vocabulary - austin independent school...

Chapter 15 Skills Practice • 843

© C

arne

gie

Lear

ning

Customary to Whom?Customary Measurement

VocabularyMatch each definition to its corresponding term.

1. to change a measurement to an equivalent measurement in

different units

a. standard units of

measure

2. units used by everyone in a certain area b. measurement

3. the magnitude of a quantity specified with a number and a unit c. convert

Lesson 15.1 Skills Practice

Name ________________________________________________________ Date _________________________

Problem SetDetermine an approximate measure in customary units for each item.

1. the height of a stamp

The height of a stamp is about one inch.

2. the capacity of a jug of milk

3. the weight of a loaf of bread 4. the weight of a slice of bread

5. the capacity of a fruit juice box 6. the average length of an adult shoe

462343_C1_Skills_CH15_843-864.indd 843 16/04/13 12:09 PM

844 • Chapter 15 Skills Practice

© C

arne

gie

Lear

ning

Choose the appropriate customary unit of measure to use when measuring

each of the following.

7. the length of a bicycle

The length of a bicycle would be best mea-

sured in inches or feet.

8. the capacity of a bottle of glue

9. the weight of a tennis ball 10. the height of a tree

11. the distance of a marathon race 12. the capacity of a swimming pool

Choose the most appropriate measurement for each of the following.

13. the capacity of a bottle of water

a. 8 oz b. 16 fl oz c. 4 lb d. 14 gal

b. 16 fl oz

14. the weight of a blue whale

a. 500 yd b. 2 t c. 300,000 lb d. 56 c

15. the length of a car

a. 13 ft b. 2000 lb c. 26 in. d. 45 qt

Lesson 15.1 Skills Practice page 2



© C

arne

gie

Lear

ning

16. the capacity of a car’s gas tank

a. 20 fl oz b. 5 mi c. 3 t d. 16 gal

17. the average weight of a newborn baby

a. 8 lb b. 9 oz c. 7 yd d. 6 gal

18. the length of a cat’s tail

a. 15 mi b. 12 in. c. 5 c d. 8 fl oz

Complete each model. Multiply to determine each measurement conversion.

19. How many inches are in 2 feet?

2 ft

? in.1 ft

12 in. ______ 1 ft

2 ft ( 12 in. ______ 1 ft

) 5 24 in.

There are 24 inches in 2 feet.

20. How many cups are in 3 pints?

3 pt

? c1 pt


Name ________________________________________________________ Date _________________________



© C

arne

gie

Lear

ning


21. How many ounces are in 2 pounds?

2 lb

? oz1 lb

22. How many yards are in 12 feet?

12 ft

? ft1 yd

23. How many quarts are in 16 cups?

16 c

? c1 qt



© C

arne

gie

Lear

ning

24. How many pounds are in 48 ounces?

48 oz

? oz1 lb

Multiply to determine each measurement conversion.


Name ________________________________________________________ Date _________________________

25. How many feet are in 3 miles?

3 mi ( 5280 ft _______ 1 mi

) 5 15,840 ft

There are 15,840 feet in 3 miles.

26. How many pounds are in 5 tons?

27. How many fluid ounces are in 8 cups? 28. How many yards are in 504 inches?

29. How many pounds are in 480 ounces? 30. How many gallons are in 200 quarts?



© C

arne

gie

Lear

ning


31. How many ounces are in 1 ton?

32. How many yards are in 2 miles?

33. How many inches are in 1 mile? 34. How many fluid ounces are in 2 pints?

35. How many pints are in 3 gallons? 36. How many fluid ounces are in 4 quarts?



© C

arne

gie

Lear

ning

It’s All Based on Powers of 10!Metric Measurement

VocabularyChoose the term from the box that best completes each statement.

gram meter prefix liter

1. The standard unit of length in the metric system is the .

2. The standard unit of capacity is the .

3. The standard unit of mass is the .

4. A is a group of letters attached to the beginning of a word which changes

the meaning of the word.

Problem SetChoose the appropriate metric unit of measure to use when measuring

each of the following.


Name ________________________________________________________ Date _________________________

1. the width of a roadway

The width of a roadway would be best mea-

sured in meters.

2. the mass of a horse

3. the capacity of a fish tank 4. the length of a road between two cities

5. the mass of a penny 6. the capacity of a pond



© C

arne

gie

Lear

ning


Choose the most appropriate measurement for each of the following.

7. the mass of a tiger

a. 30 mg b. 75 kL c. 95 kg d. 45 cm

c. 95 kg

8. the length of a basketball court

a. 29 m b. 85 mL c. 30 mm d. 12 g

9. the capacity of a mug

a. 300 L b. 250 mL c. 400 mg d. 300 km

10. the mass of a bowling ball

a. 6 mg b. 9 L c. 5 m d. 7 kg

11. the length of a pencil

a. 20 km b. 16 mg c. 18 cm d. 14 mL

12. the capacity of a bucket

a. 9 kL b. 6 L c. 8 g d. 10 mm

Complete each sentence with the appropriate number or unit of measure.

