MEASURING THE AREA

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

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

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

Visual method 63 24 25 26 27 28 29 30 62 61 60 59 58 57

Visual method 63 24 25 26 27 28 29 30 62 61 1 2 3 60 4 5 6 59 7 8 9 58 10 11 12 57

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

So, what is the correct solution?

Visual method 90 42 43 44 45 46 47 48 89 88 87 86 85 84

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

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

Correct solution - Visual method 90 42 43 44 45 46 47 48 89 l m h 88 f 87 86 85 84

TOTAL AREA Total Area = 18.34 sq. km 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

REPRESENTING HEIGHTS ON TOPOGRAPHICAL MAPS

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

Types of heights Triangulated Height Spot Height Relative Height

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

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

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

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

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

Example of relative heights Symbol Meaning Relative height of river bank is 7 metres Relative height of Sand Dune is 11 metres Relative height of Tank Embankment is 14 metres 22r Relative Depth of Well is 22 metres 7r 11r 14r

End of Presentation