This document defines sectors and segments of a circle, and provides formulas to calculate the area of sectors and segments as well as the length of arcs. It gives examples of using these formulas, such as calculating the area of a sector with a central angle of 90 degrees and radius of 6 cm, and the length of an arc with a central angle of 45 degrees and radius of 6 cm. Students are assigned problems applying these formulas, such as finding the area of a sector and arc length.

1. Areas of Circles, Sectors
and Segments
Lesson 11.6

2. H
O
Sector of a Circle
Is a region bounded by an arc of a circle and the two
radii to the end endpoints of the arc.

3. O
10 cm

4. O
6 in

5. O
Segment of a Circle
Is a region bounded by an arc and its chord.

6. Area of a segment: is equal to the
area of the sector - the area of the
triangle.
If arc PQ = 90 and the radius of
the circle is 5 cm.
5cm
90

7. Example:
Solve for the shaded region –
sin 60 = 0.8660

8. Arc Length – The distance that runs
through the curved line of the circle
making up the arc.

9. An arc of a circle measures 45
degrees. If the radius of the circle is
6cm, what is the length of the arc.
45
6cm

10. Central angle BEA = 90 degrees and
the radius is 6cm, what is the length
of the arc intercepted by the angle.
90

11. Assignment:
1. Find the area of a sector and the
arc length.
2. Find the are of the segment and the
arc length
Sin100 = 0.9848