In measuring the side of a square, an error of 5% in excess is made. The error % in the calculated area is,

Options

A. `10(1)/(4)%`
B. `10(3)/(4)%`
C. `1(3)/(4)%`
D. 0.25

Answer

To solve the problem of finding the error percentage in the calculated area of a square when there is a 5% excess error in measuring the side, we can follow these steps:

### Step 1: Understand the problem
We know that the area of a square is calculated using the formula:
\[ \text{Area} = \text{side} \times \text{side} \]
If there is a 5% excess in measuring the side, we need to determine how this affects the area.

### Step 2: Calculate the effective side length
Let the actual side length of the square be \( s \). With a 5% excess, the measured side length becomes:
\[ \text{Measured side} = s + 0.05s = 1.05s \]

### Step 3: Calculate the area with the measured side
Now, we calculate the area using the measured side length:
\[ \text{Measured Area} = (1.05s) \times (1.05s) = 1.05^2 \times s^2 \]
Calculating \( 1.05^2 \):
\[ 1.05^2 = 1.1025 \]
Thus, the measured area is:
\[ \text{Measured Area} = 1.1025s^2 \]

### Step 4: Calculate the actual area
The actual area of the square is:
\[ \text{Actual Area} = s^2 \]

### Step 5: Calculate the error in area
The error in area can be calculated as:
\[ \text{Error in Area} = \text{Measured Area} - \text{Actual Area} = 1.1025s^2 - s^2 = 0.1025s^2 \]

### Step 6: Calculate the percentage error in area
To find the percentage error in the area, we use the formula:
\[ \text{Percentage Error} = \left( \frac{\text{Error in Area}}{\text{Actual Area}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Error} = \left( \frac{0.1025s^2}{s^2} \right) \times 100 = 0.1025 \times 100 = 10.25\% \]

### Conclusion
The error percentage in the calculated area is **10.25%**.

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