Quick questions on Ratios, scale drawings and the trapezoidal rule for HSC Maths Standard 2

Real distance = drawing distance $\times$ scale factor.

When you scale every linear dimension by a factor $k$, area scales by $k^2$.

When you scale linear dimensions by $k$, volume scales by $k^3$, since volume is length cubed.

Australian topographic maps commonly use $1:25000$ or $1:50000$. A $4$ cm distance on a $1:25000$ map is $4 \times 25000 = 100000$ cm = $1$ km.

The trapezoidal rule estimates the area of a region with one straight edge (the baseline) and one irregular curved edge, by slicing it into vertical strips and treating each strip as a trapezium. It is the standard HSC tool for the area of a paddock, a lake, a block of land or a cross-section, where there is no neat formula.

$h$ is the distance between consecutive offsets, not the total baseline length. (For a single strip, $h$ is the whole baseline.)