Question

Following offsets were taken from a survey line to a hedge:

Distance (in m)	0	5	10	15	20	30	40
Offsets (in m)	3	4	5.5	5	6	4	4.5

The area between survey line and the hedge is (by trapezoidal method):

• A. $185m^2$
• B. $187.5m^2$
• C. $189.5m^2$
• D. $289.5m^2$

Answer 1

The correct option is B $187.5m^2$

For area as given by Trapezoidal method is
$A=d[\left(\frac{O_0+O_n}{2}\right)+O_1+O_2......O_{n-1}]$
Now, since 'd' is not constant
$\therefore A_1=5[\frac{3+6}{2}+4+5.5+5]=95m^2$
$a_2=10[\frac{6+4.5}{2}+4]=92.5m^2$
total area,
$A=A_1+A_2$
$=95+95.5=187.5m^2$