A square's side is measured 2% too large. What is the resulting percentage error in the computed area?

Problem restatementWhen a square's side is measured 2% in excess, the calculated area uses the inflated side. Find the percentage error in area.

Given data

• True side = s.
• Measured side = 1.02s (2% excess).

Concept/ApproachArea scales with the square of the side. Percentage error in area = [(measured area − true area) ÷ true area] × 100%.

Step-by-Step calculationTrue area = s²Measured area = (1.02s)² = 1.0404 s²Percentage error = (1.0404 − 1) × 100% = 4.04%

Verification/AlternativeUsing binomial approximation: (1 + x)² ≈ 1 + 2x + x². With x = 0.02 ⇒ 1 + 0.04 + 0.0004 = 1.0404, confirming 4.04%.

Common pitfallsDoubling the 2% to 4% and ignoring the small x² term, which here contributes 0.04%.

Final Answer4.04%