Transcript 10.7 Areas of Circles and Sectors • The area of a circle is the product of pi and the square of the.

10.7 Areas of Circles and Sectors
• The area of a circle is the product of pi and the
square of the radius.
A r
2
Finding the Area of a Circle
• The diameter of the circular region on the wrestling
mat is 32 feet. What is the area?
A r
2
A   (16)
2
A  256
 804.2477193
 804 ft.
2
Sector of a Circle
• A sector of a circle is a region bounded by an arc of
the circle and the two radii to the arc’s endpoints.
– You name a sector using one arc endpoint, the center of
the circle, and the other arc endpoint.
Area of a Sector of a Circle
• The area of a sector of a circle is the product of the
radio measure of the arc : 360 and the area of the
circle.
Finding the Area of a Sector of a Circle
• What is the area of sector GPH? Leave your answer
in terms of pi.
mGH
2
areaof sec torGPH 
 r
360
72
2

  (15)
360
 45 cm
2
Segment of a Circle
• A part of a circle bounded by an arc and the
segment joining its endpoints is a segment of
a circle.
• To find the area of a segment for a minor arc,
draw radii to form a sector.
• The area of the segment equals the area of
the sector minus the area of the triangle
formed.
Finding the Area of a Segment of a
Circle
• What is the area of the shaded segment
shown? Round your answer to the nearest
tenth.
Finding the Area of a Segment of a Circle
mAB
Areaof sec torACB 
 r 2
360
60
2

  (18)
360
 54 areaofshadedsegment  54  81 3
1
areaof ABC  bh
2
1
 (18)(9 3)
2
 81 3
 29.34988788
 29.3in.
2
More Practice!!!!!
• Homework – Textbook p. 663 – 664 # 7 – 25
ALL.