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Area Measurement Methods and Topographical Map Heights

Learn how to measure area using grid squares and visual methods, and understand how heights are determined on topographical maps. Explore triangulated heights, spot heights, and relative heights with examples.

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Area Measurement Methods and Topographical Map Heights

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  1. MEASURING THE AREA

  2. Measuring the Area - Considerations • All eastings are 2 cm (1 km) apart • All northings are 2 cm (1 km) apart • Each grid square measures • 2 cm X 2 cm • OR • 1 km X 1 km • = • 1 sq. km

  3. How do we measure the area? • Count the number of grid squares (n) • Area = n sq. km

  4. Example 1 Calculate the area enclosed within eastings 26 and 29 and northings 58 and 62. Solution • Eastings difference (p) = 29 – 26 = 3 • Northings difference (q) = 62 – 58 = 4 • Area enclosed = p X q • = 3 X 4 • = 12 sq km

  5. Visual method

  6. Visual method

  7. Example 2 Calculate the extent of cultivated area enclosed within eastings 43 and 49 and northings 85 and 89. CWrong Solution • Eastings difference (p) = 49 – 43 = 6 • Northings difference (q) = 89 – 85 = 4 • Area enclosed = p X q • = 6 X 4 • = 24 sq km

  8. So, what is the correct solution?

  9. Visual method

  10. Correct solution • Area enclosed by full grid squares (f) • Area enclosed = f X 1 • Area enclosed by half grid squares (h) • Area enclosed = h X ½ • Area enclosed by more than half grid squares (m) • Area enclosed = m X 2/3 • Area enclosed by less than half grid squares (l) • Area enclosed = l X 1/3

  11. TOTAL AREA • Total area • f X 1 • + • h X ½ • + • m X 2/3 • + • l X 1/3

  12. Correct solution - Visual method

  13. TOTAL AREA • Finding the total area • f X 1 = 10 X 1 = 10 sq. km + • h X ½ = 4 X ½ = 2 sq. km + • m X 2/3 = 7 X 2/3 = 4.67 sq. km + • l X 1/3 = 5 X 1/3 = 1.67 sq. km = • Total Area = 18.34 sq. km

  14. REPRESENTING HEIGHTS ON TOPOGRAPHICAL MAPS

  15. How are heights measured? • Start from mean sea level • Determine the heights using theodolite (principles of trigonometry) • Use these heights as bench marks to determine further heights

  16. Types of heights Triangulated Height Spot Height Relative Height

  17. Triangulated Height • Determined using principles of trigonometry • Accurate • Expressed on maps using a ∆ • For example, ∆ 224

  18. Prominent Surveyed Tree • Triangulated height written on tree bark • Tree is shown in black colour- • For example

  19. Bench Mark • Triangulated height written on nearby rock or wall • Shown using BM • For example, BM 403

  20. .544 560 540 Spot Height • Height estimated using the value of adjacent contours • Shown with a dot • For example, .544

  21. Relative Height • Height (depth) of a feature relative to surroundings • Shown using r • For example, 20r

  22. Example of relative heights 7r 11r 14r

  23. End of Presentation

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