13. A meter is 100 centimeters. 14. One thousand grams is 1 .

15. A milligram is of a gram. 16. A kiloliter is liters.

17. A is 1 ____ 100

of a meter. 18. A liter is 1000 .



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Use the metric system chart to determine each measurement conversion.

19. 5 dam 5 50 m

km(1

00

0)

hm

(10

0)

dam

(10

)

m(1

)

dm

(0.1)

cm(0

.01)

mm

(0.0

01)

5

20. 8 km 5 dam

km(1

00

0)

hm

(10

0)

dam

(10

)

m(1

)

dm

(0.1

)

cm(0

.01)

mm

(0.0

01)

8

21. dm 5 37 cm

km(1

00

0)

hm

(10

0)

dam

(10

)

m(1

)

dm

(0.1

)

cm(0

.01)

mm

(0.0

01)

3 7

22. hm 5 201 m

km(1

00

0)

hm

(10

0)

dam

(10

)

m(1

)

dm

(0.1

)

cm (

0.0

1)

mm

(0.0

01)

2 0 1



© C

arne

gie

Lear

ning

23. 95.2 dam 5 mm

km(1

00

0)

hm

(10

0)

dam

(10

)

m(1

)

dm

(0.1

)

cm(0

.01)

mm

(0.0

01)

9 5 2

24. 4.78 km 5 dm

km(1

00

0)

hm

(10

0)

dam

(10

)

m(1

)

dm

(0.1

)

cm(0

.01)

mm

(0.0

01)

4 7 8

Multiply to determine each measurement conversion.


25. How many centimeters is 3.4 kilometers?

3.4 km ( 1000 m _______ 1 km

) 5 3400 m

3400 m ( 100 cm _______ 1 m

) 5 340,000 cm

There are 340,000 centimeters in

3.4 kilometers.

26. How many meters is 350 millimeters?

27. How many milligrams is 12.9 kilograms? 28. How many grams is 25 milligrams?

29. How many liters is 3.75 kiloliters? 30. How many kiloliters is 269 milliliters?



© C

arne

gie

Lear

ning

The Language of GeometrySketching, Drawing, Naming, and Sorting Basic Geometric Figures

VocabularySketch an example of each geometric figure.


Name ________________________________________________________ Date _________________________

1. triangle 2. quadrilateral 3. square 4. rectangle 5. polygon

6. scalene triangle 7. equilateraltriangle

8. regular polygon 9. irregularpolygon

10. pentagon

11. equiangulartriangle

12. hexagon 13. isoscelestriangle

14. nonagon 15. kite

16. obtuse triangle 17. acutetriangle

18. octagon 19. rhombus 20. trapezoid

21. right triangle 22. heptagon 23. parallelogram 24. decagon 25. isoscelestrapezoid



© C

arne

gie

Lear

ning

Write the term that best completes each statement.

26. When you a geometric figure, the figure is created with the use of tools

such as a ruler, a straightedge, a compass, or a protractor.

27. A(n) is a tool used to create arcs or circles.

28. In a quadrilateral, are sides that do not share a common endpoint.

29. A(n) is a ruler with no numbers.

30. When you a geometric figure, the figure is created using only a compass

and a straightedge.

31. A(n) can be used to approximate the measure of an angle.

32. In a polygon, are sides that share a common endpoint.

33. When you a geometric figure, the figure is created without the use of

tools.




© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Problem SetName each polygon and list its sides and angles.

1.

Sample answer.

Name of Polygon: quadrilateral MTFD

Sides: MT, TF, FD, and DM

Angles: /M (or /DMT ), /T (or /MTF ),

/F (or /TFD), and /D (or FDM )

2.

Name of Polygon:

Sides:

Angles:

3.

Name of Polygon:

Sides:

Angles:

4.

Name of Polygon:

Sides:

Angles:

F

DM

T

TQ

WZ

BR

XM

H K

S C

GY



© C

arne

gie

Lear

ning


5.

Name of Polygon:

Sides:

Angles:

6.

Name of Polygon:

Sides:

Angles:

N

W

P

T

RX B

M

EZ

T XW

JA



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Sort the given polygons into the appropriate categories.

BC

D

H

KJ

A

E F G

7. Regular polygons: C, F, H, and K

Irregular polygons: A, B, D, E, G, and J

8. Polygons with at least one right angle:

Polygons with no right angles:

9. Polygons with at least one pair of congruent sides:

Polygons with no congruent sides:

10. Polygons with at least one obtuse angle:

Polygons with no obtuse angles:

11. Polygons with at least one pair of opposite sides parallel:

Polygons with no opposite sides parallel:

12. Polygons with at least one acute angle:

Polygons with no acute angles:



©

Lear

ning

Car

negi

e



© C

arne

gie

Lear

ning

Pulling a One-Eighty!Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems

VocabularyWrite the term that best completes each statement.

