Cuboid from sum of edges and diagonal — correct units for surface area: The sum of the length, breadth, and height of a cuboid is 19 cm, and its space diagonal is 5√5 cm. What is its total surface area (in cm2)?

Introduction / Context:
This is the same identity-based calculation as earlier, but with units clarified: surface area must be in square centimeters, not square meters, as all linear data are in centimeters.

Given Data / Assumptions:

• l + b + h = 19 cm
• d = 5√5 cm ⇒ d^2 = 125
• S = 2(lb + bh + hl) in cm2

Concept / Approach:
Compute pairwise products using (l + b + h)^2 − d^2, then double the sum to get surface area.

Step-by-Step Solution:
(l + b + h)^2 − d^2 = 19^2 − 125 = 361 − 125 = 236Thus S = 236 cm2

Verification / Alternative check:
Unit consistency: cm inputs imply cm2 for area, not m2.

Why Other Options Are Wrong:
361 and 125 are misinterpreted squares; 486 is unrelated to the identity result.

Common Pitfalls:
Carrying units incorrectly (e.g., writing m2).

Final Answer:
236 cm2