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

1 answer

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