Measuring Irregular shaped areas

what math formula or instrument is used to measure the area of irregular shapes.
for instance if you have a small plot of land of the shape of USA or Mexico, it's neither a square nor a circle , nor....nor... nor....
how can you tell about the squarefootage or squared meter of this area?

Thanks
jskfanAsked:
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bob_the_builderCommented:
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whatisittellmeCommented:
usually, a grid is drawn on the irregular shape. the squares in the grid are so small that, at the edges the area of the irregualr shape not included in the square is negligible. so, the total area will be number of squares in the grid that overlaps the irregular shape times the area of each square.

i hope you get the point.
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jskfanAuthor Commented:
when you go a a real field to take the measurement, you can't draw small squares.
if you go to a field that has a shape approximately similar to the map of USA. how are you going to find out the squared meter of the area? I believe there should be some instrument that does that.
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NovaDenizenCommented:
If you want to learn the area of the continental US, then to be most precise you have to take into account the facts that the earth is not flat, and it's not quite a sphere either.

One way to break the problem down is to take the original region, simplify it into a huge irregular polygon, then break the polygon up into a bunch of little triangles.  When the triangles are very small compared to the curvature of the earths surface, then their total area will be a good approximation to the actual area of the region.  You can use Heron's formula to determine the area of each triangle based on the length of each of its sides.
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jskfanAuthor Commented:
let's say you have plot of land and you want to determine the squared meter or square foot of this area.
It has no shape that has formula. it's just like countries shape on the map.
I believe for the area of the countries they might use some high tech equipment to determine the size of the area, but for small fields noone has a budget to acquire those equiments unless if there are some in the markets that are cheap.
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jskfanAuthor Commented:
that means you still need to go to the field and trace small squares.
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ozoCommented:
You can go to the field and take take gps readings at each corner
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whatisittellmeCommented:
i stumbled upon this site: http://blog.expertgps.com/blog/2008/10/calculating-the-area-of-a-farm-field/
it might be of some help to you.
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jskfanAuthor Commented:
If I understand you need to put the field in a map and use ExpertGPS software to calculate the area of the field.

Now this raises another question, how do you put your field in a map? there must be equipment to do that. correct?
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whatisittellmeCommented:
it says:
 " you could trace the boundaries of your field would be to take your GPS out and walk or drive the edge of the field, recording a GPS track ..."

that said, I have not used the software myself. so, i am sure there will be some more details that might need figuring out.
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jskfanAuthor Commented:
<<<" you could trace the boundaries of your field would be to take your GPS out and walk or drive the edge of the field, recording a GPS track ...">>>

which type of GPS that can do that?
Do you have a brand? a link to it?
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whatisittellmeCommented:
the home page of that site says ExpertGPS software works with garmin, magellan, lowrance, eagle.
(http://www.expertgps.com/default.asp)
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t0t0Commented:
The best way to 'measure' the area inside a large irregular field is to do the following:

1) 'mark off' 'best-fit' rectangle/s inside the boundaries of the field.
2) walk around the outer edges of the rectangle/s at 1m intervals, and...
3) at each metre interval, measure the distance from the nearest rectangle side to the edge of the field.
4) measure the corners at 45 degrees.

So, suppose your field is roughly the shape of two rectangles - one small and one large when placed side-by-side. Drive poles into the corners marking the rectangles and fix a ribbon (or whatever) from pole to pole (thereby marking off youor rectangle).

When you've marked off as many rectangles as you see fit (in some cases, you might only need one rectangle) complete the rectangle by tying string or ribbon tape from pole to pole.

Now, using a yard-stick (or metre-stick), walk around the outer perimeters of your rectangle/s measuring the perpendicular distance from the tape to the edge of the field. This should not be more than 10m otherwise it might have been easier to have added another rectangle. This will require two people (to hold each end of a tape measure of course).

Ideally, your rectangles will already measure to the closest metre, so you already know the area of each rectangle.

Measuring to the edge of the field will create 'smaller rectangular areas which when plotted onto a graph paper will make up the shape of your field. Naturally, this will be done to a best-fit scale.

Simple.
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jskfanAuthor Commented:
thank you all for your efforts. I guess I should have postedt his question on the GIS area if there is one.
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ozoCommented:
using the coordinates at each corner, you can plug them into the formula at
http://mathworld.wolfram.com/PolygonArea.html
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