Surveying Multiple Choice Questions on “Area Computation – Ordinate Rule”.
1. Which of the following represents the correct set of ordinate rules used?
a) Average ordinate rule, Trapezoidal rule
b) Mid-ordinate rule, Mean ordinate rule
c) Mid-ordinate rule, Average ordinate rule
d) Trapezoidal rule, Mean ordinate rule
Answer: c
Clarification: The area from offsets can be calculated by using certain rules which include Mid-ordinate rule, Average ordinate rule, Trapezoidal rule, Simpson’s one-third rule, of which the mid-ordinate and average ordinate rules come under ordinate rules set.
2. Find the length of the base line if the number of divisions are 4 and d = 1.5m.
a) 2 m
b) 6 m
c) 2.5 m
d) 8 m
Answer: b
Clarification: The value of length of the base can be found out by using the formula,
L = n*d and on substitution, we get
L = 4*1.5 = 6 m.
3. Ordinate rule is based on which of the following assumptions?
a) Boundaries of the offsets are straight lines
b) Boundaries of the offsets are perpendicular
c) Boundaries of the offsets are curves
d) Boundaries of the offsets are parabolic
Answer: a
Clarification: The ordinate rule is used with the assumption that the boundaries between the extremities of the ordinates are straight lines. The base line is divided into number of divisions and the ordinates are measured at the midpoints of each division.
4. The area of the figure from ordinate rule can be determined as__________
a) A = average ordinate * perimeter
b) A = average ordinate * breadth
c) A = average ordinate * area
d) A = average ordinate * length of base
Answer: d
Clarification: The formula for area of figure from ordinate rule can be given as,
A = average ordinate * length of base
Where, L can be determined by no. of divisions*distance of each division.
5. Calculate the area by mid-ordinate rule if the value of d = 2m and the ordinates are given as 24.69m, 42.96 m, 26.74m.
a) 188.87 sq. m
b) 881.78 sq. m
c) 188.78 sq. m
d) 198.78 sq. m
Answer: c
Clarification: The formula for the area of the mid-ordinate can be given as
A = d*∑O. On substitution, we get
A = 2 * (24.69+42.96+26.74)
A = 188.78 sq. m.
6. Among the area calculation methods, which is more accurate?
a) Area by co-ordinates
b) Area by Simpson’s one-third rule
c) Area by double mean distances
d) Area by offsets
Answer: b
Clarification: Though the area calculated by dividing into triangles helps in determining the area of the figure, the area calculated by using Simpson’s rule helps in providing accurate results than the previously mentioned process.
7. Calculate the area by average co-ordinate rule, by using the offsets provided taken at 10m interval.
4.16, 6.34, 7.89, 6.54, 5.67, 7.76, 8.52, 5.87, 6.21
a) 245.08m
b) 542.08 m
c) 524.08 m
d) 528.04 m
Answer: b
Clarification: We have, Δ = (L * ∑O) / (n+1)
Here n = number of divisions = 8; n + 1 = number of ordinates = 8 + 1 = 9
L = Length of base = 10 x 8 = 80 m
∑O = 4.16+6.34+7.89+6.54+5.67+7.76+8.52+5.87+6.21 = 58.96m
Δ = (80*58.96)/9 = 524.089m.
8. Find the value of number of divisions if the area is 543.89 sq. m and the summation of the co-ordinates is given as 223.98 m.
a) 2.42 m
b) 2.24 m
c) 4.22 m
d) 2.56 m
Answer: a
Clarification: We know that, the area by mid-ordinate can be given as, A = d*∑O. from this, the value of d can be calculated as,
d = A/∑O
d = 543.89 / 223.98
d = 2.42m.
9. The calculation of area by ordinate rule and Simpson’s rule will come under which category?
a) Area by double mean distances
b) Area by co-ordinates
c) Area by triangles
d) Area by offsets
Answer: d
Clarification: The area by offset method is suitable for long narrow strips of land. The offsets are measured from the boundary of the base line or a survey line at regular intervals. This method can also be applied to a plotted plan from which the offsets to a line can be scaled off.
10. Which of the following indicates the formula for area by average co-ordinate method?
a) Δ = (L * ∑O)/(n+1)
b) Δ = (L * ∑O)/(n-1)
c) Δ = (L + ∑O)/(n+1)
d) Δ = (L – ∑O)/(n+1)
Answer: a
Clarification: The area by average co-ordinate method is given as,
Δ = Average ordinate * length of base
Δ = (L * ∑O) / (n+1) where, ∑O = O1+O2+………+On