What the formulae are doing is taking the area of the whole circle, and then taking a fraction of that depending on what fraction of the circle the sector fills. So for example, if the central angle was 90°, then the sector would have an area equal to one quarter of the whole circle.
where:
C is the central angle in
degrees
r is the radius of the circle of which the sector is part.
π is Pi, approximately 3.142
where:
L is the arc length.
R is the radius of the circle of which the sector is part.
Similarly below, the arc length is half the circumference, and the area id half the total circle.
You can experiment with other proportions in the applet at the top of the page.