Final answer:
The area of a rectangle with sides 2.44 cm and 6.077 cm is approximately 14.8 cm² when rounded to three significant figures. For a triangle with a base of 1.007 m and a height of 0.665 m, the area is approximately 3347 cm² after converting to centimeters and rounding to four significant figures.
correct option is a 15 cm²
Step-by-step explanation:
Calculating the area of a figure or a shape typically requires using specific formulas. For example, the area of a rectangle is found by multiplying the length of one side by the length of the other side.
Let's apply this approach to the provided example: a rectangle whose sides are 2.44 cm × 6.077 cm. To find the area, multiply these two sides together:
2.44 cm × 6.077 cm = 14.82788 cm²
When expressing this result in significant figures, we should consider the precision of the values we started with. The first number, 2.44 cm, has three significant figures, and the second number, 6.077 cm, has four significant figures. The product should therefore be rounded to the lowest number of significant figures, which is three in this case. Thus, after rounding, the area is approximately 14.8 cm².
When dealing with the area of a triangle, we use a different formula: area = 1/2 × base × height. With the base being 1.007 m (converted to 100.7 cm for consistency) and the height being 0.665 m (converted to 66.5 cm), the calculation would be:
Area = 1/2 × 100.7 cm × 66.5 cm = 3346.725 cm²
However, since the number of significant figures for both the base and height is four (1.007 m and 0.665 m respectively), we should round the result to four significant figures, resulting in an area of approximately 3347 cm².