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Math Help - area by Simpson's

  1. #1
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    area by Simpson's

    A plot of land is bounded on two sides by straight roads at right angles to each other. The other boundary is irregular and the lenths of perpendicular offsets from one road to the irregular boundary are :14,16,15,15,14,14,13,12,10,12,12,13,12,10,8,7,7,6 ,6 metres, Calculate by using a suitable method the area of the plot.

    cheers..
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  2. #2
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    Quote Originally Posted by jaswinder View Post
    A plot of land is bounded on two sides by straight roads at right angles to each other. The other boundary is irregular and the lenths of perpendicular offsets from one road to the irregular boundary are :14,16,15,15,14,14,13,12,10,12,12,13,12,10,8,7,7,6 ,6 metres, Calculate by using a suitable method the area of the plot.

    cheers..
    This is asking you to use Simpson's rule to calculate the area between the
    axes and a curve which passes through the points (0,14), (h,16), (2h,15), ..., (18h,6).

    This is:

    A=(h/3)[14+4x16+2x15+4x15+ ... +4x6+6]=(h/3)x622,

    but as it seems to be keeping the value of h to itself there does not seem to be much more that can be done.

    However as we have been told last time this was asked (here) that h is 6 metres the area is:

    A = 1244 square metres.

    RonL
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  3. #3
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    Quote Originally Posted by jaswinder View Post
    A plot of land is bounded on two sides by straight roads at right angles to each other. The other boundary is irregular and the lenths of perpendicular offsets from one road to the irregular boundary are :14,16,15,15,14,14,13,12,10,12,12,13,12,10,8,7,7,6 ,6 metres, Calculate by using a suitable method the area of the plot. ...
    Hello,

    I assume that the plot of land is divided into equidistant strips with a width of 1 m. Then the shape of the plot looks like the figure in the attachment.

    You can calculate the area of every single strip, using the trapezoid area formula. I've sketched 2 of the trapezoids as examples.

    The length of the parallel sides are the given values, the height of the trapezoid is always 1 m. So the complete area is calculated by:

    A = 1 m*((14+16)/2 + (16+15)/2 + (15+15)/2 + ...)

    Collecting equal values you get:

    A = 1 m*((14+6)/2 + 16 + 15 + 15 + 14 + 14 + 13 + 12 + 10 + 12 + 12 + 13 + 12 + 10 + 8 + 7 + 7 + 6) = 206 mē

    EB
    Attached Thumbnails Attached Thumbnails area by Simpson's-jaswinder_area.gif  
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