Percentage of Error in Measuring the Side of a Square

To find the percentage of error in the calculated area of a square, we first need to understand the concept of percentage error.

Percentage error is a measure of the difference between the measured or observed value and the true or actual value, expressed as a percentage of the true value.

In this case, the error made while measuring the side of the square is 3% in excess. This means that the measured value of the side is 3% more than the true value.

Formula for Percentage Error:
Percentage Error = (Error / True Value) * 100

Calculating the Percentage Error in Measuring the Side of the Square:
Given that the error made while measuring the side of the square is 3% in excess.

Let's assume the true value of the side of the square is 'x'.

Measured Value of the Side = x + (3/100)*x = x + 0.03x = 1.03x

Now, we can calculate the percentage error using the formula mentioned above.

Percentage Error = ((Measured Value - True Value) / True Value) * 100
= ((1.03x - x) / x) * 100
= (0.03x / x) * 100
= 3%

Percentage of Error in the Calculated Area of the Square

To find the percentage of error in the calculated area of a square, we need to consider that the area of the square is directly proportional to the square of the side length.

Formula for the Area of a Square:
Area = side^2

Calculating the Percentage of Error in the Calculated Area of the Square:
Let's consider the area of the square using the true value of the side as 'x'.

True Area = x^2

Now, let's calculate the measured area using the measured value of the side, i.e., 1.03x.

Measured Area = (1.03x)^2
= 1.0609x^2

The percentage error in the calculated area can be found using the formula mentioned above.

Percentage Error = ((Measured Area - True Area) / True Area) * 100
= ((1.0609x^2 - x^2) / x^2) * 100
= (0.0609x^2 / x^2) * 100
= 6.09%

Hence, the correct answer is option (c) 6.09%, which represents the percentage of error in the calculated area of the square.