Final answer:
The question lacks specific information about the figure for solving the shaded area. However, the area of a triangle, the volume of a rectangular box, and the area of a rectangle have been calculated with examples, using given dimensions and observing the rules of significant figures.
Step-by-step explanation:
To solve for the shaded area in the question provided, we need more information about the figure and the details of the shaded region. However, we can go through the calculations for the example scenarios given:
Area of a Triangle
The area of a triangle can be calculated using the formula Area = 1/2 × base × height. For a triangle with a base of 1.007 m (100.7 cm) and a height of 0.665 m (66.5 cm), the area in square centimeters would be:
Area = 1/2 × 100.7 cm × 66.5 cm = 3346.755 cm²
This result should be expressed to three significant figures since the base and height have four and three significant figures, respectively, resulting in an answer of 3350 cm² after rounding.
Volume of a Rectangular Box
The volume of a rectangular box with the sides 1.80 cm, 2.05 cm, and height 3.1 cm is:
Volume = length × width × height = 1.80 cm × 2.05 cm × 3.1 cm = 11.4 cm³
The uncertainty of ±0.05 cm in each measurement affects the total volume uncertainty, resulting in a final volume of 11.4 ± 0.1 cm³.
Area of a Rectangle
The area of a rectangle with sides 2.44 cm and 6.077 cm is calculated by multiplying these dimensions:
Area = 2.44 cm × 6.077 cm = 14.82788 cm²
To express the answer in the proper number of significant figures based on the given measurements (four significant figures × three significant figures), we round the final answer to two significant figures, resulting in 15 cm².