Coordinate-based Polygon Area Calculation Method

Utilize a step-by-step approach to determine the area of a polygon by listing coordinates in columns, calculating trapezium areas, and summing them up. This versatile method can be applied to any polygon, not limited to triangles.

• Polygon Area Calculation
• Coordinate System
• Trigonometry Method
• Geometric Analysis

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1. Survey Plot

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

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

4. ? ?2,?2 What s the area of this triangle? ?3,?3 ?1,?1 ? ?1,0 ?2,0 ?3,0

5. ? ???+ ?? ? ???+ ?? ? ???+ ?? ?? ?? ?? ?? ?? ??

6. ? ???+ ?? ? ???+ ?? ? ???+ ?? ?? ?? ?? ?? ?? ??

7. So, list the co-ordinates in columns in a spreadsheet, repeating the first co-ordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of co-ordinates. 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

8. So, list the co-ordinates in columns in a spreadsheet, repeating the first co-ordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of co-ordinates. 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

9. So, list the co-ordinates in columns in a spreadsheet, repeating the first co-ordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of co-ordinates. 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

10. So, list the co-ordinates in columns in a spreadsheet, repeating the first co-ordinates at the end. Then enter a formula for the area of the trapezium formed by the first pair of co-ordinates. 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 This process works with ANY polygon, not just a triangle.

11. An example of what your spreadsheet could look like

12. ? This process works with ANY polygon, not just a triangle. And it doesn t have to be convex either! ?

13. This process works with ANY polygon, not just a triangle. And it doesn t have to be convex either!

14. 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

15. You should all get the same answer: 1501 sq. units. How was this achieved? The position of A, C, E and G is the same on all worksheets. The points form a parallelogram (although the shape is irrelevant). All triangles with a side of ACEG as a base share the same height (and so the same area).

17. Note to Teacher It is useful to get the pupils to insert a chart of their survey plot. Just highlight the coordinates Insert scatter chart (with points joined by straight lines) They should now see a representation of their worksheeet.

18. RESOURCES

19. Find the exact area of the polygon. Area = sq. units A SIC_28

20. Find the exact area of the polygon. Area = sq. units B SIC_28

21. Find the exact area of the polygon. Area = sq. units C SIC_28

22. Find the exact area of the polygon. Area = sq. units D SIC_28

23. Find the exact area of the polygon. Area = sq. units E SIC_28

24. Find the exact area of the polygon. Area = sq. units F SIC_28

25. Find the exact area of the polygon. Area = sq. units G SIC_28

26. Find the exact area of the polygon. Area = sq. units H SIC_28

27. Find the exact area of the polygon. Area = sq. units I SIC_28

28. Find the exact area of the polygon. Area = sq. units J SIC_28

29. Find the exact area of the polygon. Area = sq. units K SIC_28

30. Find the exact area of the polygon. Area = sq. units L SIC_28

31. Find the exact area of the polygon. Area = sq. units M SIC_28

32. Find the exact area of the polygon. Area = sq. units N SIC_28