Find the total surface area of a cuboid that is 16 m long, 14 m broad and 7 m high.

Introduction / Context:
Questions on the surface area of cuboids are common in aptitude tests and basic geometry. They help learners revise how the dimensions of a three dimensional object relate to the total area of its outer surfaces. Here, we are asked to find the total surface area of a cuboid whose length, breadth and height are given in metres.

Given Data / Assumptions:

• The solid is a cuboid.
• Length l = 16 m.
• Breadth b = 14 m.
• Height h = 7 m.
• We are asked for the total surface area in square metres.

Concept / Approach:
For a cuboid, the total surface area is the sum of the areas of all six rectangular faces. The formula for total surface area (TSA) is:
TSA = 2 * (l * b + b * h + l * h) This works because opposite faces are equal in area and there are three distinct pairs: top and bottom, front and back, left and right.

Step-by-Step Solution:
Step 1: Compute l * b = 16 * 14 = 224. Step 2: Compute b * h = 14 * 7 = 98. Step 3: Compute l * h = 16 * 7 = 112. Step 4: Add these three products: 224 + 98 + 112 = 434. Step 5: Multiply by 2 for the total surface area: TSA = 2 * 434 = 868 square metres.

Verification / Alternative check:
We can quickly check the reasonableness. Each face has area between about 100 and 250 square metres, and we have six faces, so a value near 6 * 150 = 900 square metres is expected. The calculated 868 square metres is close to this estimate and is internally consistent with the formula, so the value is reliable.

Why Other Options Are Wrong:
796 square metres is less than the correct total surface area and would result from undercounting one of the faces or misadding the products.
812 square metres is also smaller than the correct value and indicates an error in adding 224, 98 and 112 or in doubling the sum.
902 square metres is larger than the correct value and could come from incorrectly rounding or adding an extra area term.
840 square metres is another nearby but incorrect approximation and does not match the exact formula based calculation.

Common Pitfalls:
Students often confuse lateral surface area with total surface area and forget to include the top and bottom faces. Another common mistake is to change units or to misplace a dimension. It is important to plug the length, breadth and height carefully into the formula and to perform the arithmetic accurately. Forgetting to multiply the sum by 2 is another frequent source of error.

Final Answer:
The total surface area of the cuboid is 868 square metres.