Section 2.2 Solutions
Homework #1-4: Find the circumference of each circle. Make sure to include the proper units
in your answer. Leave your answer in terms of 𝜋.
1)
𝐶 = 2𝜋𝑟
C = 2𝜋(14𝑚)
Answer: 28𝜋 m
3)
C = 𝜋𝑑
Answer: 16𝜋 𝑐𝑚
5)
P = 2(8cm + 4cm)
P = 2(12 cm)
Answer: 24 cm
7) Assume opposite sides have equal lengths.
Don’t include the 3 cm when finding the
perimeter. It is the height, and not one of
the sides.
P = 4 cm + 4 cm + 10 cm + 10 cm
P = 28 cm
9)
P = 124 ft + 156 ft + 156 ft
Answer: 436 ft
11)
P = 5 in + 8 in + 3 in + 4 in
Answer: 20 in
Homework: #13 – 24 Find the area of each figure. Use appropriate units.
13) Assume the lengths are in inches.
Area =
(25𝑖𝑛)(18𝑖𝑛)
2
Area = 225 in2
15)
Area =
(10𝑚)(14𝑚)
2
Answer: 70m2
17) Find “a”, then find the area of the
triangle. Assume lengths are given in inches.
a2 + 242 = 252
a2 + 576 = 625
a2 = 49
a = 7 in
Area =
(24𝑖𝑛)(7𝑖𝑛)
2
Area = 84 in2
19) Find “t”, then find the area of the
triangle. Assume lengths are given in
centimeters.
t2 + 122 = 132
t2 + 144 = 169
t2 = 25
t=5
Area =
(12𝑐𝑚)(5𝑐𝑚)
2
Answer: 30 cm2
21)
Area = (3cm)(10cm)
Answer: 30 cm2
23)
A = (10.3 cm)(6.2 cm)
Answer: 63.86 cm2
25).
Area =
(13.4 𝑚+7.2𝑚)(10.6𝑚)
2
Area= 128.26 m2
27)
Area =
(20 𝑐𝑚+6𝑐𝑚)(10𝑐𝑛)
2
Area = (260 cm2)/2
Answer: 130 cm2
29)
Area =
(3𝑚+6𝑚)(4𝑚)
2
Area = (36m2)/2
Answer: 18 m2
31)
A = (9cm)(16cm)
Answer: 144 cm2
33) Assume units are given in inches.
A = (8 in)2
Answer: 64 in2
35)
A = 𝜋(4𝑐𝑚)2
Answer: 16𝜋 𝑐𝑚2
37)
Diameter = 6”
radius = 3”
A = 𝜋(3")2
Answer: 9𝜋 𝑠𝑞𝑢𝑎𝑟𝑒 𝑖𝑛𝑐ℎ𝑒𝑠
39)
Radius = 8 cm
A = 𝜋(8𝑐𝑚)2
Answer: 64𝜋 cm2
Homework #41-56: Find the area of the shaded region. Use appropriate units.
41) use 3.14 for 𝜋
First calculate the area as if the entire shape
was shaded.
Area if entire shape was shaded:
Area all shaded = (18cm)(12cm) = 216 cm2
Next find the area of the unshaded region.
Area unshaded = 3.14(4cm)2 = 50.24 cm2
Finally subtract the results.
Answer: 216 cm2 – 50.24 cm2 = 165.76 cm2
43) Leave your answer in terms of 𝜋.
Assume measurements are given in feet.
First calculate the area as if the entire shape
was shaded.
Area all shaded = 𝜋(10𝑓𝑡)2 = 100𝜋 𝑓𝑡 2
Next find the area of the unshaded region.
Area unshaded = 𝜋(5𝑓𝑡)2 = 25𝜋 𝑓𝑡 2
Finally subtract the amounts.
Answer: 100𝜋 𝑓𝑡 2 − 25𝜋 𝑓𝑡 2 = 75𝜋 𝑓𝑡 2
45) Use 3.14 for 𝜋. Assume measurements
are given in meters.
First calculate the area as if the entire shape
was shaded.
Area if entire shape was shaded:
This is a circle with radius 5 m.
Area all shaded = 3.14(5m)2 = 78.5 m2
Next find the area of the unshaded region.
Area unshaded = (7m)2 = 49 m2
Finally subtract the amounts.
Answer: 78.5 m2 – 49 m2 = 29.5 m2
47) Find the length of the diagonal “d”
rounded to 2 decimals. Use “d” to find the
radius. Round the radius to 2 decimals.
Then find the shaded area. Use 3.14 for 𝜋.
Assume measurements are given in meters
I need to use the Pythagorean theorem to
find the length of the diagonal.
22 + 22 = c2
8 = c2
Diagonal = 2.83 m
Divide by two to get the radius
Radius = 1.42 m
First calculate the area as if the entire shape
was shaded.
Area all shaded = 3.14(1.42 m)2 = 6.33 m2
Next find the area of the unshaded region.
Area unshaded = (2m)2 = 4m2
Now subtract
Shaded area = 6.33m2 – 4 m2
Answer: 2.33 m 2
49)
First calculate the area as if the entire shape
was shaded.
Area all shaded = (15mm)2 = 225mm2
Next find the area of the unshaded region.
Area unshaded = (5mm)2 = 25mm2
Finally subtract the results
Answer: 225 mm2 – 25 mm2 = 200 mm2
51)
First calculate the area as if the entire shape
was shaded.
Area all shaded = (30cm)(15cm)= 450 cm2
Next find the area of the unshaded region.
Area unshaded = (11cm)(22cm) = 242 cm2
Finally subtract the amounts
Answer: 450 cm2 – 242 cm2 = 208 cm2
53) Use 3.14 for 𝜋. Assume lengths are given First calculate the area as if the entire shape
in centimeters. Round your answer to 2
was shaded.
decimals.
The entire shape is a square that measures
12 cm on each side.
Area all shaded = (12cm)2 = 144cm2
Next find the area of the unshaded region.
If we put the unshaded region together we
get a circle of radius of 6 cm.
Area unshaded = 3.14(6cm)2 = 113.04 cm2
Finally subtract the amounts.
Answer: 144 cm2 – 113.04 cm2 = 30.96 cm2