An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?

Options

A. A. 4.04%
B. B. 4%
C. C. 2.02%
D. D. 2%

Answer

To find the percentage error in the calculated area of a square when there is a 2% error in measuring the side, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Correct Measurement of the Side:**
Let the correct measurement of the side of the square be \( s = 100 \) units.

2. **Calculate the Measured Side with Error:**
Since there is a 2% error in excess, the measured side will be:
\[ s' = s + 2\% \text{ of } s = 100 + 0.02 \times 100 = 102 \text{ units} \]

3. **Calculate the Correct Area of the Square:**
The area of the square with the correct side length is:
\[ A = s^2 = 100^2 = 10000 \text{ square units} \]

4. **Calculate the Area with the Measured Side:**
The area of the square with the measured side length is:
\[ A' = (s')^2 = 102^2 = 10404 \text{ square units} \]

5. **Calculate the Error in Area:**
The error in the area can be calculated as:
\[ \text{Error in Area} = A' - A = 10404 - 10000 = 404 \text{ square units} \]

6. **Calculate the Percentage Error in Area:**
The percentage error in the area is given by:
\[ \text{Percentage Error} = \left( \frac{\text{Error in Area}}{\text{Correct Area}} \right) \times 100 = \left( \frac{404}{10000} \right) \times 100 = 4.04\% \]

### Final Answer:
The percentage of error in the calculated area of the square is **4.04%**.

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