Final answer:
The area of a triangle with a base of 166 mm and a height of 930.0 mm, after converting to meters, is 0.0771 m² when rounded to three significant figures.
Step-by-step explanation:
The formula for the area of a triangle is 1/2 × base × height. To calculate the area of a triangle in square meters when the base is 166 mm and the height is 930.0 mm, we need to convert the millimeters to meters first by dividing by 1000. This gives us a base of 0.166 m and a height of 0.930 m.
Now we apply the area formula:
Area = 1/2 × base × height
Area = 1/2 × 0.166 m × 0.930 m
Area = 0.077145 m²
When expressing this area in terms of significant figures, we notice that the base has three significant figures (166 mm is the same as 166. mm) and the height has four significant figures (930.0 mm), so our final answer should be rounded to the least number of significant figures, which is three.
Therefore, the area of the triangle is 0.0771 m² to three significant figures.