Final answer:
The maximum measurement error for the area of the Shipyard complex, which is calculated as 100m by 340m, is approximately 445 square meters. This error arises due to the rounding of each dimension to the nearest meter, with a maximum error of half a meter for both the length and the width.
Step-by-step explanation:
To determine the possible measurement error due to rounding in the area calculation of the Shipyard complex, we must consider the degree to which each dimension (length and width) could be rounded. As the lengths are given as whole numbers, we can assume they have been rounded to the nearest meter. Therefore, the maximum error for each dimension is half a meter because rounding to the nearest meter means any measurement could be up to 0.5 meters larger or smaller than the stated value.
For the length of 100 m, the possible error ranges from 99.5 m to 100.5 m. For the width of 340 m, the value could range from 339.5 m to 340.5 m. To calculate the maximum measurement error in the area, we first consider the smallest possible area, which would be obtained using the smallest possible length and width (99.5 m * 339.5 m), and the largest possible area, using the largest possible length and width (100.5 m * 340.5 m).
Smallest Area = 99.5 m * 339.5 m = 33780.25 m²
Largest Area = 100.5 m * 340.5 m = 34225.25 m²
The difference between these areas will give us the measurement error due to rounding:
Error = Largest Area - Smallest Area
Error = 34225.25 m² - 33780.25 m²
Error = 445 m²
Therefore, the measurement error due to rounding in the calculation of the area of the Shipyard complex is approximately 445 m².