A square field measure 12m by 12m. A student measure the side of the field as 12.2m and uses the measurements to calculate the field. Find the percentage error . Find the length of side. Area of the field

The actual side length of the square field is $L_{actual} = 12 \text{ m}$. The student's measured side length is $L_{measured} = 12.2 \text{ m}$.

Step 1: Calculate the absolute error in the side measurement. $\text{Absolute Error} = |L_{measured} - L_{actual}| = |12.2 \text{ m} - 12 \text{ m}| = 0.2 \text{ m}$

Step 2: Calculate the percentage error in the side measurement. $\text{Percentage Error} = \frac{\text{Absolute Error}}{L_{actual}} \times 100\%$ $\text{Percentage Error} = \frac{0.2 \text{ m}}{12 \text{ m}} \times 100\%$ $\text{Percentage Error} = \frac{1}{60} \times 100\%$ $\text{Percentage Error} = 1.666...\% \approx 1.67\%$

Step 3: State the length of the side used by the student. The student used the measured length to calculate the field. $\text{Length of side used} = 12.2 \text{ m}$

Step 4: Calculate the area of the field using the student's measurement. $\text{Calculated Area} = (L_{measured})^{2}$ $\text{Calculated Area} = (12.2 \text{ m})^{2}$ $\text{Calculated Area} = 148.84 \text{ m}^{2}$

• Percentage error: $\boxed{1.67\%}$
• Length of side: $\boxed{12.2 \text{ m}}$
• Area of the field: $\boxed{148.84 \text{ m}^{2}}$