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64
Math Busters Reproducible Worksheets These worksheets practice math concepts explained in Figuring Out Geometry (ISBN: 978-0-7660-2880-7), written by Rebecca Wingard-Nelson. Math Busters Figuring Out Geometry reproducible worksheets are designed to help teachers, parents, and tutors use the books from the Math Busters series in the classroom and the home. The answers to the problems are contained in the Answers section starting on page 59. Teachers, librarians, tutors, and parents are granted permission and encouraged to make photocopies of these worksheets. These worksheets are reproducible for educational use only and are not for resale. © 2008 Enslow Publishers, Inc. Visit www.enslow.com and search for the Math Busters series to download worksheets for the following titles: Algebra and Pre-Algebra Figuring Out Geometry 978-0-7660-2879-1 978-0-7660-2880-7 Decimals and Fractions Ratios and Percents 978-0-7660-2877-7 978-0-7660-2878-4 Division and Multiplication Subtraction and Addition 978-0-7660-2876-0 978-0-7660-2875-3 Titles in this series can be purchased directly from: Enslow Publishers, Inc. 40 Industrial Road, Box 398 Berkeley Heights, NJ 07922-0398 Phone: 1-800-398-2504 email: [email protected] Web Page: http://www.enslow.com 2

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Math Busters Reproducible Worksheets

These worksheets practice math concepts explained in FFiigguurriinngg OOuuttGGeeoommeettrryy (ISBN: 978-0-7660-2880-7), written by RReebbeeccccaa WWiinnggaarrdd--NNeellssoonn..

MMaatthh BBuusstteerrss FFiigguurriinngg OOuutt GGeeoommeettrryy reproducible worksheets are designedto help teachers, parents, and tutors use the books from the Math Bustersseries in the classroom and the home. The answers to the problems arecontained in the Answers section starting on page 59.

Teachers, librarians, tutors, and parents are granted permission andencouraged to make photocopies of these worksheets.

These worksheets are reproducible for educational use only and are not forresale. © 2008 Enslow Publishers, Inc.

Visit www.enslow.com and search for the MMaatthh BBuusstteerrss series to downloadworksheets for the following titles:

AAllggeebbrraa aanndd PPrree--AAllggeebbrraa FFiigguurriinngg OOuutt GGeeoommeettrryy978-0-7660-2879-1 978-0-7660-2880-7

DDeecciimmaallss aanndd FFrraaccttiioonnss RRaattiiooss aanndd PPeerrcceennttss978-0-7660-2877-7 978-0-7660-2878-4

DDiivviissiioonn aanndd MMuullttiipplliiccaattiioonn SSuubbttrraaccttiioonn aanndd AAddddiittiioonn978-0-7660-2876-0 978-0-7660-2875-3

Titles in this series can be purchased directly from:

Enslow Publishers, Inc.40 Industrial Road, Box 398Berkeley Heights, NJ 07922-0398Phone: 1-800-398-2504email: [email protected] Page: http://www.enslow.com

2

Points, Lines, and Planes

a. Name four points.

b. Name three lines.

c. Name the plane.

d. Name a horizontal line.

e. Name a vertical line.

f. Name an oblique line.

g. Name all four lines.

h. Name any four points.

i. Name the plane.

j. Name a horizontal line.

3

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

A p C

n

D

B

A C

m

D B

Points, Lines, and Planes

Use the correct symbols in your answers.

a. Name four points.

b. Name three lines.

c. Name the plane.

d. Name a horizontal line.

e. Name a vertical line.

f. What kind of line is line AC?

g. A straight set of points that extends forever in two directions is

called a __________.

h. A(n) __________ names an exact location in space.

i. A flat surface that continues in all directions is called a _______.

j. A(n) _________ line is not horizontal or vertical.

k. A(n) __________ line appears to go straight up and down.

l. A(n) __________ line appears to lie flat from left to right.

Name __________________________________ Date ___________________

4

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

A

E

m

G

C

A

Rays and Line Segments

Use the drawing to answer the following questions.

a. Name five rays.

b. Name five line segments.

c. Which can be measured, a ray or line segment? __________

d. A line segment has ______ end points.

Use the figure below for items e–i.

e. Name four line segments.

f. Name three rays.

g. Are TK and KT the same ray?

h. Are TA and AT the same line segment?

i. Are TK and KT the same line?

TK

M

P

5

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

R

N

T

S

Rays and Line Segments

a. Draw a ray PQ.

b. Draw a line segment RS .

c. Name three rays.

d. Name four line segments.

e. Name the ray.

f. Name the two rays that make

up this angle.

g. How many rays are in this

figure?

Name __________________________________ Date ___________________

6

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

D A T

R A E L

R K

L

P T

P

Z

V

K

7

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only. Score:

Line relationships

a. MN intersects PQ at ______.

b. SV is ____________ to MN.

c. MN and ST are the same distance

apart at all points. These lines are

called __________________.

d. Two lines in different planes that do

not intersect and are not parallel

are called _______________ .

e. What is the relationship between

KA and RN ?

