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# calculate an area of Non Standard shapes

Posted on 2011-10-23
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I wonder if there is a way to calculate an area of non standard shapes.
for instance, there formulas about calculating the area for a square,triangle,Rectangle,etc....but if I have a shape like a cloud , how am I going to calculate the exact area of it.
I am not sure if knowing calculus will help calculating those kind of areas?

Thanks
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Question by:jskfan

LVL 43

Accepted Solution

If you know the coordinates of the boundary of the cloud then you can use the formula given in this article

http://www.mathopenref.com/coordpolygonarea.html
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LVL 17

Assisted Solution

This might be WAY off of how you are looking to solve this question, but this is how it is done in some old labs to quantify curves. You could start with a standard shape, like a rectangle, get several with different sizes, measure them and calculate area. Then cut them out and weigh them to create a graph of areas versus weight. Then cut out the cloud,weigh it and extrapolate off of the standard graph to get the area.
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LVL 26

Assisted Solution

"how am I going to calculate the exact area of it"
Unless you know the exact equation(s) of the boarder you cannot calculate the exact area.
One way to get the area as close as you want is to
copy the cloud onto graph pager and count the squares.
-
nanharbison: suggestion is very ingenious and well worth considering
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Author Comment

So, using Math Integrals would not be able to solve the problem.
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LVL 17

Assisted Solution

nanharbison's method is very good.  I remember years ago we calculated Avagadro's number using a similar method in one step in college level chemistry.  Simple if you have an accurate scale.

Trace the outline on paper, cut out the shape and weight.  Weigh a standard shape and calculate your outline.
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LVL 43

Assisted Solution

Math integrals will only be applicable if you have a relation between x and y. Otherwise if you have coordinates then my method is the best. If none of these is available then the other two methods are appropriate.
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LVL 37

Assisted Solution

To calculate the exact area, you would need to know the exact shape. This exact shape would naturally take the form of a function of x and y. In that case, the integrals are definitely the best way to get the solution.

If you do not have an exact definition of the shape, you cannot get the exact area.

If the exact definition of the shape is in parts (e.g. this part of the cloud is drawn by 1/3 of a circle of radius 3) then you just cut it up into pieces and add them all up.
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LVL 26

Assisted Solution

"So, using Math Integrals would not be able to solve the problem.'
If you do not have a mathematical form for the cloud boarder, the above statement is correct.
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Author Comment

So how do the scientists calculate the area of country lands.
is GPS nowadays, the right tool ?
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Author Comment

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LVL 43

Assisted Solution

Such land areas are calculated by coordinates.

With a GPS one can get all the boundary points and when applied to a formula will give the exact area "IF" the coordinates are exact.

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LVL 37

Assisted Solution

The way they used to do it was to approximate the shape as a polygon, measuring all the sides and angles. Then you break the polygon up into triangles or use any other polygon area method.

Of course this does not give an exact area, just very close.

If they do use satellite images now, then even using coordinates is just approximating it as a polygon. So GPS or guys with measuring rods and sextants, it boils down to approximating the shape as a polygon.
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Author Closing Comment

Thank you Guys!
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