Question

Find the minimum and maximum possible areas for a rectangle measuring 4.15 cm by 7.34 cm. Round to the nearest hundredth.


minimum area: 30.40 cm2
maximum area: 30.52 cm2


minimum area: 31.76 cm2
maximum area: 34.98 cm2


minimum area: 29.89 cm2
maximum area: 31.04 cm2


minimum area: 24.97 cm2
maximum area: 36.46 cm2

Answer 1

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