They are _________________ .

f. What is the relationship between

MB and NR?

They are _________________ .

MR

P

SQ

NV

M

N

S

T

K

M

B R

AN

Name __________________________________ Date ___________________

8

© Enslow Publishers, Inc. Sheets are reproducible for educational use only. Score:

Line Relationships

a. What line intersects ZR?

b. BL is __________ to FP.

c. Lines that are always the same

distance apart are called

_______________________ .

d. Point E is called the point of

_______________________ .

e. What does the symbol � mean?

f. JU and ST are parallel.

Write this using a symbol.

____________________

g. If all four angles at an intersection

are right angles, the two lines are

called ____________ .

B

R

F

L

P

Z

A

C

B

D

E

J

S

UF

T

I

Angles

a. Name this angle in three ways.

b. What is the vertex of this angle?

c. Name the two rays.

d. Do �RKM and �MKR name the

same angle?

e. Name �RKM without using letters.

f. Name �1 using three letters.

g. Classify �1 by its measurement.

h. Classify �2 by its measurement.

i. Classify �STU by its measurement.

9

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

A

B 2

C

R

K

5

M

S

R

T

U21

Name __________________________________ Date ___________________

Angles

a. Angles that measure less than 90° are called _________ angles.

b. Angles that measure greater than 90°, but less than 180° are

called _________ angles.

c. Angles that measure exactly 90° are called _________ angles.

d. Angles that measure exactly 180° are called _________ angles.

e. Angles that measure greater than 180°, but less than 360° are

called _________ angles.

f. Draw an acute angle. g. Draw a right angle.

h. Draw an obtuse angle. i. Draw a reflex angle.

10

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Angle Relationships

a. Two angles that share a vertex and a side are called _________.

b. If two angles are supplementary, their sum is __________.

c. If two angles are complementary, their sum is __________.

d. Angles that have the same measure are called __________.

e. What angles are adjacent to �1?

f. What angles are adjacent to �2?

g. In the figures above, which two angles are complementary?

h. In the figures above, which two angles are supplementary?

11

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

12

3

5 6 78

4

Name __________________________________ Date ___________________

12

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Angle Relationships

a. Name the complementary angles.

b. Name the supplementary angles.

c. �P and �R are supplementary angles. If the measure of �R is

37°, what is the measure of �P?

d. �C and �D are complementary angles. If the measure of

�C is 23°, what is the measure of �D?

e. �A and �B are congruent angles. If the measure of �A is 65°,

what is the measure of �B?

f. �F and �G are supplementary angles. If they are also

congruent, what is the measure of �F?

g. �X and �Y are complementary angles. If they are also

congruent, what is the measure of �X?

80°1

30°3

60°2

120°4

13

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Angles of Intersecting Lines

a. Name two linear pairs.

b. Name two sets of vertical angles.

Circle the correct answer.

c. Linear pairs are always congruent complementary supplementary.

d. Vertical angles are always congruent complementary supplementary.

Use the following to fill in the blanks for e–j.

point of intersection 360° vertical angles

linear pairs 180° intersecting

e. ___________ are the adjacent angles where two lines intersect.

f. Where lines cross is the ________________.

g. The four angles where two lines intersect have a sum of _____.

h. Lines that cross are __________.

i. The angle sum of a linear pair is _____.

j. __________ are the opposite angles where two lines intersect.

1

432

14

Angles of Intersecting Lines

a. The measure of �2 is 73°.

What is the measure of �1?

b. The measure of �2 is 73°.

What is the measure of �4?

c. The measure of �2 is 73°.

What is the measure of �3?

d. Name two pairs of vertical angles.

____ and ____

____ and ____

e. Name four linear pairs.

____ and ____

____ and ____

____ and ____

____ and ____

f. �1 and �2 are vertical angles. g. �1 and �2 are a linear pair.

The measure of �1 is 113°. The measure of �1 is 113°.

What is the measure of �2? What is the measure of �2?

1

43

2

58

7

6

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

15

Plane FiguresUse figures a-f to answer the following questions.

a. Is figure e a polygon?

b. Figure ___ is an open figure.

c. Which figure is NOT a plane figure?

d. Which figure is a regular polygon?

e. How many polygons are there?

f. What polygon has four sides?

g. What polygon has three sides?

h. What polygon has eight equal sides?

i. An octagon has ________ sides.

j. A decagon has _____ angles.

k. A pentagon has _____ sides and _____ angles.

l. The line segments that form a polygon are called __________.

m. Where line segments meet on a polygon is called a _________.

ba

c

d

e f

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Plane Figures

a. Draw an example of b. Draw an example of

an open figure. a closed figure.

c. Draw an example of d. Draw an example of

a plane figure that a plane figure that

is NOT a polygon. is a polygon.

e. Draw an example of f. Draw an example of a

a regular polygon. polygon that is NOT regular.

