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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