Square – side increased by 25%:\nIf each side of a square is increased by 25% (one–fourth more than the original), by what percentage does its area change overall?

Introduction / Context:
Questions that ask for the percentage change in area when each side changes are classic geometry percentage problems. Area of a square depends on the square of its side length, so proportional side changes scale area quadratically.

Given Data / Assumptions:

• Original square side = s.
• New side = s increased by 25% = 1.25*s.
• We need overall % change in area.

Concept / Approach:
The area of a square is side^2. If side is multiplied by k, area is multiplied by k^2. Percentage change = (new/old − 1) * 100%.

Step-by-Step Solution:

Verification / Alternative check:
1.25 = 5/4; (5/4)^2 = 25/16 = 1.5625 → increase 9/16 = 0.5625 → 56.25%.

Why Other Options Are Wrong:

• 36.25%, 16.25%, 12.25% underestimate the quadratic effect; they may stem from linear thinking.
• None of these is invalid because 56.25% is available.

Common Pitfalls:
Using 25% directly on area (linear) instead of squaring the side-scale factor; forgetting that area scales with side^2.

Final Answer:
56.25%