1. The states that the measure of an exterior angle of a

triangle is greater than the measure of either of the remote interior angles of the triangle.

2. The states that the sum of the measures of the interior

angles of a triangle is 180°.

3. The states that the measure of an exterior angle of a

triangle is equal to the sum of the measures of the remote interior angles of the triangle.

4. The are the two angles that are

non-adjacent to the specified exterior angle.

Problem SetDetermine the measure of the unknown angle in each triangle.

1.

A

B

C78° 37°

2. P80˚ 66˚

Q

R

m/B 5 180° 2 (78° 1 37°) 5 65°


Name _______________________________________________________Date _________________________



© C

arne

gie

Lear

ning


3. 35˚

28˚

K

LM

4.

90˚ 32˚

F E

G

5.

60˚

60˚

W

X

Y

6.

110˚

35˚

T

V U

List the side lengths from shortest to longest for each diagram.

7. a

b

c

48°

21°

A

B

C 8.

60˚ 54˚

S

T

r t

s R

m/C 5 180° 2 (48° 1 21°) 5 111°

The shortest side of a triangle

is opposite the smallest angle.

So, the side lengths from shortest

to longest are a, b, c.



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

9.

28˚118˚

M

K

L

k

l

m

10.

42˚

84˚

Z

YX

yx

z

11.

64˚

79˚67˚

27˚

X Y

W Ze

dca

b 12.

50˚

30˚

60˚90˚

A

u

v

s

r

D

CB

t



© C

arne

gie

Lear

ning


Identify the interior angles, the exterior angle, and the remote interior angles of each triangle.

13.

WX

Y

Z

14.

R S

UT

Interior angles: /XYZ, /YZX, /ZXY

Exterior angle: /WXZ

Remote interior angles: /XYZ, /YZX

15.

E

F

G H

16. B

C

A

D

17. L

MKJ

18.

Q

P

SR



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

Solve for x in each diagram.

19.

F

Gx

H

J

K

130°

99°

20. V

S

TU

R 140˚

132˚

x

m/GFH 5 180° 2 130° 5 50°

m/GHK 5 m/GFH 1 m/FGH

99° 5 50° 1 x

49° 5 x

21.

H

I

JK

81˚

x2x

22.

R T V S

U

64˚

90˚ (x + 8)



© C

arne

gie

Lear

ning


23.

132˚

112˚

(2x + 4)

K

L

J

N

M

24.

90˚

(3x + 2) (2x + 18)

F

G

D E

Compare the angles in each triangle and determine the unknown information.

25.

S

RQ

T 26.

S

Q

R

P

m/ QRT .m/RST m/PQR m/QRS

m/ RTS , m/QRT m/QSR , m/



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

27. T

U

VW

28. J

F G H

m/TUV m/UWV m/ m/GHJ

m/WVU m/TUV m/GJH m/FGJ

29. K L M

N

30.

D

C

A B

m/LMN m/KLN m/ABC m/BCD

m/LNM m/KLN m/BAC , m/



© C

arne

gie

Lear

ning



© C

arne

gie

Lear

ning

Triangle Construction IConstructing Triangles

Problem SetDetermine whether each combination of given sides and/or angles determines a unique triangle.

1. You are given three angles.

No.

2. You are given three sides.

3. You are given two sides and the included angle.

4. You are given two angles and a side not specified.

5. You are given two angles.

6. You are given two sides.


Name _______________________________________________________Date _________________________



© C

arne

gie

Lear

ning

Construct each triangle using the given sides and/or angles.

7. Construct PQR using the three line segments shown.

Q R

P R

P Q

P R

Q

8. Construct UVW using the three line segments shown.

U

U

W

W

V

V




© C

arne

gie

Lear

ning

9. Construct DEF using the three line segments shown.

D F

ED

E F

10. Construct MNP using the three line segments shown.

M P

PN

M N


Name _______________________________________________________Date _________________________



© C

arne

gie

Lear

ning


11. Construct HJK using the three line segments shown.

H K

KJ

H J

12. Construct ABC using the two line segments and included angle shown.

A B

A

A

C



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

13. Construct PQR using the two line segments and included angle shown.

P

P

P R

Q

14. Construct DEF using the two line segments and included angle shown.

D E

E

E

F



© C

arne

gie

Lear

ning


15. Construct KMN using the two line segments and included angle shown.

K M

M

M

N

16. Construct WXZ using the two line segments and included angle shown.

W

W

W

Z

X



© C

arne

gie

Lear

ning

Triangle Construction IICongruent Figures and Constructing Congruent Triangles

VocabularyDefine each term in your own words.

