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Cornel19-Tanzanite
19-Tanzanite
May 10, 2024
Solved

How to calculate each colored area for this graph made by points?

Hello,

I have these points:

Cornel_1-1715330011989.png


How to calculate each colored area from below plot made with above points?

Cornel_0-1715330587262.png

 

Mathcad Prime 9 fille attached.

Werner_E
Werner_EAnswer
25-Diamond I
May 10, 2024

A1 is quite different from the rest so it has to be treated separately:

Werner_E_0-1715334008430.png

 

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21 replies

LucMeekes23-Emerald IV
23-Emerald IV
May 10, 2024

If it weren't for the weird placement of A1, you could use an integral over the (absolute value of the) function.

So what's left is brute force. like this:

LucMeekes_0-1715331552035.png

Success!
Luc

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    Cornel19-TanzaniteAuthor
    19-Tanzanite
    May 10, 2024
    @LucMeekes wrote:

    If it weren't for the weird placement of A1, you could use an integral over the (absolute value of the) function.

    And how A1 should look like in order to be able to use an integral over the (absolute value of the) function?

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    ttokoro
    ttokoro21-Topaz I
    21-Topaz I
    May 10, 2024

    Same with unit.

    image.pngimage.pngimage.png

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    t.t.
      Werner_E
      Werner_E25-Diamond IAnswer
      25-Diamond I
      May 10, 2024

      A1 is quite different from the rest so it has to be treated separately:

      Werner_E_0-1715334008430.png

       

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        Cornel19-TanzaniteAuthor
        19-Tanzanite
        May 10, 2024

        And for this?

        Cornel_1-1715335285204.png

         

        Cornel_0-1715335595907.png

         

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        Werner_E
        Werner_E25-Diamond I
        25-Diamond I
        May 10, 2024
        @Cornel wrote:

        And for this?

         

        Are you sure about A4???

        Otherwise the answer would be here: https://community.ptc.com/t5/Mathcad/How-to-calculate-each-colored-area-for-this-graph-made-by-points/m-p/948887/highlight/true#M211719

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        DJF16-Pearl
        16-Pearl
        May 10, 2024

        Just a thought - I'd think that since any solution is going to have the vertices known - you could then use the surveyor formula/shoelace formula to find the area.  A nifty trick Werner taught me years ago that has helped me a lot.

        2024-05-10_08-44-04.jpg

         

        (OR = origin)

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        Cornel19-TanzaniteAuthor
        19-Tanzanite
        May 10, 2024

        Hm,,,I to make also the Area(x,y) to give the same answer as Area2 or maybe Area3? Do not know what is the correct answer in this case..

        Cornel_4-1715352572816.png


        Even if I put like that the answer is different than Area(x,y):

        Cornel_6-1715352631825.png

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        DJF16-Pearl
        16-Pearl
        May 10, 2024

        only a guess, but since the shoelace formula closes itself (i.e. back to (0,0) the negative y values act as a negative area - since the lines cross themselves.  But if you define A1, A2, etc as unique closed areas of vertices those areas should give the same values as integrating or other geometry.  Since you have a mix of triangles and rectangles and others, this one formula will suffice once your have the vertices defined.

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