Read all directions carefully. Circle or box all final answers.
Finding the Area of a Sector of a Circle
From Geometry it is known that the area of a sector of a circle is proportional to the
measure of the central angle. Consider the circle to the right to explore this.
1. Let the central angle be the entire circle or 2 radians. What is the area of this sector, which represents the area of the whole circle, or ___________?
2. Using proportions yields: 2 area of a sector
r= and solving the equation
for the area of a sector gives the equation, area of a sector =
Area of a Sector Theorem: The area A of the sector of a circle of radius r formed by a central
angle of θ radians is: A = area of a sector =
1. Find the area of the sector of a circle of radius 5 feet formed by an angle of 40°. Round the answer to two decimal places, if necessary.
2. Find the area of the sector of a circle of radius 3 𝑐𝑚 formed by an angle of 𝜃 = 2. Round your answer to two decimal places, if necessary.
3. Find the length of arc 𝑠 cut off by 𝜃, if 𝜃 = 𝜋
6 and 𝑟 = 12 𝑐𝑚. Round your answer to two
decimal places. In addition, draw a picture of this calculation.
Math 347 – Skills for Trigonometry
Worksheet – Area of a Sector
- Read all directions carefully. Circle or box all final answers.
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