GATE 2019 CE (CE2) – Question 53

Geomatics Engineering · Maps, scale, coordinate systems, cartography and map projections · 2 marks · Numerical answer

Perpendicular offsets from a curved boundary to a straight survey line at 6 m spacing are 1.22, 1.67, 2.04, 2.34, 2.14, 1.87 and 1.15 m. Use Simpson’s rule to find area bounded by the survey line, curved boundary and first and last offsets (m²), to two decimal places.

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Correct answer: 67 to 70

Explanation

Six equal intervals permit Simpson’s one-third rule: $$A=\frac63[1.22+1.15+4(1.67+2.34+1.87)+2(2.04+2.14)]=68.50\ \mathrm{m^2}.$$ Answer **68.50 m²**.