Final answer:
Without specific details about the shape in question, it is not possible to determine if the statement regarding its area being approximately 86.2 cm² is true or false. However, general principles such as vector component relationships, the Pythagorean theorem, and calculations involving significant figures have been explained with examples.
Step-by-step explanation:
To determine if the statement 'The area of the shape is approximately 86.2 cm²' is true or false, we need more information about the shape itself. However, we can go through a few examples based on given formulas and principles that may be relevant.
Vector components creating a right-angle triangle is true, as the x and y components of a vector can indeed be perpendicular to each other, forming a right-angle triangle.
The use of the Pythagorean theorem to calculate the length of the resultant vector when adding two vectors at right angles to each other is also true. For instance, if a vector with x-component of 3 cm and y-component of 4 cm are added together, the resultant vector would have a length of 5 cm, as calculated by the Pythagorean theorem (3² + 4² = 5²).
When dealing with significant figures in multiplication, such as 0.6238 cm x 6.6 cm, which equals 4.11708 cm², the answer should be rounded to the least number of significant figures in any of the numbers used in the calculation. In this case, that would be two significant figures, so the area would be 4.1 cm².
To calculate the volume of a rectangular box with sides of 1.80 cm, 2.05 cm, and 3.1 cm, one would multiply these dimensions together. The volume would be approximately 1.80 cm x 2.05 cm x 3.1 cm = 11.451 cm³, which rounds to 11.4 cm³ when considering significant figures and measurement accuracy.