Final answer:
The lower bound for the area of a rectangle is found by multiplying the lower bounds of the length and width. In this case, the lower bound is 370 mm multiplied by 19.35 mm, resulting in an area of 7159.5 mm².
Step-by-step explanation:
The lower bound for the area of a rectangle is calculated by multiplying the lower bounds of the length and width. The length of the rectangle is measured as 370 mm, and this is a precise measurement. The width, measured to one decimal place, is stated as 19.4 mm. Since the value is correct to one decimal place, the lower bound would be half of the last significant digit, or 0.05 mm, less than the measured value. Therefore, the lower bound for the width is 19.4 mm - 0.05 mm = 19.35 mm. To find the lower bound for the area, we multiply the length and the width's lower bounds: 370 mm × 19.35 mm.
The lower bound for the area of the rectangle is then: 370 mm × 19.35 mm = 7159.5 mm2. This value is presented with the correct number of significant digits according to the precision of the measurements.