Figure 1-13.-Segment and sector of a circle,
A sector is a part of a circle bounded by two
radii and their intercepted arc. The formula for
its area is
where r and n have the same designation as above.
Area of Regular Polygons
Figure 1-14 is a regular polygon. In any regular
polygon, the area is equal to one-half the
perimeter of the polygon times the radius of the
inscribed circle. This is expressed in formula form
as follows:
You can verify the above formula by dividing
the polygon into equal triangles with the sides as
their bases and with r as their altitudes; if you
multiply the areas of the individual triangles
by the number of sides in the polygon, you will
arrive at the above formula.
Area of an Ellipse
The derivation of an
section and methods of
ellipse from a conic
drawing ellipses are
Figure 1-14.-Regular polygon.
explained in chapter 3. An ellipse is shown in
figure 1-15, The longer axis, AB, is called the
major axis, and the shorter axis, CD, the minor
axis. Call the length of the major axis a and that
of the minor axis b. The area equals the product
of half the major axis times half the minor axis
times n. In formula form, it is stated as
1-13
Figure 1-15.-Ellipse.
