To find the minimum and maximum possible areas for a rectangle with dimensions 4.15 cm and 7.34 cm, we need to consider the rounding of the measurements.
Area Calculation: The area \( A \) of a rectangle is calculated using the formula: \[ A = \text{length} \times \text{width} \]
In this case, with the given dimensions:
- Length = 4.15 cm
- Width = 7.34 cm
Before performing the calculation, we must round the dimensions to a reasonable level of accuracy. Suppose the measurements are rounded to two decimal places, we can consider the following ranges for both dimensions:
-
For Length (4.15 cm):
- Minimum: 4.145 cm (if we round down)
- Maximum: 4.155 cm (if we round up)
-
For Width (7.34 cm):
- Minimum: 7.335 cm (if we round down)
- Maximum: 7.345 cm (if we round up)
Calculating Minimum Area: Now, using the minimum values: \[ \text{Minimum Area} = 4.145 , \text{cm} \times 7.335 , \text{cm} \approx 30.40 , \text{cm}^2 \]
Calculating Maximum Area: Using the maximum values: \[ \text{Maximum Area} = 4.155 , \text{cm} \times 7.345 , \text{cm} \approx 30.52 , \text{cm}^2 \]
Rounded Areas: After rounding both results to the nearest hundredth:
- Minimum area: 30.40 cm²
- Maximum area: 30.52 cm²
Based on these calculations, the minimum and maximum possible areas for the rectangle actually are:
- Minimum area: 30.40 cm²
- Maximum area: 30.52 cm²
Thus, the correct answer is:
- minimum area: 30.40 cm²
- maximum area: 30.52 cm²