Square from Diagonal — Compute Area: If the diagonal AC of square ABCD is 5.2 cm, find the area of the square ABCD (in square centimetres).

Introduction / Context:
For any square, the diagonal relates to the side by d = s * √2. Once the side is known, area follows directly from s^2. This question checks your ability to manipulate the diagonal–side relationship and maintain consistent units (centimetres).

Given Data / Assumptions:

• Diagonal d = 5.2 cm
• Square property: d = s * √2
• Area of square: A = s^2
• All measures in centimetres

Concept / Approach:
The diagonal of a square is the hypotenuse of an isosceles right triangle with legs equal to the side length s. Therefore, s = d / √2. After computing s, square it to obtain the area in square centimetres. Only simple arithmetic and the √2 relation are required—no advanced trigonometry.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 15.12 and 12.62 result from rounding √2 or squaring errors.
• 10 sq.cm underestimates, implying a side near 3.16 cm, which would give a diagonal far below 5.2 cm.
• 14.04 sq.cm is a near miss from using √2 ≈ 1.45 or other approximations.

Common Pitfalls:

• Using area = (diagonal)^2 instead of dividing by 2; remember A = d^2 / 2 for a square.
• Mixing units or rounding too early; keep sufficient precision until the final step.

Final Answer:
13.52 sq.cm.