7.7 Areas of Circles and Sectors
Quick Review• What is the circumference of a circle?
• What is the area of a circle?
• The interior angle sum of a circle is ?
• What is the arc length formula?
2r
r2
360o
mA) B
3602r
mA) B
360C
Sector of a Circle
• Formula is very similar to arc length
• Notation is slightly different!- The center pt is used
when describing a sector. - The is not used for sectors.
How can we find area, based on what we already know?
mA) B
360r2Area of a sector =
1. Find the area of the shaded sector2. Find the arc length of the shaded sector.
Segmentany ideas of how to
find the shaded area?
Finding the Area of a Segment of a Circle
– =
Area of Sector
Area of Triangle
Area of Segment
minus equals
Find the area of segment RST to the nearest hundredth.
Use formula for area of sector.
Substitute 4 for r and 90 for m.
= 4π m2
Step 1 Find the area of sector RST.
Simplify.
Step 2 Find the area of ∆RST.
Continued
Find the area of segment RST to the nearest hundredth.
ST = 4 m, and RS = 4m.
= 8 m2
Step 3
area of segment = area of sector RST – area of ∆RST
4.57 m2
Find the area of segment RST to the nearest hundredth.
Continued
= 4π – 8
A segment of a circle
Find the area of segment LNM to the nearest hundredth.
Finding the Area of a Segment
Use formula for area of sector.
Substitute 9 for r and 120 for m.
= 27π cm2
Step 1 Find the area of sector LNM.
Find the area of segment LNM to the nearest hundredth.
Continued
Step 2 Find the area of ∆LNM. Draw altitude NO.
Find the area of segment LNM to the nearest hundredth.
Continued
Step 3
area of segment = area of sector LNM – area of ∆LNM
= 49.75 cm2
Find the area of the shaded portion
Find the area of the red portion Of the Tube Sign.
Find the shaded area with r = 2 , 4 , & 10
1cm3cm
5cm
What is the Area of theBlack part?
If you have 2 circles A and B that intersect at 2 points and the distance between the centers is 10. What is the area of the intersecting region?
A B
10
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