Final answer:
The area of a triangle with a base of 166 mm and a height of 930.0 mm is calculated using the formula for the area of a triangle (1/2 × base × height). After converting the units to meters, the area is found to be 0.07719 m² and is then expressed in three significant figures as 0.0772 m².
Step-by-step explanation:
To calculate the area of a triangle with a base of 166 mm and a height of 930.0 mm, we use the formula:
Area = ½ × base × height
First, we convert the measurements to meters for consistency, because the desired unit for area is square meters:
- Base = 166 mm = 0.166 m
- Height = 930.0 mm = 0.930 m
Now we can plug in these values into the formula:
Area = ½ × 0.166 m × 0.930 m
Area = 0.07719 m²
With attention to significant figures, the base has three significant figures, and the height has four. However, for multiplication, the number of significant figures in the result is determined by the original number with the fewest significant figures, which is three in this case. So the area must be expressed in three significant figures.
Therefore, the area of the triangle is 0.0772 m².