Calculating Polygon Area and Trapezium Area with Known Coordinates

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The content above guides you on finding the exact area of a polygon by calculating the areas of individual triangles within it. It also demonstrates how to list coordinates in a spreadsheet, calculate the area of trapeziums formed by pairs of coordinates, and sum their areas to determine the total area of the polygon. Additionally, it poses a question about handling polygons with holes in them.

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Survey Plot

Find the exact area of the polygon. Area = sq. units L

? ?2,?2 What s the area of this triangle? ?3,?3 ?1,?1 ?

? ?2,?2 What s the area of this triangle? ?3,?3 ?1,?1 ?

? ?2,?2 What s the area of this triangle? ?3,?3 ?1,?1 ? ?1,0 ?2,0 ?3,0

? ???+ ?? ? ???+ ?? ?1,?1 ? ???+ ?? ?? ?? ?? ?? ?? ??

? ???+ ?? ? ???+ ?? ?1,?1 ? ???+ ?? ?? ?? ?? ?? ?? ??

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of coordinates. Copy down this formula to the last point (point 3). Finally, sum the areas of the trapezium. Point Trapezium area 1 2?2+ ?1 ?2 ?1 1 2?3+ ?2 1 2?1+ ?3 ? ????? ? ????? ?1 ?1 1 ?2 ?2 2 ?3 ?2 ?3 ?3 3 ?1 ?3 ?1 ?1 1 Total

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of coordinates. Copy down this formula to the last point (point 3). Finally, sum the areas of the trapezium. Point Trapezium area 1 2?2+ ?1 ?2 ?1 1 2?3+ ?2 1 2?1+ ?3 ? ????? ? ????? ?1 ?1 1 ?2 ?2 2 ?3 ?2 ?3 ?3 3 ?1 ?3 ?1 ?1 1 Total

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of coordinates. Copy down this formula to the last point (point 3). Finally, sum the areas of the trapezium. Point Trapezium area 1 2?2+ ?1 ?2 ?1 1 2?3+ ?2 1 2?1+ ?3 ? ????? ? ????? ?1 ?1 1 ?2 ?2 2 ?3 ?2 ?3 ?3 3 ?1 ?3 ?1 ?1 1 Total

So, list the coordinates in columns in a spreadsheet, repeating the first coordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of coordinates. Copy down this formula to the last point (point 3). Finally, sum the areas of the trapezium. Point Trapezium area 1 2?2+ ?1 ?2 ?1 1 2?3+ ?2 1 2?1+ ?3 ? ????? ? ????? ?1 ?1 1 Think of this point as point 4 in the list. ?2 ?2 2 ?3 ?2 ?3 ?3 3 ?1 ?3 ?1 ?1 1 Total What if the polygon had a hole in it?

So to include a hole insert its co-ordinates into the existing list taking care to repeat connecting points (i.e. J and K) and avoid crossing over previous lines. F D G C E N H B hole L R A I O K Q J P M S