Find the area of a square in square metres if one of its diagonals is 3.8 m long.

Introduction / Context:
This question uses a well known property of a square relating its diagonal to its side. In many quantitative aptitude tests, candidates are required to compute either side or area when the diagonal is given. The square is a special case of a rectangle where all sides are equal and all angles are right angles, which simplifies the relationship between side length and diagonal.

Given Data / Assumptions:
• The figure is a square.• The length of the diagonal is 3.8 m.• We need to find the area of the square in square metres.

Concept / Approach:
For a square with side s and diagonal d, by Pythagoras theorem we have d^2 = s^2 + s^2 = 2s^2. Thus s^2 = d^2 / 2. The area A of the square is s^2, so A = d^2 / 2. Once the diagonal is known, we can square it, divide by 2 and obtain the area directly. This formula avoids separate computation of the side and is very convenient in exams.

Step-by-Step Solution:
Step 1: Write the relation between diagonal and side.d^2 = 2s^2, so s^2 = d^2 / 2.Step 2: Compute d^2.d = 3.8 m, so d^2 = 3.8 * 3.8 = 14.44.Step 3: Compute the area using A = d^2 / 2.A = 14.44 / 2.Step 4: Perform the division.A = 7.22 square metres.

Verification / Alternative check:
We can also approximate 3.8 m as slightly less than 4 m. A square with diagonal 4 m has area 4^2 / 2 = 16 / 2 = 8 sq. m. Since our diagonal is 3.8 m, which is slightly smaller, the area should be slightly less than 8 sq. m. The value 7.22 sq. m is consistent with this expectation and therefore seems reasonable.

Why Other Options Are Wrong:
Option A: 4.22 sq. m is too small and would correspond to a much shorter diagonal.Option B: 5.22 sq. m also underestimates the area for a diagonal of 3.8 m.Option C: 6.22 sq. m is still smaller than the correct value and does not satisfy A = d^2 / 2.

Common Pitfalls:
Some candidates mistakenly use the formula A = d^2 instead of d^2 / 2 or they treat the diagonal as if it were a side. Others miscalculate 3.8^2 due to errors in decimal multiplication. Writing the relation d^2 = 2s^2 clearly and carrying out the arithmetic slowly helps to avoid errors in this type of problem.

Final Answer:
The area of the square is 7.22 sq. m.