Aim #13: How do we compute the area of a segment of a circle CC Geometry H
and shaded areas?
T
Do Now: AZ BZ , radius ZB = 24 in.
1. Find the shaded area, nearest tenth.
2. Find the length of AB, nearest tenth.
A
Z
A
24
B
Z
24
B
1) Equilateral ΔGHI is inscribed in circle O, and chord GH is 12 feet long. The length
of the radius of circle O is
. Find the exact area of the shaded region.
G
O
I
J
H
A SEGMENT ("wedge") of a circle is the region bounded by a chord and an arc.
segment (shaded black)
O
Explain how to compute the area of a segment:
2) In a circle whose radius is 12 cm, find the exact area of a minor segment whose
o
arc has a central angle of 60 .
O
12
60o
B
A
3) In a circle whose radius is 6 in., find to the nearest square inch, the area of a
o
segment whose chord has an arc which measures 80 .
O
6
A
B
C
80
0
4) Find the shaded area (exact and to the nearest hundredth).
A
B
C
D
5) Find, to the nearest hundredth, the area of the shaded region.
6) ΔABC is an equilateral triangle with edge length 20 cm. D, E, and F are
midpoints of the sides. The vertices of the triangle are the centers of the circle
creating the arcs shown. Find the following, to the nearest hundredth:
a) Area of the sector with center A
b) Area of ΔABC
7) Find, to the nearest hundredth, the shaded area. The diameter of the larger
circle is 10 cm. and the diameter of the smaller circle is 7.6 cm.
8) Find, to the nearest hundredth, the shaded area.
2 cm
6 cm
620
Name: ____________________
Date: ______
CC Geometry 10H
HW #13
1. Find, to one decimal place, the area of the shaded region.
2. Find, to one decimal place, the area of the shaded region. The radius is 2 units.
3. Find, to the nearest hundredth, the shaded area.
620
Review
4. BH is tangent to circle A. DF is a diameter. Find the angle measurements.
a) m≮BCD =
b) m≮BAF =
c) m≮BDA =
d) m≮FBH =
e) m≮BGF =
o
5. DC || BA. If the m≮DCB = 35 , find the m≮BOA.
0
0
6. If line P ll line L, AB ll DF, ≮LFE = 50 , and ≮ABC = 88 , find m≮DCE.
D
P
A
C
E
B
L
F
7. Describe what rigid motions, using proper notation, map ΔACD onto ΔGFH.
E
B
C
A
H
F
D
G