Areas of Circles, Sectors and Segments Lesson 11.6
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Areas of Circles, Areas of Circles, Sectors and Segments Sectors and Segments Lesson 11.6 Lesson 11.6
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Areas of Circles, Sectors and Segments Lesson 11.6. As you remember, the area of a circle is. A = r 2. Definition of the Area of a Sector: a region bound by 2 radii and an arc. H. Sector HOP. O. P. O. Theorem108 : A sec = ( mHP) r 2. 360. - PowerPoint PPT Presentation
Transcript of Areas of Circles, Sectors and Segments Lesson 11.6
Areas of Circles, Sectors Areas of Circles, Sectors and Segmentsand Segments
Lesson 11.6Lesson 11.6
A = r2
Definition of the Area of a Sector: a region bound by 2 radii and an arc.
O
H
OP
Sector HOP
As you remember, the area of a circle is
Theorem108: A sec = (mHP) r2
360
Where r is the radius and the arc HP is measured in degrees.
Find the area, leave in terms of .
12m60º
A = 60π(122) 360A = 24π m2
Area of a segment: a segment is a region bound by a chord and its corresponding arc.
X
YZ
The area of a segment is equal to the area of the sector - the area of the triangle.
X
YZ
Given arc XY is 90º and ZX = 8
Find the shaded area.Segment = sector – triangle
= 90π(82) – ½(8)(8) 360
= 16π – 32 units2