1. geometric figures

2. congruent geometric figures

3. corresponding sides

4. corresponding angles

5. included angle

6. included side


Name _______________________________________________________Date _________________________



© C

arne

gie

Lear

ning


Problem SetUse measuring tools to determine whether the given figures are congruent. If the figures are congruent,

then identify and list the corresponding sides and angles. If the figures are not congruent, explain why

they are not.

1. A

D

B

C

E

H

F

G

The figures are congruent.

___

AB > ___

FE , ___

BC > ___

EH , ___

CD > ____

HG , ___

AD > ___

FG , /A > /F, /B > /E, /C > /H, and /D > /G

2. J K

N

P

S

Q

RM



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

3. B C

D Z

W X

YA

4. D E

FB C

A



© C

arne

gie

Lear

ning


5. M

N

K

G

H

J

6.

Q

R

S

T

U

P



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

Construct each triangle using the given sides and/or angles.

7. Three sides are given.

a b

c

c

ab


f

e

d



© C

arne

gie

Lear

ning



h

g k

10. Two sides and the included angle are given.

b

a



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________


c d


e

f



© C

arne

gie

Lear

ning


13. Two angles and the included side are given.

g



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

14. Two angles and the included side are given.

h

Use the congruence symbol to show the corresponding sides and angles that are congruent based on

each congruence statement.

15. MAT > JEF

___

MA > __

JE , ___

AT > ___

EF , ___

MT > __

JF , /M > /J,

/A > /E, /T > /F

17. CAT > DOG

19. PQR > XYZ

16. LMN > GHJ

18. ABC > KTV

20. DEF > RST



© C

arne

gie

Lear

ning



© C

arne

gie

Lear

ning

Pasta Anyone?Triangle Inequality Theorem

VocabularyUse the given figure to complete the statement.

1. According to the Triangle Inequality Theorem, 1 . AC.

A C

B

Problem SetWithout measuring the angles, list the angles of each triangle in order from least to greatest measure.

1.

F

G

H8 in.

9 in.

11 in.

2.

X W

Y

4.7 cm3.6 cm

2.1 cm

The smallest angle of a triangle is

opposite the shortest side. So, the

angles from least to greatest

are /H, /F, /G.


Name _______________________________________________________Date _________________________



© C

arne

gie

Lear

ning


3. Q

RP

8 ft 4 ft

6.43 ft

4. T S

U

9 in

12 in

15 in

5. F

E G6 yd

9.2 yd

4.6 yd

6. K

M

L

4.2 m

5.2 m

5.8 m

Determine whether it is possible to form a triangle using segments with the given measurements.

Explain your reasoning.

7. 3 in., 2.9 in., 5 in. 8. 8 ft, 9 ft, 11 ft

Yes. Because 3 1 2.9 5 5.9, and

5.9 is greater than 5.



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

9. 4 m, 5.1 m, 12.5 m 10. 7.4 cm, 8.1 cm, 9.8 cm

11. 10 yd, 5 yd, 21 yd 12. 13.8 km, 6.3 km, 7.5 km

13. 112 mm, 300 mm, 190 mm 14. 20.2 in., 11 in., 8.2 in.

15. 30 cm, 12 cm, 17 cm 16. 8 ft, 8 ft, 8 ft



© C

arne

gie

Lear

ning


Write an inequality that expresses the possible lengths of the unknown side of the given triangle.

17. What could be the length of ___

AB ? 18. What could be the length of ___

DE ?

A

10 m

B 8 m C

D

6 cm

F 9 cm E

AB , AC 1 BC

AB , 10 m 1 8 m

AB , 18 m

AC , AB 1 BC

AC 2 BC , AB

10 m 2 8 m , AB

2 m , AB

2 m , AB , 18 m



© C

arne

gie

Lear

ning


Name _______________________________________________________Date _________________________

19. What could be the length of ___

HI ? 20. What could be the length of ___

JL ?

I

20 in.

H 14 in. G

J

12 ft

K 7 ft L



© C

arne

gie

Lear

ning


21. What could be the length of ____

MN ? 22. What could be the length of ___

QR ?

M

3 cm

N 11 cm O

P

9 mm 13 mm

R Q



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Weaving a RugArea and Perimeter of Rectangles and Squares

Problem SetCalculate the perimeter of each given rectangle. Each square on the grid represents a square that

is 1 foot long and 1 foot wide.

1. 2.

Perimeter 5 2(12) 1 2(8)

5 24 1 16 5 40 feet

3. 4.



© C

arne

gie

Lear

ning


5. 6.

Calculate the perimeter of each given rectangle.

7.

3 in.

5 in.

8. 2 in.

9 in.

