Math CentralQuandaries & Queries


Question from chris, a student:

finding square footage of a polygon with unequal measurements

Hi Chris,

There are a number of ways of finding the area of an irregular polygon. The first point is that if the polygon has more than three sides then you need to know more than just the lengths of the sides. There is an explanation of this in one of our earlier postings.

One technique is to choose a vertex and then draw diagonal lines from this vertex to all the remaining vertices to partition the polygon into triangles. If you can find the areas of these triangles then the area of the polygon is the sum of the areas of the triangles. If you know the lengths of these diagonal lines the you can use Heron's Formula to find the areas of the triangles. There is an example in an earlier posting. If you don't know the lengths of the diagonals but you do know the measurements of the interior angles of the polygon at each vertex you can use the Law of Cosines and the Law of Sines to determine the lengths of the diagonals. Again we have an example in an earlier posting.

There are also Surveyor's Area Formulae in an earlier posting that may be useful depending on what information you have about the polygon. One of these expressions used determinants and the other trigonometry.

I hope this helps,
Stephen La Rocque and Harley Weston

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