Which process involves subtracting the area of a triangle from the area of a sector?

To understand why the correct answer is finding the area of a segment of a circle, it’s important to look at the definitions of the terms involved.

A segment of a circle is the region enclosed by a chord (a line segment whose endpoints lie on the circle) and the arc connecting the endpoints of the chord. To find the area of this segment, you typically start by calculating the area of the sector formed by the two radii that extend to the points on the circumference. This sector is a "pie slice" of the circle, representing a portion of the whole circle.

Once you have the area of the sector, subtracting the area of the triangle formed by the two radii and the chord gives you the area of the segment. By removing the triangular area, which is not part of the segment, you isolate the toroidal or curvilinear area that is indeed the segment of the circle.

None of the other processes listed involve this specific subtraction of a triangle's area from a sector's area. Calculating the area of a rectangle or measuring the perimeter of a circle are different geometric concepts that do not apply in this context, and calculating the area of a triangle involves only that shape without any relation to circular segments. Thus, the