P 5 2(5) 1 2(3) 5 10 1 6 5 16 in.

9.

4 m

2 m

10.

12 m

8 m



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

11. 12.

Calculate the area of each given rectangle. Each grid square is 1 foot long and 1 foot wide.

13. 14.

Area 5 6(13) 5 78 square feet

15. 16.

8 ft

4.5 ft

9.5 m

9.5 m



© C

arne

gie

Lear

ning


17. 18.

Calculate the area of each given rectangle.

19. 3 cm

11 cm

20. 4 cm

7 cm

A 5 11(3) 5 33 cm2

21.

2.5 m

1.75 m

22.

11.2 m

2.3 m



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

23. 14 ft

14 ft

24. 12 in.

12 in.

In each rectangle, the length, width, or area is unknown. Calculate the value of the unknown measure.

25.

Length: 4 ft

Area: 12 ft2

26.

Length: 7 ft

Area: 35 ft2

A 5 lw

12 5 4w

3 5 w

The width is 3 feet.

27.

6 yd

2 yd

28.

5 yd

13 yd



© C

arne

gie

Lear

ning


29.

Area: 30 in.2 Width: 4 in.

30.

Area: 65 m2 Width: 5 m

Calculate the missing measures using the given measure for each square.

31. Side length: 6 feet 32. Side length: 18 centimeters

Area: 36 square feet Area:

Perimeter: 24 feet Perimeter:

33. Side length: 34. Side length:

Area: 16 square inches Area:

Perimeter: Perimeter: 36 meters

35. Side Length: 5.5 inches 36. Side Length:

Area: Area: 400 square meters

Perimeter: Perimeter:

Calculate the perimeter and area of a rectangle or square whose dimensions are double

the dimensions of each given rectangle or square.

37. A rectangle with a perimeter of 14 meters and an area of 10 square meters

The rectangle whose dimensions are doubled will have the following perimeter and area.

Perimeter 5 2 (14)

5 28 meters

Area 5 4 (10)

5 40 square meters



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

38. A rectangle with a perimeter of 30 feet and an area of 54 square feet

39. A square with a perimeter of 60 meters and an area of 225 square meters

40. A square with a perimeter of 14 inches and an area of 12.25 square inches

41. A rectangle with a perimeter of 42 meters and an area of 20 square meters



© C

arne

gie

Lear

ning


42. A square with a perimeter of 72 feet and an area of 324 square feet

Calculate the area of each composite figure.

43.

8 m

8 m

8 m

8 m 8 m

A 5 24 (8) 1 8 (8)

5 192 1 64

5 256 m2

44.

2 ft

4 ft

6 ft

11 ft

45.

6 in.6 in.

5 in.

5 in.

5 in.

8 in.14 in.14 in.

46.

9 ft

6 ft

6 ft

10 ft 18 ft

5 ft

8 ft



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

47. 5 m

4 m5 m

4 m

16 m5 m

48. 7 m 7 m

7 m

14 m

7 m

16 m

49.

6 ft

6 ft

8 ft

7 ft7 ft

20 ft

20 ft 50. 6 m

8 m

6 m4 m

3.5 m 3.5 m

6 m

6 m

4 m

6 m



© C

arne

gie

Lear

ning



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Boundary LinesArea of Parallelograms and Triangles

VocabularyDefine each term in your own words.

1. altitude of a parallelogram

2. height of a parallelogram

3. altitude of a triangle

4. height of a triangle



© C

arne

gie

Lear

ning


Problem SetCalculate the area of each given parallelogram. Each square on the grid represents a square that

is 1 centimeter long and 1 centimeter wide.

1. 2.

Area 5 6(9) 5 54 square centimeters

3. 4.

5. 6.



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Calculate the area of each parallelogram.

7. 4 mi

8 mi

8.

11 mi

6 mi

A 5 8(4) 5 32 mi2

9.

32 yd

14 yd

10.

16 yd

7 yd

In each given parallelogram, the base, height, or area is unknown. Calculate the value of

the unknown measure.

11.

8 in.

8.5 in.

12.

4.5 ft

20 ft

A 5 8.5(8) 5 68 in.2



© C

arne

gie

Lear

ning


13.

Area: 63 m2

9 m

14. Area: 36 m2

18 m

15. Area: 96 ft2

12 ft

16.

Area: 286 ft2

22 ft

17.

12 ft

15 ft

18.

Area: 138 m2

9.2 m



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

The base of each triangle is labeled. Draw a segment that represents the height of the triangle.

19.

b

h

20.

b

21.

b

22.

b

23.

b

24.

b



© C

arne

gie

Lear

ning


Calculate the area of each given triangle. Each square on the grid represents a square that is 1 foot

long and 1 foot wide.

25. 26.

Area 5 1 __ 2 (12)(8) 5 48 square feet

27. 28.

