Square from its diagonal (14 cm) The diagonal of a square is 14 cm. Compute the area of the square (in cm²).

Introduction / Context:The diagonal of a square relates to its side by s√2. From the diagonal, we find the side and then the area s^2. This avoids unnecessary approximation because √2 cancels neatly when squaring.

Given Data / Assumptions:

• Diagonal d = 14 cm
• Relation: d = s * √2 ⇒ s = d / √2
• Area = s^2

Concept / Approach:Compute s from the diagonal, then square to get area: s^2 = (d^2) / 2, a convenient identity derived from d = s√2.

Step-by-Step Solution:

Verification / Alternative check:Explicitly: s = 14 / √2 = 7√2; s^2 = (7√2)^2 = 49 * 2 = 98, which matches the shortcut above.

Why Other Options Are Wrong:49 sq cm is side^2 if s were 7; 196 sq cm is d^2, not area; 77 sq cm has no basis here.

Common Pitfalls:Using area = (1/2)*d^2 is correct for squares; forgetting this identity or mishandling √2 often causes errors.

Final Answer:98 sq cm