The area of the segment of a semi-circle depends on its specific shape, i.e., the proportion it occupies within the entire semi-circle. Calculating the area of a segment usually requires considering the size of the central angle. Assuming the central angle of the segment is θ (in radians) and the radius is R, the area S of the segment can be calculated using the following formula:

S = (θ / 2π) * π * R^2 – (1 / 2) * R^2 * sin(θ)

This formula consists of two parts:

(θ / 2π) * π * R^2: This represents the area of the sector (the circular part that contains the segment), where θ is the central angle of the sector.
(1 / 2) * R^2 * sin(θ): This is the area of the triangle within the sector, formed by the center of the circle and the two endpoints of the segment.

When θ = π (i.e., 180 degrees), the segment becomes a semi-circle, and the segment area formula simplifies to the semi-circle area formula: S = 1/2 * π * R^2.

If the central angle of the segment is not 180 degrees, then the above formula needs to be used to calculate the segment area. In practical applications, once the central angle and radius of the segment are known, this formula can be used to calculate the area of the segment.