To find the area \( A \) of a rectangle, you use the formula:
\[ A = \text{length} \times \text{width} \]
Given the measurements of the rectangle are \( 4.15 , \text{cm} \) and \( 7.34 , \text{cm} \), we can calculate the area:
\[ A = 4.15 , \text{cm} \times 7.34 , \text{cm} \]
Now performing the multiplication:
\[ A = 4.15 \times 7.34 = 30.481 , \text{cm}^2 \]
Next, we round this to the nearest hundredth:
\[ A \approx 30.48 , \text{cm}^2 \]
Since the problem asks for the minimum and maximum possible areas, we need to consider rounding the measurements to determine these areas. Let's evaluate both dimensions at their possible minimal and maximal values due to rounding.
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For \( 4.15 , \text{cm} \):
- Minimum value: \( 4.145 , \text{cm} \) (rounded down)
- Maximum value: \( 4.155 , \text{cm} \) (rounded up)
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For \( 7.34 , \text{cm} \):
- Minimum value: \( 7.335 , \text{cm} \) (rounded down)
- Maximum value: \( 7.345 , \text{cm} \) (rounded up)
Now we will calculate the possible minimum and maximum areas:
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Minimum Area: \[ \text{Minimum Area} = 4.145 , \text{cm} \times 7.335 , \text{cm} = 30.399825 , \text{cm}^2 \approx 30.40 , \text{cm}^2 \]
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Maximum Area: \[ \text{Maximum Area} = 4.155 , \text{cm} \times 7.345 , \text{cm} = 30.564675 , \text{cm}^2 \approx 30.56 , \text{cm}^2 \]
Thus, the minimum and maximum possible areas for the rectangle are:
- Minimum Area: \( 30.40 , \text{cm}^2 \)
- Maximum Area: \( 30.56 , \text{cm}^2 \)