If the side of a square is increased by 30%, by what percentage does its area increase?

Introduction / Context:
Area of a square scales with the square of its side. When a linear dimension changes by a certain percent, the area changes by the square of the scale factor. This checks understanding of geometric scaling and percentage growth.

Given Data / Assumptions:
Side increases by 30% ⇒ side factor = 1.30.

Concept / Approach:
If side increases by factor k, the area increases by factor k^2. The percentage increase in area is (k^2 − 1) * 100%. With k = 1.3, compute 1.3^2 and translate to a percent change relative to the original area.

Step-by-Step Solution:

Verification / Alternative check:
Assume initial side s = 10 units. Initial area = 100. New side = 13; new area = 169. Increase = 69 over 100 ⇒ 69%.

Why Other Options Are Wrong:
30% treats area like a linear dimension. 60% is close but incorrect; 9% is 0.3^2 without referencing the total; 75% has no basis here.

Common Pitfalls:
Adding 30% twice (to get 60%) or squaring 30 (instead of 1.3). Always convert percent changes to scale factors before squaring for area.

Final Answer:
69%