To determine whether the statement is true or false, let's first review the concept of the area of a sector.
A circle has an area which can be calculated using the formula:
[tex]\[ \text{Area of a circle} = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
A sector of a circle is a portion of the circle defined by two radii and the included arc. The area of a sector is a fraction of the total area of the circle. This fraction is determined by the central angle [tex]\( \theta \)[/tex] (in degrees) of the sector relative to the total 360 degrees of the circle.
The formula to find the area of a sector is:
[tex]\[ \text{Area of a sector} = \frac{\theta}{360} \times \pi r^2 \][/tex]
This shows that the area of the sector is indeed the product of the area of the circle and the fraction [tex]\(\frac{\theta}{360}\)[/tex], which represents the part of the circle covered by the sector.
Given the explanation, we see that the statement is correct.
The area of a sector is the area of the circle multiplied by the fraction of the circle covered by that sector.
Therefore, the correct answer is:
A. True
