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Areas

Regular Figures Mathematical Formulae Method of Coordinates Irregular Figures Graphical Method Give and Take Method Trapezoidal Rule Simpson’s One-Third Rule. Areas. Area is divided into triangles, rectangles, squares or trapeziums

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Areas

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  1. Regular Figures • Mathematical Formulae • Method of Coordinates • Irregular Figures • Graphical Method • Give and Take Method • Trapezoidal Rule • Simpson’s One-Third Rule Areas

  2. Area is divided into triangles, rectangles, squares or trapeziums Area of the one figure (e.g. triangles, rectangles, squares or trapeziums) is calculated and multiplied by total number of figures

  3. Mathematical Formulae

  4. Mathematical Formulae

  5. Areas by Method of Coordinates

  6. Areas by Method of Coordinates

  7. Areas by Method of Coordinates

  8. Areas by Method of Coordinates

  9. Area = 0.5(| 136840.01 – (-84890.94) |) = 110865.48 ft2 Areas by Method of Coordinates

  10. Irregular Figures • Give and Take Method • Graphical Method • Trapezoidal Rule • Simpson’s One-Third Rule Areas

  11. In this method, the irregular figure is replaced by a regular one of approximately equal area that can be calculated by one of the methods explained earlier. Give and take Method

  12. Graphical Method Area=( number of compelet squer* area of each squer)+ (area of the uncompelet sqer

  13. Graphical Method =1 cm2

  14. Trapezoidal Rule

  15. Trapezoidal Rule

  16. Trapezoidal Rule

  17. Example

  18. Example

  19. Simpson’s One-Third Rule Offset Intercept ONLY used with Odd number of offsets (i.e. Even number of Intercepts)

  20. Simspon’s One-Third Rule

  21. Example

  22. Areas with mechanical Tools

  23. Planimeters Digital Planimeter Optical Polar Planimeter

  24. Planimeters

  25. From internet : Measure areas using Google Maps http://www.acme.com/planimeter/

  26. Calculate area with computer

  27. Scanner the map then calculate the area by specialized program

  28. By Auto cad

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