Final answer:
To find the area of the triangle, use the formula: area = (1/2) * base * height and substitute the given values. The length of the base is increasing at a rate of 2 cm/in, which can be converted to inches. The rate of change of the base is 0.7874 in/s. The rate of change of the area requires additional information about the rates of change for the base and the height.
Step-by-step explanation:
To find the area of the triangle, we will use the formula: area = (1/2) * base * height. Given that the base is 1.007 m and the height is 0.665 m, we can substitute these values into the formula: area = (1/2) * 1.007 * 0.665 = 0.333 cm² (rounded to the proper number of significant figures).
The length of the base would be given in the same units as the altitude, which is increasing at a rate of 2 cm/in. So, if we assume the base is also measured in inches, then the length of the base would be increasing at a rate of 2 cm/in * (1 in / 2.54 cm) = 0.7874 in/s.
The rate of change of the base can be determined by taking the derivative of the base with respect to time. In this case, the rate of change would be 0.7874 in/s.
The rate of change of the area can be found by taking the derivative of the area formula with respect to time. Since the area formula involves multiplying the base and height, and both are changing over time, we would need more information about the rates of change for the base and the height to evaluate the area change rate.