Survey Plot

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There are a series of 8 sided polygons for which the areas are to be calculated. The area of each one turns out to be the same. This provides a lead in to asking how the polygons themselves were formed.

A method is introduced whereby the area of a triangle on a Cartesian grid can be calculated by splitting the triangle parallel to the y-axis, and then finding the areas of three trapezia. The method is then extended to find the area of any polygon. A support spreadsheet allows the coordinates to be inputted and the resulting area determined. There is an extension to polygons ‘with a hole’ in them, for which a small adaptation of the earlier method holds true.

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