Arc Lengths and Areas of
Sectors
Lesson 11.6
Geometry Honors
Objective: Know and use the formulas
for Arc Lengths and Areas of Sectors.
Lesson Focus
This lesson shows how the length of an arc of
a circle and the area of a region or sector of a
circle can be calculated.
Basic Terms
Sector of a Circle
A region bounded by two radii and an arc of
the circle.
Arc Length
Arc Length
If the measure of minor arc AB = x°,
then the length of minor arc AB = (x°/360°)(2πr)
Do not confuse arc measure with
arc length.
Arc measure equals the measure
of the corresponding central
angel and is independent of the
size of the circle.
Arc length depends on the size
of the circle because it is a part
of the circumference of the
circle.
Area of a Sector
Area of a Sector
If the measure of minor arc AB = x°,
then the area of sector AOB = (x°/360)(πr2)
Except for special cases,
finding the area of a
region bounded by a
chord and its arc usually
requires the use of
trigonometry.
Practice
The radius of a circle is 3 cm.
Find (a) the lengths of the given arcs, and
(b) the areas of the sectors determined by the given
arcs.
1. 50°
2. 20°
3. 140°
Written Exercises
Problem Set 11.6, p.453: # 2 – 14 (even)
Handout: 11-6