|
Let's review what we know about the
area of circles and sectors.
|
 |
Area
(circle)
 |
|
Area of sectors of
circle
(Sectors are similar to
"pizza pie slices" of a circle.) |
|
Semi-circle
(half of circle = half of area)
|
Quarter-Circle
(1/4 of circle = 1/4 of area)
 |
Any Sector
(fractional part of the area)
|
where n is the
number of degrees in the central angle
of the sector. |
where CS is
the arc length of the sector. |
|
|
Notice that when finding the area
of a sector, you are actually finding a
fractional part of the area of the entire
circle. The fraction is determined by the
ratio of the central angle of the sector to the
"entire central angle" of 360 degrees, or by the
ratio of the arc length to the entire
circumference. The second formula can be
algebraically reduced, but it is easier to
remember that you are dealing with fractional
parts. |
|
EXAMPLE:
Find the area of a sector with a
central angle of 60 degrees and a radius
of 10. Express answer to the
nearest tenth.
 |
Solution:
 |
|
EXAMPLE:
Find the area of a sector with an arc length
of 40 cm and a radius of 12 cm.
Solution:
 |
|
Now, let's expand our investigation to a new section of the circle.
|
 |
Segment of a
Circle
While a sector looks like a "pie"
slice, a segment
looks like the "pie" slice with the triangular
portion cut off. The segment is only the small
curved figure left when the triangle is removed. |
| Definition:
The segment of a
circle is the region bounded by a chord and the arc
subtended by the chord. |
 |
Finding the Area of a
Segment of a Circle:
Dealing with the area of a segment is very
similar to working with the area of a sector. Let's
look at an example problem.
 |
|
square
units