Final answer:
The area of a triangle with a base of 100.7 cm and height of 66.5 cm is calculated using the formula for the area of a triangle. After calculation, the area is found to be approximately 3348.275 cm² which needs to be expressed to the proper number of significant figures (3.35 x 10² cm²).
Step-by-step explanation:
The area of a shape can be calculated using various formulas depending on the geometry of the shape. In the case of a triangle, the area is calculated using the formula Area = 1/2 × base × height. Converting the dimensions from meters to centimeters (as 1 meter = 100 centimeters), the base would be 100.7 cm (1.007 m × 100) and the height would be 66.5 cm (0.665 m × 100). Applying the formula:
Area = 1/2 × 100.7 cm × 66.5 cm
Area = 50.35 cm × 66.5 cm
Area = 3348.275 cm²
Expressing the area to the proper number of significant figures, which is determined by the least number of significant figures in any of the given measurements (in this case, the height with three significant figures), the result is:
Area ≈ 3,350 cm²
Correctly expressed, the answer is 3.35 × 10² cm², or 3,350 cm² in scientific notation to maintain significant figures.