Final answer:
The set of sides provided (a=1, b=9, C=9) does not form a valid triangle, and thus we cannot find its area using those dimensions. When converting units for area calculation, the conversion numbers do not affect the number of significant figures in the result.
Step-by-step explanation:
To find the area of a triangle with given side lengths, we often use Heron's formula when all three sides are given, or the basic formula for the area of a triangle, which is 1/2 × base × height. However, with the sides provided (a=1, b=9, C=9), it's clear that this set of sides cannot form a valid triangle, as one side is too short (a must be longer than the difference of b and C, and shorter than their sum, to form a valid triangle).
When working with measurements given in different units, we need to ensure that they are converted properly before calculating the area. In the example given, the base is 1.007 m, and the height is 0.665 m. Converting meters to centimeters is straightforward because 1m equals 100cm. As the numbers used for conversion (1 and 100) are exact, they do not limit the number of significant figures. The area is found by multiplying the base by the height and then dividing by 2, keeping in mind significant figures: A = 1/2 × (1.007 m × 100 cm/m) × (0.665 m × 100 cm/m). The result must be expressed in square centimeters.
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