Chapter 12 Geometry

Solve.

1. / How many degrees are in one half
of a revolution? / 2. / Find the supplement of a 116° angle. / 1.
2. / ______
______
3. / Find the complement of a 75° angle. / 4. / Find the complement of a 128° angle. / 3.
4. / ______
______
5. / Find the supplement of a 128° angle. / 6. / Find the complement of a 49° angle. / 5.
6. / ______
______
7. / Find the complement of a 66° angle. / 8. / Find the supplement of a 138° angle. / 7.
8. / ______
______
9. / Find the supplement of a 42° angle. / 10. / Find the complement of a 12° angle. / 9.
10. / ______
______
11. / Find the complement of a 81° angle. / 12. / Find the supplement of a 171° angle. / 11.
12. / ______
______

Solve.

1. / A triangle has a 34° angle and a 83°
angle. Find the measure of the other
angle. / 2. / A triangle has a 103° angle and a
24° angle. Find the measure of the
other angle. / 1.
2. / ______
______
9. / Find the radius of a circle with a
diameter of 18 in. / 10. / Find the diameter of a circle with
a radius of 38 cm. / 9.
10. / ______
______
11. / The radius of a sphere is 2.7 cm.
Find the diameter. / 12. / The radius of sphere is ft.
Find the diameter. / 11.
12. / ______
______

Find the measures of angles a and b.

1. / a
b 76° / 2. / a
b 48° / 1.
2. / ______
______
3. /
b a
90° / 4. / b
a 10° / 3.
4. / ______
______

Find the measures of angles a and b.

5. / t
35°
a
b
/ 6. / t
142° a
b
/ 5.
6. / ______
______
7. / t
76°
a b / 8. / t
a
27° b / 7.
8. / ______
______

Find the perimeter. Use 3.14 for p.

1. / 21 cm
6 cm
11 cm
10 cm
30 cm / 2. / ft
ft ft
ft ft
ft / 1.
2. / ______
______
3. /
10 m
18 m / 4. / 14.6 m
13.6 m 13.5 m
12.4 m 14.1 m
23.6 m / 3.
4. / ______
______
5. /
25 cm 24 cm / 6. / 20 m
8 m
20 m / 5.
6. / ______
______
7. /
2 ft 3 ft / 8. / ft
ft
12 ft
ft
ft / 7.
8. / ______
______

Solve.

1. / Find the number of feet of fence
needed to fence a park that is mi
long and mi wide. / 2. / A horse trainer is planning to enclose
a circular exercise area. How much
fencing is needed if it has a diameter
of 80 ft. Use 3.14 for p. / 1.
2. / ______
______
3. / An irrigation system waters a circular
field, which has a 60-foot radius. Find
the distance around the outside edge
of the field. Use 3.14 for p. / 4. / Find the length of weather stripping
needed to put around a rectangular
window that is 9 ft high and 22 ft long. / 3.
4. / ______
______
5. / Find the length of aluminum framing
needed to frame a picture that is 6 ft
by 4 ft. / 6. / Find the length of a rubber gasket
needed to fit around a circular
porthole that has a 16 in. diameter.
Use 3.14 for p. / 5.
6. / ______
______
7. / A rain gutter is being installed on a
home has the dimensions shown
below. At $9.10 per meter, how much
does it cost to install the rain gutter?
20 m
12 m 10 m 12 m
6 m 6 m / 8. / A metal frame is being built to
install around a rectangular sign
which is 2 m wide and 3.5 m long.
At $2.12 per meter, find the cost of
the frame. / 7.
8. / ______
______
9. / A security fence is to be built around
a factory. The lot on which the factory
is located is 1000 ft by 500 ft. If the
fencing costs $3.25 per foot, what is
the total cost of installing the fence? / 10. / The dimensions of a rectangular
classroom are 30 ft by 24 ft. At
$1.10 per foot, how much does it
cost to purchase an outlet strip to
go around the room? Subtract 3 ft
for a doorway. / 9.
10. / ______
______

Solve.

