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lvl10720-Turquoise
20-Turquoise
December 7, 2025
Solved

Area of Parametric (closed) Curve ?

  • December 7, 2025
  • 3 replies
  • 816 views


Hello Everyone.
From :

Parametric (closed) Curve.PNG

To :
  How to calculate Area of Parametric (closed) Curve, the above ? ( MathCad 15 )
  Thanks in advance.
  Regards.
  Loi

Best answer by DJF

While this problem is solvable with calculus - there are tricks to doing it other ways that can come in handy for other less mathematical shapes.  Shoelace formula (Surveyor's formula) works just using coordinate points.  Something Werner taught me years ago.

shoelace.png

3 replies

N
NickKemaev12-Amethyst
12-Amethyst
December 7, 2025

---------------------------------Screenshot_1.png

N
NickKemaev12-Amethyst
12-Amethyst
December 7, 2025

I'm getting better.Screenshot_3.png

W
Werner_E25-Diamond I
25-Diamond I
December 7, 2025

Attachments don't work OK at the time, we just see "Virus scan in progress..." and can't download the attachment.
I already notified @unknown  and @PTCModerator  yesterday but so far there was no reaction - its weekend 😞

 

Your curve may look like a cardioide on first glance, but it isn't

Werner_E_0-1765141031559.png

Actually what you show is part of a larger curve with the parameter representation

Werner_E_1-1765141293724.png

and you get the curve you show for t running from 0 to pi

ani1.gif

 

To calculate the area enclosed you can use Green's theorem  which possibly should be attributed to C.F.Gauß.

Werner_E_2-1765141397336.png

Using the parameter representation shown above and the limits 0 and pi for the parameter t, we get the enclosed area with

Werner_E_4-1765141505328.png

ani2.gif

 

 

 

 

 

    AndrewK
    AndrewKCommunity Manager
    Community Manager
    December 8, 2025

    Hi @Werner_E Thanks for pointing out this issue we are investigating now.

      W
      Werner_E25-Diamond I
      25-Diamond I
      December 9, 2025
      @AndrewK wrote:

      Hi @Werner_E Thanks for pointing out this issue we are investigating now.

      Thanks!

      It looks like the problem has now been solved since a few hours ago.

      D
      DJF16-PearlAnswer
      16-Pearl
      December 8, 2025

      While this problem is solvable with calculus - there are tricks to doing it other ways that can come in handy for other less mathematical shapes.  Shoelace formula (Surveyor's formula) works just using coordinate points.  Something Werner taught me years ago.

      shoelace.png

        W
        Werner_E25-Diamond I
        25-Diamond I
        December 8, 2025

        Yes, and in fact, the shoelace formula can also be traced back to C. F. Gauß! -> Shoelace formula - Wikipedia

        He really was simply a genius.

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