how to find the area of polygon?

Question

how to find the area of polygon if we have the vertisces of it in cartesian coordinate with matlab.

Answer 1

What do you mean by cartesian coordinate with matlab? This is how I understand your question...

Given the three vertices of any triangle P1(x1,y1), P2(x2,y2), P3(x3,y3), its area is given by the formula:

A = 1/2[(x1y2 + x3y1 + x2y3) - x3y2 - x1y3 - x2y1]

For a polygon with n non-overlapping vertices, the area is given by:

A = 1/2[(x1y2 + x2y(n-1) + x(n-1)yn + xny1) - x2y1 - x(n-1)y2 - xny(n-1) - x1yn]

Answer 2

Well, you can use Microsoft Excel as this will work well, also.
You will have x and y coordinates. Put these numbers, (x,y), in two columns, side by side. Now take the first entry in the left most column and multiply it by the second entry in the right column (Second down). Continue all the way down to get a sum in the next right most column (new column). Now due the same with the leftmost column. Multiply the first number in the rightmost colum with the second number down in the left column. Put this product into a separate column. Now add both columns of products to get a sum in each column. Take the difference of the two columns. Now divide by two. The answer is in square units.
This may be a bit confusing, but it works as I do surveying calculations with coordinates for polygons with this spreadsheet that I developed.
Good Luck.

Answer 3

I did this in O-level; it's relatively easy. I've got the formula somewhere. Anyhows you need the formula or to try and work it out.

If you're really stuck come back to me but I got to tell you, that I've a big exam comming up in maths and I won't answer for a couple of weeks.

Ya know, there's a different formula for each polygon, so it would help if you said how many sides it had.

Answer 4

Use the same method that Archimedes used.