1. / Find the area of a triangle with a base
of 8 ft and a height of ft. / 2. / Find the area of a right triangle with a
base of 11 cm and a height of 6.4 cm. / 1.
2. / ______
______
3. / Find the area of a square with a side
of 7 ft. / 4. / Find the area of a square with a side
of 29 cm. / 3.
4. / ______
______
5. / Find the area of a rectangle with a
length of 52 cm and a width of 27 cm. / 6. / Find the area of a rectangle with a
length of 25 in. and a width of 13 in. / 5.
6. / ______
______
7. / Find the area of a circle with a radius
of 11 in. Use 3.14 for p. / 8. / Find the area of a square with a side
of 7.8 cm. / 7.
8. / ______
______
9. / Find the area of a triangle with a base
of 27 cm and a height of 30 cm. / 10. / Find the area of a rectangle with a
length of 39 cm and a width of 25 cm. / 9.
10. / ______
______

Find the area. Use 3.14 for p.

1. / 16 m
5 m
4m 4m / 2. / 5 ft
10 ft
25 ft / 1.
2. / ______
______
3. /
6 cm
18 cm / 4. /
Radius = 10 cm / 3.
4. / ______
______
5. / 20 m
8 m
20 m / 6. / 20 ft
16 ft
14 ft
20 ft / 5.
6. / ______
______
7. /
2 ft 3 ft / 8. / 14 cm
24 cm
24 cm / 7.
8. / ______
______

Solve.

1. / Find the area of a circular rug that is
18 ft. in diameter. / 2. / Find the area of a circular portrait
that has a 24 in. diameter. / 1.
2. / ______
______
3. / A circular skating rink has a 144-foot
radius. Find the area of the surface of
the ice rink. / 4. / Find the area of a rectangular park
that is 300 m long and 180 m wide. / 3.
4. / ______
______
5. / Find the area of a concrete driveway
with the following measurements.
58 ft
24 ft 15 ft
28 ft / 6. / A carpet is to be placed in two rooms
as shown in the diagram. At $17.50
per square meter, how much will it cost
to carpet the area?
6 m 40 cm
4 m 80 cm
4 m 3 m
80 cm 60 cm
11m 20 cm / 5.
6. / ______
______
7. / How many square yards of carpet are
needed to cover the indoor arena?
90 ft
200 ft / 8. / Find the area of the 3-meter boundary
around the swimming pool.
25 m
3 m
12 m / 7.
8. / ______
______

Solve.

1. / Find the volume of a cylinder with a
radius of 10 cm and a height of 21 cm.
Use for p. / 2. / Find the volume of a cylinder with a
radius of 22 cm and a height of 35 cm.
Use for p. / 1.
2. / ______
______
3. / Find the volume of a cube with a side
of 5 ft 3 in. Round to the nearest
hundredth. / 4. / Find the volume of a cube with a side
of 22 cm. / 3.
4. / ______
______
5. / Find the volume of a cube with a side
of 6 ft 4 in. Round to the nearest
hundredth. / 6. / Find the volume of a sphere with a
radius of 6 mm. Use 3.14 for p. Round
to the nearest hundredth. / 5.
6. / ______
______
7. / Find the volume of a sphere with a
radius of 12 cm. Use 3.14 for p. Round
to the nearest hundredth. / 8. / Find the volume of a sphere with a
radius of 1.4 mm. Use 3.14 for p.
Round to the nearest hundredth. / 7.
8. / ______
______
9. / Find the volume of a rectangular solid
with a length of 2 m 24 cm, and a
width of 75 cm, and a height of 50 cm. / 10. / Find the volume of a rectangular
solid with a length of 5 m, and width
of 240 cm, and a height of 150 cm. / 9.
10. / ______
______

Find the volume. Write measurements involving two units in terms of the larger unit before working the problem. Use 3.14 for p.

1. /
2 ft
4 ft / 2. /
12 in. 4 in.
6 in. / 1.
2. / ______
______
3. /
10 in.
12 in.
24 in. / 4. /
20 cm
8 cm
60 cm
2 m 30 cm / 3.
4. / ______
______
5. /
3 in.
1.5 in.
6 in.
3 in. 18 in. / 6. /
20 cm
45 cm / 5.
6. / ______
______

Solve.

