The diagonal of a square is 14 cm. What is the area of the square (in sq cm)?

Introduction / Context:This question tests the relationship between a square’s diagonal and its area. In a square, the diagonal forms a right triangle with the two sides. By the Pythagoras theorem, diagonal d and side s satisfy d = s*sqrt(2). Instead of calculating s with square roots and then squaring again, a useful shortcut is: Area = s^2 = (d^2)/2. This works because s = d/sqrt(2), so s^2 = d^2/2. With diagonal 14 cm, d^2 is 196, and dividing by 2 gives a clean area value. Units remain consistent: diagonal is in cm, so area is in sq cm.

Given Data / Assumptions:

• Diagonal d = 14 cm
• For square: d = s*sqrt(2)
• Area = s^2
• Shortcut: Area = d^2 / 2

Concept / Approach:Compute area using Area = d^2/2. This avoids dealing with sqrt(2) directly and reduces rounding errors.

Step-by-Step Solution: Area = d^2 / 2 d^2 = 14 * 14 = 196 Area = 196 / 2 = 98 sq cm

Verification / Alternative check:Find side: s = 14 / sqrt(2) = 7*sqrt(2). Then area s^2 = (7*sqrt(2))^2 = 49*2 = 98 sq cm. This matches the shortcut result and confirms correctness.

Why Other Options Are Wrong: 196 sq cm happens if you wrongly treat diagonal as side and compute 14^2. 49 sq cm can come from using half the diagonal as side (7^2), which is incorrect. 77 and 100 are distractors from arithmetic or rounding errors.

Common Pitfalls:Confusing diagonal with side, forgetting the division by 2 in d^2/2, or applying Pythagoras incorrectly.

Final Answer:The area of the square is 98 sq cm.