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Calculate area of subsection of a three-dimensional surface

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  1. Dec 1, 2014 #1
    For the following three-dimensional surface, z = -4.53 + 2.67x + 2.78y - 1.09xy, I would like to calculate the area for each of three subsections of this surface: (1) for which z is in between the corresponding x and y values (i.e., x < z < y OR y < z < x); (2) for which x is in between the corresponding z and y values (i.e., z < x < y OR y < x < z); (3) for which y is in between the corresponding z and x values (i.e., z < y < x OR x < y < z). Can anybody give me a formula for doing this so that I can do additional versions of this with different coefficient values?

    If it helps to clarify and if you have Mathematica, I have plotted the surface in Mathematica and colored the regions indicated above.

    f[x_, y_] = -4.53 + 2.67 x + 2.78 y - 1.09 x y // Rationalize // Simplify;

    Plot3D[f[x, y], {x, 1.8, 2.6}, {y, 1.8, 2.6}, PlotRange -> {1.7, 2.6}, PlotPoints -> 101, AxesLabel -> (Style[#, Bold, 14] & /@ {"x", "y", "z"}), Ticks -> {{1.8, 2., 2.2, 2.4, 2.6}, {1.8, 2., 2.2, 2.4, 2.6}, {1.8, 2., 2.2, 2.4, 2.6}}, BoxRatios -> {1, 1, 1}, Mesh -> None, ColorFunction -> Function[{x, y, z}, Piecewise[{{Pink, (x < z < y) || (y < z < x)}, {Gray, (z < x < y) || (y < x < z)}}, Yellow]], ColorFunctionScaling -> False]

    The three regions above are colored pink, gray, and yellow, respectively.

    Thanks in advance,
    Keith
     
  2. jcsd
  3. Dec 6, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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