Total surface area of a cube (side = 7.5 cm)\nFind the total surface area (in cm²) of a cube whose edge length is 7.5 cm.

Introduction / Context:
Cubes have six congruent square faces. A standard mensuration task is to compute total surface area (TSA) from the edge length, then ensure unit consistency (cm² here).

Given Data / Assumptions:

• Edge length a = 7.5 cm
• Total surface area formula for a cube: TSA = 6 * a^2
• Answer required in square centimetres (cm²).

Concept / Approach:
Each face is a square with area a^2. Since there are 6 faces in a cube, TSA = 6 * a^2. Compute a^2 first, then multiply by 6, taking care with decimal multiplication.

Step-by-Step Solution:

Verification / Alternative check:
Break 7.5 into 15/2 ⇒ a^2 = (15/2)^2 = 225/4 = 56.25; multiplying by 6 yields 337.5 exactly, confirming the decimal computation.

Why Other Options Are Wrong:
364.5 and 446 arise from mis-multiplication; 684 mistakenly doubles 342; only 337.5 matches 6 * a^2.

Common Pitfalls:
Using lateral surface area (4 * a^2) instead of total, or squaring 7.5 incorrectly (e.g., 7.5 * 7 = 52.5) leads to wrong values.

Final Answer:
337.5