Basic Example: Terrain Features V-shaped contours pointing uphill vs pointing downhill.

Intermediate Example: Interpolation A point P lies exactly halfway between the $100\text{m}$ and $105\text{m}$ contour lines.

Advanced Example: Slope Calculation The map distance between $100\text{m}$ and $110\text{m}$ contours is $40\text{m}$ at a 1:1000 scale.

Basic Example: Profile Grades Station $1+200$ is at $150.0\text{m}$, Station $1+450$ is at $155.0\text{m}$. Find the grade.

Intermediate Example: Vertical Curves A $+2\%$ grade meets a $-1\%$ grade. The curve length is $150\text{m}$.

Advanced Example: Station Equations A realignment causes the new route to be $15\text{m}$ shorter, creating an equation at $1+500$ Back = $1+515$ Ahead.

Basic Example: Average End Area Cut area at $0+020$ is $15.0\text{m}^2$, at $0+040$ is $25.0\text{m}^2$. Find volume.

Intermediate Example: Mass Haul Diagram A mass haul diagram goes up, then down, crossing the balance line.

Advanced Example: Prismoidal Formula Used for highly irregular terrain where end areas differ greatly.