To find the percent error in the calculated area of the rectangle, we first need to calculate the area and then consider the measurement errors.
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Calculate the area: The formula for the area \( A \) of a rectangle is: \[ A = \text{length} \times \text{width} \] Given the dimensions are 18 ft and 4 ft, the area is: \[ A = 18 , \text{ft} \times 4 , \text{ft} = 72 , \text{ft}^2 \]
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Consider measurement error: We need to know the measurement errors for both dimensions. For this example, let’s assume there is a measurement error of ±0.5 ft for each dimension.
- For length (18 ft), the possible measurements including error can vary from: \[ 17.5 , \text{ft} , \text{to} , 18.5 , \text{ft} \]
- For width (4 ft), the possible measurements can vary from: \[ 3.5 , \text{ft} , \text{to} , 4.5 , \text{ft} \]
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Calculate the minimum and maximum areas:
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Minimum area (using minimum dimensions): \[ A_{\text{min}} = 17.5 , \text{ft} \times 3.5 , \text{ft} = 61.25 , \text{ft}^2 \]
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Maximum area (using maximum dimensions): \[ A_{\text{max}} = 18.5 , \text{ft} \times 4.5 , \text{ft} = 83.25 , \text{ft}^2 \]
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Calculate percent error: Percent error can be calculated using the formula: \[ \text{Percent Error} = \left( \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right) \times 100% \]
Using the calculated areas:
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For minimum area: \[ \text{Percent Error}_{\text{min}} = \left( \frac{61.25 - 72}{72} \right) \times 100% \approx -14.5% \]
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For maximum area: \[ \text{Percent Error}_{\text{max}} = \left( \frac{83.25 - 72}{72} \right) \times 100% \approx 15.6% \]
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Finding overall percent error: The percent error in the calculated area will consider both the maximum and minimum possible areas. The average of the absolute percent errors gives a general sense of the overall measurement error. Let’s calculate both:
- Average absolute error: \[ \text{Average Absolute Error} = \frac{|-14.5| + |15.6|}{2} = \frac{14.5 + 15.6}{2} = 15.05% \]
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Round the answer: Therefore, the percent error in the calculated area, rounded to the nearest tenth of a percent, is: \[ \boxed{15.1%} \]
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