Answer: C
Explanation:
To find the percentage of error in the calculated area of the square when there is a 2% error in measuring its side, you can use the formula for the area of a square:
Area = side × side
Let's assume the actual side of the square is "S," and the measured side with a 2% error is "S_actual."
Given that there's a 2% error in measuring the side, we have:
S_actual = S + 0.02S
Now, let's calculate the area with the actual side and the measured side:
Actual Area = S × S
Measured Area = S_actual × S_actual = (S + 0.02S) × (S + 0.02S) = S^2 + 0.04S^2 + 0.0004S^2
Now, let's find the percentage error in the calculated area:
Percentage Error = [(Measured Area - Actual Area) / Actual Area] × 100
Percentage Error = [(S^2 + 0.04S^2 + 0.0004S^2 - S^2) / S^2] × 100
Percentage Error = [(0.04S^2 + 0.0004S^2) / S^2] × 100
Percentage Error = [(0.0404S^2) / S^2] × 100
Percentage Error = 4.04%
So, the percentage of error in the calculated area of the square is 4.04%, which corresponds to option (c).