Final answer:
To find the area of a triangle with a base of 1.007 m and height of 0.665 m, we first convert these measurements to centimeters, then use the formula for the area of a triangle (½ × base × height), and round the result to three significant figures to get 3350 cm².
Step-by-step explanation:
The area of a triangle can be calculated using the formula ½ × base × height. When the base is given in meters and the height is given in meters, we must ensure that the units are consistent before performing the calculation. Therefore, the base and height must be converted from meters to centimeters by multiplying them by 100, since 1 meter equals 100 centimeters. After conversion, the base is 1.007 m × 100 cm/m = 100.7 cm, and the height is 0.665 m × 100 cm/m = 66.5 cm.
To calculate the area of the triangle and express it to the proper number of significant figures, we multiply the base and height and then divide by 2: Area = ½ × 100.7 cm × 66.5 cm. Let's carry out the calculation:
½ × 100.7 cm × 66.5 cm = 3352.335 cm²
Since the base was given to four significant figures (1.007 m) and the height was given to three significant figures (0.665 m), our final answer should be in three significant figures because we round to the least number of significant figures used in the measurements provided. Hence, the triangle's area is 3350 cm² when rounded to three significant figures.