Final answer:
The formula for finding the area of a triangle is A = 1/2 * base * height. When calculating the area, it's important to convert units if necessary and to express the final answer with the correct number of significant figures. Using this formula, the area of two different triangles was calculated respecting unit conversion and significant figures.
Step-by-step explanation:
The correct formula for finding the area of a triangle is option a) A = 1/2 * base * height. To calculate the area of a triangle in square centimeters when provided with measurements in meters, such as a base of 1.007 m and a height of 0.665 m, you first need to convert the units from meters to centimeters. There are 100 centimeters in a meter, so the base becomes 100.7 cm and the height becomes 66.5 cm.
Using the formula:
A = 1/2 * base * height
A = 1/2 * 100.7 cm * 66.5 cm
A = 3346.725 cm²
However, because the base was given with four significant figures and the height with three, the answer should be reported with three significant figures, which is 3350 cm².
For the second scenario with a base of 166 mm and a height of 930.0 mm:
A = 1/2 * 166 mm * 930.0 mm (Converted to meters: A = 1/2 * 0.166 m * 0.9300 m)
A = 7713.9 mm² (Converted to meters: A = 0.077139 m²)
But we must respect the number of significant figures, so the area in square meters will be reported as 0.0771 m² because the base was given to three significant figures.