29. 30.



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Calculate the area of each given triangle.

31.

8 in.

6 in. 32.

7 ft

7 ft

A 5 1 __ 2

(6)(8) 5 1 __ 2 (48) 5 24 in.2

33.

11 mm

20 mm

34.

4 m

4.5 m

35.

7.5 in

18 in

36.

12 m

14 m



© C

arne

gie

Lear

ning


In each given triangle, the base, height, or area is unknown. Calculate the value of

the unknown measure.

37. Area: 30 sq. m

15 m

38. 2 ft

3 ft

A 5 1 __ 2

bh

30 5 1 __ 2

(15)h

60 5 15h

4 5 h

The height of the triangle is 4 meters.

39.

Area: 35 sq. in.

10 in.

40.

3 yd

Area: 6 sq. yd

41.

8 ft

Area: 88 sq ft 42.

6 in.Area: 31.5 sq in.



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Calculate the area of each shaded region.

43. The figure is composed of 2 triangles.

9 m

15 m

20 m

The area of the large triangle is: The area of the small triangle is:

A 5 1 __ 2 bh A 5 1 __

2 bh

5 1 __ 2

(20)(15) 5 1 __ 2

(20)(9)

5 150 m2 5 90 m2

The shaded area 5 150 2 90 5 60 m2

44. The figure is composed of a parallelogram and a triangle.

10 yd

5 yd 2 yd

7 yd



© C

arne

gie

Lear

ning



6 m

14 m

16 m

46. The figure is composed of a parallelogram and a triangle.

8 ft

9 ft

3 ft



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________


6 in.

12 in.

8 in.

3 in.

48. The figure is composed of 2 parallelograms and 1 triangle.

9 m

9 m

3 m

22 m



© C

arne

gie

Lear

ning



© C

arne

gie

Lear

ning

The Keystone EffectArea of Trapezoids

VocabularyExplain how the set of terms are related.

1. legs of a trapezoid and bases of a trapezoid

2. altitude of a trapezoid and height of a trapezoid

Problem SetCalculate the area of each trapezoid. Each square on the grid represents a square that is 1 inch long

and 1 inch wide.

1. 2.

A 5 1 __ 2 (8 1 4) 5

5 1 __ 2

(12)(5)

5 30

The area of the trapezoid is 30 square inches.


Name ________________________________________________________ Date _________________________



© C

arne

gie

Lear

ning


3. 4.

5. 6.

Calculate the area of each trapezoid with the given dimensions, where h represents the height, b1

represents the length of a base, and b2 represents the length of the other base.

7. h 5 2, b1 5 4, b2 5 3 8. h 5 6, b1 5 5, b2 5 3

A 5 1 __ 2 (4 1 3)2 5 1 __

2 (7)(2) 5 7

The area is 7 square units.

9. h 5 3, b1 5 11, b2 5 7 10. h 5 5, b1 5 9, b2 5 1



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

11. h 5 1 __ 2

, b1 5 10, b2 5 14 12. h 5 4, b1 5 2 __ 3 , b2 5 4 __

3

In each given trapezoid, the length of one base, the height, or the area is unknown. Calculate

the value of the unknown measure.

13. 4 feet

3 feet

2 feet

14. 3 centimeters Area: 8 square centimeters

2 centimeters

A 5 1 __ 2 (2 1 4)3 5 1 __

2 (6)(3) 5 9

The trapezoid has an area of

9 square feet.

15. Area: 5 square feet

3 feet

1 feet

16. 5 yards

8 yards

Area: 25 square yards



© C

arne

gie

Lear

ning


17. 2 millimeters

4 millimeters

Area: 14 square millimeters

18. 15 yards

Area: 70 square yards

5 yards

19. Area: 13.5 square inches

3 inches

3 inches

20. 13 feet

5 feet

22 feet

21.

5 yards 2 yards 8 yards

22. 13 meters

7 meters

Area: 98 square meters



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Use the given information to answer each question.

23. The side of a staircase has the shape of a trapezoid with the dimensions shown in

the diagram. You want to paint this side of the staircase. How many square feet will

you need to cover with paint?

26 feet

13 feet

11 feet

A 5 1 __ 2 (b1 1 b2)h

A 5 1 __ 2 (26 1 13)11

A 5 214.5

You will need to cover 214.5 square feet with paint.

24. Yvonne cut a picture into the shape of a trapezoid to place into her scrapbook. The picture is

shown. What is the area of the picture?

5 in.

7 in.4 in.



© C

arne

gie

Lear

ning


25. A mosaic on a CD cover is in the shape of an isosceles trapezoid with the

dimensions shown in the diagram. The artist needs to tell the production

company the area of the mosaic. How many square inches is the mosaic?

