To determine the area of a sector, which metric must be calculated first?

To determine the area of a sector, the angle in degrees is essential because the area calculation requires this specific information as part of the formula used. The area of a sector can be given by the formula:

[ \text{Area} = \frac{\theta}{360} \times \pi r^2 ]

where (\theta) is the angle of the sector in degrees and (r) is the radius of the circle. Without knowing the angle, you cannot determine what portion of the circle's area pertains to the sector, rendering calculations incomplete.

While the radius is also important to compute the area since it contributes directly to the overall size of the sector, the angle is the critical factor that defines the proportion of the circle you are considering. As a result, it is necessary to establish the angle before proceeding to use the radius in the sector area formula.