Academic AAG
Unit 7 – Circles
Name & Date
Vocabulary and Formulas for Circles:
Definition of a Circle:
What is  ?
Radius:
Diameter:
Chord:
Tangent Line:
Circumference:
Arc Length:
Area:
Sector Area:
Directions: Consider C to answer the following questions.
1) Find the circumference of the circle.
Exact:
Approximate:
2) Find the area of the circle.
Exact:
Approximate:
.
3) Find the length of AB
.
4) Find the area of the sector bound by AC , BC , and AB
.
5) Find the length of AD
.
6) Find the area of the sector bound by AC , DC , and AD
 is approximately 40cm, what is mDE
?
7) If the length of DE
Academic AAG
Name & Date
Unit 7 – Circles
Directions: Consider A with radius 10ft to answer the following questions.
8) Find the area and circumference of the circle.
Area:
C
B
Circumference:
.
9) Find the length of BC
60°
A
Exactly:
Approximately:
.
10) Find the area of the sector bound by AB , AC , and BC
Exactly:
D
Approximately:
 is 40 , find mCD
 to the nearest degree.
11) If the area of the sector bound by AD , AC , and CD

mCD
 and use this information to find the length of BD
 and the area of the sector bound by
12) Find mBD
.
AD , AB , and BD

mBD

BD
Sector Area =
13) A CD with a diameter of 12cm is packed in a square case which measures 13cm along a side. How much
space is around the CD?
14) A rectangular pool is 24 feet wide and 30 feet long. It is surrounded by a walk that is 2 feet wide, as
shown below.
A) What is the outer perimeter of the walkway?
B) What is the area of the walkway?
15) RSTU is a square with a side length of 18 units. A semicircle is placed so its diameter lies along one side of
the square and is equal in length to the side of the square. To the nearest tenth of a unit, what is the area of
the shaded region?
16) The sketch below shows three circular disks cut from a rectangular sheet of metal. Explain how you can
tell the sketch is labeled incorrectly. How do you think the sketch should be labeled? Using your labels,
calculate the amount of metal that is wasted.
Academic AAG
Unit 7 – Circles
Name & Date
17) Consider the circle below with center O (circle O).
A
A) Find the area and circumference of the circle.
D
.
C B) Find the length of AC
70°
O
5 inches
.
C) Find the area of the sector bound by AO , CO , and AC
D) Find the area of AOC .
E) Find the area of the shaded region.
18) Find the area of the shaded region in L below.
A) Find the area and circumference of the circle.
L
D
.
B) Find the length of DP
75°
12
P
.
C) Find the area of the sector bound by LD , LP , and DP
D) Find the area of LDP .
E) Find the area of the shaded region.
Academic AAG
Unit 7 – Circles
Name & Date
22) ABCDE is a regular pentagon with side length 6 yards. The circle that circumscribes ABCDE has a center
at point O.
B
A) m AOB 
B) m ABC 
C) Area (ABO ) 
A
C
O
D) Area (Pentagon ) 
D
E) Area (O ) 
F) Find the area of the space between the pentagon and the circle.
G) Find the area of one of the regions that is outside the pentagon but inside the circle.
H) Circumference (O ) 

I) AB
=
J) ABC
E
23) The figure below is a regular polygon with a side length of 18 in, inscribed in a circle. Find the area of the
shaded region.
24) The figure below is a regular polygon inscribed in a circle with a radius of 10 cm. Find the approximate area
of the shaded region rounded to the nearest tenth.
Academic AAG
Unit 7 – Circles
Name & Date
22) The figure below is a regular polygon with perimeter 180 cm, inscribed in a circle.
A) Find the area of the region between the polygon and the circle.
F
G
E
H
D
O
I
C
A
.
B) Find the length of ABC

C) What is the area of the sector bound by GO , DO , and GFED ?
B
1

23) In the figure below, the length of arc BC is
the circumference of a circle with center A and AB = 6.
9
What is the m A and the area of the sector of the circle show below?
B
A
C
24) Consider the figure below, where CF / /DE and DF = 7.1cm to complete the following.
A(CDEF ) 
A
A(ACF ) 
B
A(B ) 
32°
F
C
24°
D
E