1. / A propane gas storage tank, which is
in the shape of a cylinder, is 10 m
high and has a 6-meter diameter. Find
the volume of the gas storage tank.
Use 3.14 for p. / 2. / A silo, which is the shape of a
cylinder, is 27 ft in diameter and has
a height of 48 ft. Find the volume of
the silo. Use 3.14 for p. / 1.
2. / ______
______
3. / Find the volume of a spherical oxygen
tank that is 9 m in diameter. Use 3.14
for p. Round to the nearest tenth. / 4. / Find the volume of a spherical water
tank that is 18 ft in diameter. Use 3.14
for p. Round to the nearest hundredth. / 3.
4. / ______
______
5. / Find the volume of a railroad car that
is 16 m long, 5 m wide, and 5.2 m high. / 6. / A hole is being dug for installing a
swimming pool. The hole is 24 ft long,
12 ft wide, and 8 ft deep. Find the
volume of the hole. / 5.
6. / ______
______
7. / How many gallons of water will fill a
fish tank that is 24 in. long, 12 in.
wide, and 10 in. high? Round to the
nearest tenth. (1 gal = 231 in.3) / 8. / How many gallons of water will fill
an aquarium that is 10 in. wide, 18 in.
high, and 8 in. long? (1 gal = 231 in.3) / 7.
8. / ______
______
9. / Find the volume of the concrete
needed to build the steps.
ft
2 ft ft
5 ft
4 ft / 10. / The floor of a building is shown
below. The concrete floor is 6 in.
thick. Find the cost of the floor at
$2.50 per cubic foot.
60 ft
40 ft
70 ft / 9.
10. / ______
______

12

Find the square root. Round to the nearest thousandth.

1. / 5 / 2. / 17 / 3. / 19 / 1.
2.
3. / ______
______
______
7. / 35 / 8. / 46 / 9. / 52 / 7.
8.
9. / ______
______
______
16. / 86 / 17. / 89 / 18. / 92 / 16.
17.
18. / ______
______
______

Find the unknown side of the triangle. Round to the nearest hundredth.

1. /
6 in.
8 in. / 2. /
14 cm
12 cm / 1.
2. / ______
______
3. /
10 cm
8 cm / 4. /
30 cm
27 cm / 3.
4. / ______
______
5. /
18 ft
12 ft / 6. /
20 cm
15 cm / 5.
6. / ______
______

Solve. Round to the nearest thousandth.

1. / A guy wire holds a television antenna
in place. Find the distance along the
ground from the base of the antenna
to the guy wire.
30 m
16 m / 2. / Find the length of a ramp used to
move a forklift from the ground to
the loading ramp.
4 ft
9 ft / 1.
2. / ______
______
3. / A car is driven 24 mi west and then
10 mi north. How far is the car from
the starting point?
10 mi
24 mi / 4. / Find the distance around the hiking
trail.
6 km
8 km / 3.
4. / ______
______
5. / Find the distance between the
center of the holds in the metal plate.
4 in.
7 in. / 6. / Find the length of the rafters for
the building shown.
3 ft
14 ft
2 ft / 5.
6. / ______
______

Find the ratio of the corresponding sides for the similar triangles.

1. /
8 m 24 cm
6 m 18 cm / 2. /
8 m
4 m
9 m 18 m / 1.
2. / ______
______

Triangles ABC and DEF and similar. Find the indicated distance. Round to the nearest tenth.

3. / Find side AC.
E
5 cm B 25 cm
6 cm
A C D 20 cm F / 4. / Find side BC.
E
B 20 in.
A C D F
4 in. 28 in. / 3.
4. / ______
______
5. / Find side DE.
C
F
16 m 12 m
A B D E
18 m / 6. / Find side DE.
11 ft 24 ft
A C D F
10 ft
B E / 5.
6. / ______
______
7. / Find the height of triangle ABC.
C
4 in. F 10 in.
12 in.
A B D E / 8. / Find the height of triangle DEF.
C E
9 cm
A B D F
16 cm 20 cm / 7.
8. / ______
______

Solve.

1. / Find the height of the flagpole.
height 11 ft
27 ft
Shadow 9 ft / 2. / Find the height of the flagpole.
height 10 ft
14 ft 4 ft / 1.
2. / ______
______
3. / Find the height of the building.
12 m
4 m 7 m / 4. / Find the height of the building.
5.2 ft
6 ft 1.3 ft / 3.
4. / ______
______

Triangles ABC and DEF are similar.

5. / Find the perimeter of triangle ABC.
E
B
5 cm
6 cm
A C D 20 cm F / 6. / Find the area of triangle DEF.
C F
30 cm 50 cm
A 81 cm B D E / 5.
6. / ______
______
7. / Find the area of triangle ABC.
C F
26 cm
A 20 cm B D 65 cm E / 8. / Find the area of triangle DEF.
C E
5 m 12 m
A B D F
15 m / 7.
8. / ______
______