Percent error propagation in area of a square: If the measured side of a square is 2% too large, what is the percentage error in the calculated area?

Introduction / Context:Area of a square varies with the square of its side. A small percentage error in the side propagates roughly twice to area, but exactly it follows the square of the multiplicative factor.

Given Data / Assumptions:

• Measured side = 1.02 * true side (2% excess).
• Area scales with side^2.

Concept / Approach:New area factor = (1.02)^2 = 1.0404 → 4.04% excess in area. Hence the percent error in area is +4.04%.

Step-by-Step Solution:

Verification / Alternative check:Linear approximation gives ~2 * 2% = 4%, close to exact 4.04%, validating the calculation.

Why Other Options Are Wrong:5.04%, 6.04%, 7.04%, 3.96% do not match the exact square of 1.02.

Common Pitfalls:Doubling the percentage and ignoring the small quadratic term, or subtracting instead of adding when error is in excess.

Final Answer:4.04%