Final answer:
To calculate the area of a sector of a circle with a given arc length, additional information such as the radius or central angle is required. Without this, the appropriate answer cannot be determined.
Step-by-step explanation:
To find the area of a sector of a circle when the arc length is given, we must know the radius of the circle or the central angle of the sector. The area A of a sector can be calculated using the formula:
A = (θ/360) × πr²
where θ is the central angle in degrees and r is the radius of the circle. Since the arc length is known to be 6 meters but the radius or central angle is not provided, additional information is needed to determine the area. Without this information, it is impossible to correctly answer the question provided. The correct process involves using a calculator to determine the area to an appropriate number of significant figures based on the precision of the given measurements, such as when calculating the area of a circle using the formula A = πr². It's also important to remember that the area should be expressed in square units, such as m².