How to Measure the Area of ​​the Polygon With Excel

Measure the area of ​​a polygon that is known only corner points is not an easy job. If you find that the actual polygon composed of some form, then you will try to divide the polygon into several small pieces to be a square or triangle so you can easily calculated and combines all the small parts area. Of course it is not a practical way. 
For example in the picture above, the corner  coordinates of the  polygon are  (1,1), (​​1,3), (​​3.5), (​​5,3) and (5.1). We can suppose that the polygon is composed of two forms. The first form is rectangular and other shapes are triangles. Therefore, the actual area of the polygon is

Total Area = Area of ​​Rectangle + Area of ​​triangle = 8 + 4 = 12

But what if the polygon is composed of many forms, Do you want to count one by one and then summing the breadth? Here I will show how to calculate area of ​​polygon with excel (regardless of the number of vertex) if the corner  coordinates of the polygon are available.

1. Open New Excel Document and type in all the coordinates of polygon corner with separate columns in X and Y. Note that you have to sort the coordinates in sequence clockwise or counterclockwise. You can choose which coordinates will be written fot the first, in this example I mark the lower left coordinates as the first coordinates.

2.  Rewrite the first coordinates and place it in the bottom of your table. see the pictures below.

3. Multiply the first row of column X with the second row in column Y. The results are put in a new column next to it.  Suppose this new column name is X1.Y2. Copy the formula in cell next to the bottom for a five row or the same as the number of polygon corner (I assume you can copy the formula in a cell).


4. Do the same as in step 3, but this time multiply the first row of column Y with the second row of column X. name the new column as Y1.X2. Look at the picture.

5. Sum all the number ​​in each column. In this example, the sum  in column X1.Y2 is 27 and in column Y1.X2 is 51.

6. Calculate the difference of two columns and divide the result by 2 (Area must be marked positive, neglect the negative value). In the form of a mathematical equation:
L = (51- 27) : 2 = 12

The result is the same with the manual way.