculator for Area of cycloid given perimeter, enter Perimeter (P) and hit the calculate button. Here is how the Area of cycloid given perimeter calculation can be explained with given input values -> 18.47911 = 3*pi*(20/((8+(2*pi))))^2.

FAQ

What is Area of cycloid given perimeter?
The Area of cycloid given perimeter formula is defined as measure of the total area that the surface of the object occupies of a cycloid, where a = radius of cycloid, A = Area of cycloid and is represented as A = 3*pi*(P/((8+(2*pi))))^2 or area = 3*pi*(Perimeter/((8+(2*pi))))^2. The perimeter of a figure is the total distance around the edge of the figure.
How to calculate Area of cycloid given perimeter?
The Area of cycloid given perimeter formula is defined as measure of the total area that the surface of the object occupies of a cycloid, where a = radius of cycloid, A = Area of cycloid is calculated using area = 3*pi*(Perimeter/((8+(2*pi))))^2. To calculate Area of cycloid given perimeter, you need Perimeter (P). With our tool, you need to enter the respective value for Perimeter 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?
In this formula, Area uses Perimeter. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • area = 1/2*Base*Height
  • area = sqrt((Side A+Side B+Side C)*(Side B+Side C-Side A)*(Side A-Side B+Side C)*(Side A+Side B-Side C))/4
  • area = Length*Breadth
  • area = Length*(sqrt((Diagonal)^2-(Length)^2))
  • area = Breadth*(sqrt((Diagonal)^2-(Breadth)^2))
  • area = (Side A)^2
  • area = 1/2*(Diagonal)^2
  • area = (Diagonal A*Diagonal B)/2
  • area = (1/2)*(Diagonal A)*(sqrt(4*Side^2-(Diagonal A)^2))
  • area = Base*Height
  • area = ((Base A+Base B)/2)*Height
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