Name ______Module 5
Area of Sectors
Learning Target: I can calculate the area of a sector.
Opening Exercise
1. What is the area of a circle with radius 10 cm.
2. A circular pizza with a 12 inch diameter is cut into eight congruent pieces. What is the area of each slice?
Area of Sectors
Sector: Let AB be an arc of a circle with center O and radius r. The union of all segments OP, where P is any point of AB, is called a sector.
In the opening exercise we calculated the area of a circle with radius 10 cm. Now let’s calculate the area of a fraction of that circle.
a. What is the area of half of the circle? Write and explain the formula.
b. What is the area of a quarter of the circle? Write and explain the formula.
c. Make a conjecture about how to determine the area of a sector defined by an arc measuring 60°.
d. Circle O has a minor arc AB with an angle measure of 60°. Sector AOB has an area of 24π. What is the radius of circle O?
The area of a sector defined by an arc of angle measure x° on a circle of radius r is
x360πr2.
1. Find the area of sector POQ.
2. The area of sector AOB in the following image is 28π. Find the measurement of the central angle
labeled x°.
Asegmentof a circle is the region bounded by a chord and the arc subtended by the chord.
3. Find the area of the shaded segment in circle C.
Name ______Module 5
Area of Sectors Problem Set
1. Find the area of a sector of a circle with a central angle of 120 degrees and a radius of 8.
2. In the diagram below of circle O, diameter AB and radii OC and OD are drawn. The length of AB is
12 and the measure of ∠COD is 20 degrees. If AC=BD, find the area of sector BOD in terms of π.
3. The circle below has a radius of 2. A chord is drawn that intercepts an arc that measures 90°.
Determine the area of the shaded region.
4. Determine the area of sector CD.
5. Find the area of the shaded region (round to the nearest hundredth).
6. Find the area of the entire circle given the area of the sector.
Name ______Module 5
Area of Sectors Exit Ticket
1. Find the area of sector OR of Circle O.
2. Find the area of the shaded segment if the radius is 5.