Name __________________________________ Date ___________________

16

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Triangles

a. Name the triangle.

b. �K + �L + �M = ___________oo

c. In �ABC the hash marks on AB and

BC mean that the sides are _______.

d. The marks at �A and �C mean that

the angles are __________.

e. If �A, �B and �C are all less than 90°, �ABC is ____________.

f. A right triangle has one angle that measures ________.

g. An obtuse triangle has one angle that measures ________.

h. A triangle with three equal sides is called __________.

i. A triangle with two equal sides is called __________.

j. A triangle with no equal sides is called __________.

17

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

K

L

M

A

B

C

Name __________________________________ Date ___________________

TrianglesFind the missing angle measure for each triangle.

a. �ABC: m�A = 27°, m�B = 90° m�C = _____

b. �ABC: m�B = 120°, m�C = 30° m�A = _____

c. �ABC: m�A = 62°, m�C = 54° m�B = _____

d. e.

Classify each triangle by both its angle measures and side lengths.

f. g.

________ and __________ ________ and __________

h. i.

________ and __________ ________ and __________

Name __________________________________ Date ___________________

18

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

45°

°

45°75° °

85°

19

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Quadrilaterals

a. Any polygon with four sides is called a __________________.

Use figures A-E to answer the following questions.

b. Which quadrilaterals can be called squares? ___________

c. Which can be called rectangles? ____________________

d. Which is a rhombus? ____________

e. The most specific name for figure E is a _______________.

Use the following questions to classify figure F.

f. Is this figure a kite? ______________

g. Is this figure a trapezoid? _________

h. Is this figure a parallelogram? ______

i. Is this figure a rectangle? __________

j. Is this figure a square? ____________

k. This figure can be called a __________, a __________,

a __________, and a __________.

A B C D E

F

Quadrilaterals

a. A kite has two distinct pairs of _______ sides that are ________.

b. A parallelogram has two pairs of ___________ sides.

c. A rectangle has four _______ angles.

d. A square is a rectangle with four ________ sides.

e. Draw an example f. Draw an example

of a kite. of a trapezoid.

The table below gives the measurement of three angles in a

quadrilateral. Find the measurement of the missing angle.

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

20

QuadrilateralABCD

m�A m�B m�C m�D

g. 78° 87° 99° _____

h. 95° 88° _____ 103°

i. 100° _____ 125° 118°

j. _____ 37° 135° 77°

Circles

a. Point O is the ________ of the circle.

b. Name a diameter of the circle.

c. Name two radii of the circle.

d. �BOA is a _________ angle.

e. DE is a _________.

f. In �COA, point O is the ___________.

g. Arc AC is a ________ arc.

h. Name a minor arc. _____________

i. Arc BAC is a __________ arc.

j. Arc MPN is a ___________ arc.

k. If ON is 5 m how long is NP? ______

l. PN is a __________ of the circle.

m. Name a semicircle. _____________

21

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

OA

B

C

D

E

A

B

C

M N

O

P

Name __________________________________ Date ___________________

22

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Circles

a. The center of the circle is point ____.

b. Name a central angle. ______

c. BE is a(n) ______________.

d. AD is a(n) _____________.

e. OA is a(n) ____________.

f. How many radii are drawn? ______

g. How many chords are drawn?

h. How many diameters are drawn?

i. Arc AB is a __________ arc.

j. Arc ADE is a __________ arc.

k. Arc ACD is a __________.

l. The vertex of every central angle is the ________ of the circle.

m. If the radius of a circle is 3.6 mm, the diameter is __________.

n. If the radius of a circle is 18 cm, the diameter is __________.

o. If the radius of a circle is 51

2feet, the diameter is __________.

p. If the diameter of a circle is 11.6 m, the radius is __________.

q. If the diameter of a circle is 1 in, the radius is __________.

AB

C

D

E

O

Prisms

a. Which figures are solid figures? ________________________

b. Which figures are polyhedrons? ________________________

c. Which figures are prisms? _____________________________

d. How many faces does this prism have? ___

e. How many bases does this prism have? ___

f. How many edges does this prism have? ___

g. How many vertices does this prism have? _____

h. What type of prism is this? _____________________________

23

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

AA B C D

E F G H

Prisms

a. Which figures above are polyhedrons? ____________________

b. How many faces are there on the figure on the left?

c. How many edges are there?

d. How many vertices are there?

Complete the chart with the number of faces, edges, and vertices.