4 inches

4 inches

3 inches

26. The planning committee submitted a plan to the town architect to revitalize the town square.

Their plan includes a new flagpole with a concrete base in the shape of a trapezoid. The base

of the trapezoid and its dimensions are shown. What is the area of the base proposed by the

planning committee?

5 feet4 feet

7 feet



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

27. An aeronautical engineering student has painted a rocket-shaped design on her T-shirt.

The design is composed of a triangle, a rectangle, and a trapezoid. How many square

inches is the design?

3 in.

6 in.

4 in.

4 in.

9 in.



© C

arne

gie

Lear

ning


28. An advertising company has designed its new logo. The logo is composed of two trapezoids.

What is the area of the shaded region?

8 cm

14 cm

25 cm

12 cm

10 cm



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Go Fly a KiteArea of Rhombi and Kites

Problem SetCalculate the area of each given rhombus or kite. Each square on the grid represents a square

that is 1 foot long and 1 foot wide.

1. The polygon is a rhombus. 2. The polygon is a rhombus.

A 5 bh

5 10 (8)

5 80

The area of the rhombus is 80 square feet.



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

5. The polygon is a kite. 6. The polygon is a kite.



© C

arne

gie

Lear

ning


Calculate the area of each given rhombus or kite.

7. The polygon is a rhombus.

13 in.

15 in.

A 5 bh

5 15 (13)

5 195

The area of the rhombus is 195 square

inches.


8.5 m

7 m


12 yd

11 yd



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

10. In the given kite, AE 5 6 ft, CE 5 6 ft, BE 5 9 ft, and DE 5 15 ft.

E

B

D

CA

11. In the given kite, JK 5 3 meters, FK 5 7 meters, GK 5 12 meters, and HK 5 7 meters.

KGJ

H

F



© C

arne

gie

Lear

ning


12. In the given kite, SZ 5 WZ 5 10 yards, TZ 5 12 yards, and RZ 5 32 yards.

ZTR

W

S


13. The figure is composed of 2 congruent rhombi.

16 ft

20 ft

The area of 1 rhombus is:

A 5 bh

5 20 (16)

5 320 square feet

The area of the figure is 2(320) 5 640 square feet.



© C

arne

gie

Lear

ning

14. The figure is composed of a kite and a square.

Given: AG 5 7 meters, BG 5 FG 5 8 meters, DG 5 13.5 meters, and CE 5 9 meters.

C

A

F

E

B

GD


Name ________________________________________________________ Date _________________________



© C

arne

gie

Lear

ning


15. The figure is composed of a trapezoid and a rhombus.

8.5 in.

11 in.

10 in.

24 in.

16. The figure is composed of 2 kites.

Given: MR 5 RS 5 5 feet, ST 5 PT 5 10 feet, and NS 5 QS 5 12 feet.

M

Q

N

S TRP



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

17. The figure is composed of a square and a kite.

Given: AE 5 9 inches, BE 5 DE 5 7 inches, and CE 5 15 inches.

C

A

EB D



© C

arne

gie

Lear

ning


18. The figure is composed of 2 congruent triangles and a rhombus.

4 in.

4 in.5 in.

4 in.



© C

arne

gie

Lear

ning

Street SignsArea of Regular Polygons

VocabularyDraw an example of each given term.

1. congruent polygons

2. apothem

Problem SetDetermine whether each polygon is a regular polygon.

1. 2.

The polygon is not a regular polygon.


Name ________________________________________________________ Date _________________________



© C

arne

gie

Lear

ning


3. 120° 120°

120°120°

120° 120°

5 cm

5 cm

5 cm

5 cm

5 cm

5 cm

4. 4 inches

4 inches4 inches

7 inches

70° 70°

110° 110°

5.

3 ft

3 ft 3 ft120°

100° 100°

110°110°

3 ft

3 ft

6.

135° 135°

135°

135° 135°

135° 135°

135°

Draw an apothem of each given figure.

7. 8.

9. 10.

11. 12.



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Write a formula for the area of each regular polygon. State the area in terms of

an apothem a of the polygon.

13. regular octagon with side h

A 5 ( 1 __ 2

ha ) 8 5 4 ha

14. regular hexagon with side c

15. regular nonagon with side b 16. regular decagon with side d

17. regular pentagon with side length g 18. regular heptagon with side length t

Calculate the area of each regular polygon.

19. 8 cm

6.3 cm

20.

12 ft

8.3 ft

A 5 1 __ 2

(8)(6.3)(6)

A 5 151.2

The area is 151.2 square centimeters.



© C

arne

gie

Lear

ning


21.

20 km

24.1 km

22. 10 yd

10.4 yd

23.

15 in.

4.3 in.

24. 4 in.

7.5 in.

25.

2 m

1 m

26. 12 m

6 m

Use the given information to calculate the area of each regular polygon.

