Canal in banking/cutting — berm design and area relations Identify the correct statements regarding canal classification relative to natural surface level (NSL), area of canal in cutting, area of canal bank, and berm width design with respect to full supply depth (FSD).

Introduction / Context:
In canal design and estimation, sections may lie in embankment (banking), cutting, or a combination. Basic geometric relations for trapezoidal sections and empirical berm widths tied to full supply depth (FSD) are standard checks in preliminary design and quantity takeoff.

Given Data / Assumptions:

• Trapezoidal section with bed width B and side slopes represented by a factor S for both sides combined.
• Bank (embankment) geometry quantified similarly with B1 (top width) and d1 (bank height above NSL).
• Empirical berm rules linked to FSD are used in preliminary design.

Concept / Approach:
For a trapezoid, area A in cutting can be written A = Bd + Sd^2 when S represents the sum of the two side-slope run factors. Embankment (bank) area follows an analogous form. Classification relative to NSL determines whether the canal is in banking, cutting, or mixed, guiding berm width prescriptions (e.g., 3d for full banking, 2d for mixed situations), as adopted in many textbooks and departmental practices.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional reasonableness: each term in the area expressions has units of area; berm rules align with conventional thumb-rule practices used for preliminary sizing.

Why Other Options Are Wrong:

• Each individual option (a–d) is consistent with common preliminary design guidance; hence selecting a single one would omit the others.

Common Pitfalls:
Confusing whether S denotes one side slope or combined; forgetting that berm rules are thumb-rules and may be tuned by local standards, stability checks, and right-of-way limitations.

Final Answer:
All the above