Final answer:
The area of the triangle with a base of 1.007m and a height of 0.665m, converted to centimeters and calculated using the formula for the area of a triangle, results in 3350 cm² when rounded to three significant figures.
Step-by-step explanation:
The student's question seems to mix details about several problems. The request asks for the area of a shaded region in a square divided by two straight lines but then provides a formula for the area of a triangle, which does not directly answer the student's question. However, to calculate the area of a triangle using the given dimensions and formula, you must use the following steps:
- Convert the base and height from meters to centimeters by multiplying each by 100 (since 1m = 100cm).
- Plug in the base and height into the formula “1/2 × base × height”.
- Calculate the area and express the answer to the correct number of significant figures.
Here are the calculations:
- Base in cm = 1.007m × 100cm/m = 100.7cm
- Height in cm = 0.665m × 100cm/m = 66.5cm
- Area in cm² = 1/2 × 100.7cm × 66.5cm
- Area in cm² = 3346.725 cm² (rounded to three significant figures, the area is 3350 cm²)
To report the correct number of significant figures, LibreTexts mentions that the conversion factors (1 and 100) are exact numbers, and they do not affect the determination of significant figures.