27. A regular decagon has a side length of 26 yards and an apothem length of

40 yards. What is the area of the regular decagon?

A 5 1 __ 2 (26)(40)(10)

5 5200

The area of the regular decagon is 5200 square yards.



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

28. A regular 15-gon has a side length of 10 feet and an apothem length of 23.5 feet.

What is the area of the regular 15-gon?

29. A regular 12-gon has a side length of 11 meters and an apothem length of

20.5 meters. What is the area of the regular 12-gon?

30. A regular octagon has a perimeter of 36 millimeters and an apothem length of

5.4 millimeters. What is the area of the regular octagon?

31. A regular pentagon has a perimeter of 625 centimeters and an apothem length

of 86 centimeters. What is the area of the regular pentagon?

32. A regular 20-gon has a perimeter of 1000 inches and an apothem length of

157.8 inches. What is the area of the regular 20-gon?



© C

arne

gie

Lear

ning



33. The figure is composed of a regular pentagon and a square.

9 in.

20 in.

13 in.

The area of the square is: The area of the pentagon is:

A 5 s2 A 5 ( 1 __ 2

la ) n5 (20)2 5 1 __

2 (13)(9)(5)

5 400 square inches 5 292.50 square inches

The area of the shaded region is 400 2 292.50 5

107.50 square inches.

34. The figure is composed of a regular hexagon and a square.

8.7 ft

11 ft

10 ft



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

35. The figure is composed of a regular pentagon and 2 congruent trapezoids.

19 cm

10 cm

13.3 cm 9.7 cm

14 cm

36. The figure is half of a regular octagon.

14.5 in.

12 in.



© C

arne

gie

Lear

ning


37. The figure is composed of 2 regular pentagons.

10.3 m

10 m

15 m

6.9 m

38. The figure is composed of 4 congruent regular hexagons.

22 ft

19 ft



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Backyard Barbecue, Anyone?Volume of Rectangular Prisms

Problem SetCalculate the volume of each rectangular prism.

1.

8 in.

5 in.

2 in.

2.

1.5 cm3 cm

14 cm

V 5 (8) ? (2) ? (5)

V 5 80 in.3

3.

8 m

3.5 m2 m

4.

8 m

13 m5 m

5.

4 in.

4 in.4 in.

6.

21 ft6 ft

9 ft



© C

arne

gie

Lear

ning


Describe how you would separate each solid to calculate the volume.

7.

Separate the solid into two rectangular

prisms—one prism is the bottom of the “L”,

and the other prism is the top of the “L”.

8.

9. 10.



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

11. 12.

Calculate the volume of each solid formed by the rectangular prisms.

13.

2 ft

1 ft

1 ft

3 ft

1 ft

14.

5 m

1 m

6 m

4 m

1 m

V 5 top prism 1 bottom prism

V 5 (1)(1)(1) 1 (4)(1)(1)

V 5 1 1 4

V 5 5 ft3



© C

arne

gie

Lear

ning


15. 2 cm 2 cm

1 cm

2 cm

2 cm

2 cm

6 cm

1 cm

6 cm

16.

6 yd

4 yd

1 yd

2 yd2 yd

2 yd

17.

12 ft

2 ft

1 ft9 ft

1 ft 2 ft 18. 1 mm 1 mm

19 mm

15 mm1 mm

12 mm



© C

arne

gie

Lear

ning


Name ________________________________________________________ Date _________________________

Determine the volume for each problem.

19. A storage box with a square base has a side length of 2 feet and a height of 2 1 __ 2

feet. What is the

volume of the storage box?

V 5 2(2) ( 2 1 __ 2

) 5 4 ( 5 __ 2 ) 5 10

The volume of the storage box is 10 cubic feet.

20. Your uncle and aunt bought new bedroom furniture including a dresser. The rectangular dresser is

5 feet tall, 3 1 __ 2

feet wide, and 2 feet long. What is the volume of this new dresser?

21. A carpenter is building a new table. Each of the four legs is a rectangular prism with a height

of 3 feet, a width of 0.5 foot, and a length of 0.5 foot. What is the total volume of wood that the

carpenter used to make the table legs?

22. A square stained glass window is created for a kitchen. The window has a side length of 1 3 __ 4

feet,

and a width of 0.08 foot. What is the volume of the square window?



© C

arne

gie

Lear

ning

23. Susan bought a new ottoman for her living room. It opens so she can store items inside. The

height of the ottoman is 1 1 __ 2

feet, the width is 2 feet, and the length is 2 1 __ 4

feet. What is the total

volume of the ottoman?

24. Bryce is installing new gutters around the outside of his backyard shed. Each gutter is 10 feet

long, 1 __ 4 foot high, and 1 __

3 foot wide. What is the total volume of the four gutters Bryce is installing on

his shed?



vocabulary - austin independent school...

Documents