Arc Length & Area of a Sector

7.4: Arc Length & Area of a Sector

Objective: Use proportional reasoning to find arc length and area of a sector

Arc Length

Ex 1: Find the length of the minor arc

Ex 2:

Multiple Choice

A central angle measures $$230\degree$$ and its radius is 6 cm. What is the length of the arc intercepted by the angle? 

• 12.o4 cm

• 144.51 cm

• 24.08 cm

• 72.26 cm

Multiple Choice

What is the radius of a circle that has a central angle of 230 degrees and an arc length of 60 miles.

• 6.10 miles

• 74.95 miles

• 29.89 miles

• 14.95 miles

Area of a Circle & Semicircle

Area of a Quarter-Circle

If I want to find the area of an part of a circle, how would I do it?

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Area of a Sector

Ex 1:

Ex. 2:

Multiple Choice

Find the area of a sector with a radius of 9ft and an angle measure of

$$132\degree$$  

• $$10.37\ ft^2$$  

• $$93.31\ ft^2$$  

• $$29.7\ ft^2$$  

• $$85\ ft^2$$  

Multiple Choice

Find the central angle of the sector of the circle with a radius of 12 ft, and a sector area of 72 square feet.

• $$12.75\degree$$  

• $$45\degree$$  

• $$57.30\degree$$  

• $$48.82\degree$$  

Fill in the Blanks