Problem Statement
A surveyor measures the width of an irregular parcel of farmland along a $40\text{ m}$ baseline at regular intervals of $h = 8\text{ m}$. The measured perpendicular offsets in metres are: $0, 14, 22, 18, 12, 0$.
**(a)** [4 marks] Use the trapezoidal rule to estimate the total surface area of the farmland parcel.
**(b)** [2 marks] State one way the surveyor could obtain a more accurate estimate of the farmland area.
Verified Solution & Marking Scheme
Part (a) [M1]
Trapezoidal rule: $\text{Area} \approx \frac{h}{2} [y_0 + y_n + 2(y_1 + y_2 + \dots + y_{n-1})]$ with $h = 8$
Part (a) [A1]
$\text{Area} \approx \frac{8}{2} [0 + 0 + 2(14 + 22 + 18 + 12)] = 4 [2(66)]$
Part (a) [A1]
$\text{Area} \approx 4 \times 132 = 528\text{ m}^2$
Part (b) [R1]
Decrease the strip width $h$ (or take more measurements at smaller, closer intervals).