Name __________________________________ Date ___________________

24

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

AB

C D

Base ShapeFaces = base sides

+ 2Edges = base sides

x 3Vertices = base

sides x 2

e. Square

f. Pentagon

g. Nonagon

h. Dodecagon

Pyramids

a. What type of pyramid is on the left?

b. �ABE is what part of the figure?

c. AE is a(n) _________ of the figure.

d. Point E is the __________.

e. How many vertices are in the above pyramid?

f. Name the base in the above pyramid.

g. A pyramid has ____________ base(s).

h. What shape is a lateral face on any pyramid?

i. How many faces are there on a pyramid whose base

has 16 sides?

j. How many vertices are there on a pyramid whose

base has 9 sides?

25

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

B

A

D

E

C

Pyramids

a. What shape is the base? __________

b. How many lateral faces are there? ____

c. How many edges are there? _____

d. Point X is called the ________ .

e. What shape is each lateral face? __________

f. Name each lateral face.

Complete the chart with the number of faces, edges, and vertices.

Name __________________________________ Date ___________________

26

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

D

AB

E

X

C

Base ShapeFaces = base sides

+ 1Edges = base sides

x 2Vertices = base

sides + 1

g. Triangle

h. Decagon

i. Dodecagon

j. 20-sided

Cones and Cylinders

a. How many lateral faces does a cone have?

b. The height of the cone is a line segment

that is __________ to the base.

c. In a right circular cone, the height is

measured at the __________ of the

circular base.

d. PJ is the __________.

e. Point P is the __________.

f. The figure on the left is a __________.

g. What shape is the lateral face of this

figure?

h. The shape of a base is a(n) ________.

i. LV is the _________.

j. How many bases does a cone have? _____

k. How many bases does a cylinder have? _____

27

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

P

J

L

V

Cones and Cylinders

a. If you unroll the lateral face of a

cylinder, what shape do you have?

b. What shape are the bases of a

cylinder?

c. How many vertices are there on

a cylinder?

d. The dotted line shows the

__________ of the cone.

e. Is this a right circular cone? _____

f. Name two common items that are shaped like a cylinder.

g. Name two common items that are shaped like a cone.

Name __________________________________ Date ___________________

28

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

29

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Spheres

a. How many bases are on a sphere? _____

b. How many lateral faces on a sphere? ___

c. What shape is a cross section of a sphere? __________

d. The largest cross section of a sphere passes through the __________ of the sphere.

e. Are all cross sections of a sphere the same size? _____

f. What is the difference between a sphere and a circle?

g. Name three common items that are shaped like a sphere.

Spheres

Classify each of the following shapes.

a. _____________ b. _____________

c. _____________ d. _____________

e. _____________ f. _____________

Name __________________________________ Date ___________________

30

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

31

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Line Symmetry

Draw all of the lines of symmetry on each figure.

a.

b.

c. The letters in the word MATH are all symmetrical. Are the letters in your name symmetrical? (Use capital letters.)

d. Which of the numerals 0 - 9 are symmetrical?

Name __________________________________ Date ___________________

32

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Line Symmetry

Draw all of the possible lines of symmetry for each figure.

a. Which figures have no lines of symmetry? __________

b. Which figures have only one line of symmetry? __________

c. Which figures have exactly two lines of symmetry? __________

d. Which figures have three or more lines of symmetry? ________

e. Which figure has the most lines of symmetry? ____________

E FD

A B C

CongruenceCorresponding sides:

a. AB � _______

b. BC � _______

c. CA � _______

Corresponding angles:

d. �A � _______

� ABC � � XYZ e. �B � _______

f. �C � _______

Corresponding sides:

g. PO � _______

h. ON � _______

i. NY � _______

j. YP � _______

Corresponding angles:

k. �P � _______

l. �O � _______

Figure PONY � Figure BEAR m. �N � _______

n. �Y � _______

33

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

A

B

CX

Y

Z

P Y

O N

B R

E A

Name __________________________________ Date ___________________

Congruence

a. JI � ________

b. CY � _______

c. �R � ______

d. �D � ______

Figure JIGR � Figure CODY e. RJ � ________

�DEF � �LMN

f. FD � ________, so the measure of FD is ________.

g NM � ________, so the measure of NM is ________.

h. �N � ________, so the measure of �N is ________.

i. �E � ________, so the measure of �E is ________.

J

I

G

R

O

C Y

D

34

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

D

EF16 cm

60°

L

MN

9 cm

30°

Similarity

a. List the corresponding angles. _____ � _____

_____ � _____

_____ � _____

_____ � _____

b. Write a ratio of the lengths for each pair of corresponding sides.

length of AB = =

length of BC = =

length of WX length of XY

length of CD = =

length of DA = =

length of YZ length of ZW

c. Are figures ABCD and WXYZ similar? ________

d. Similar figures have the same __________, but do not

have to be the same __________.

35

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

CB

DA

X Y

ZW

20

20 40

40

14

2828

1440°

140°

140°

40°

40°

140°

140°

40°

Similarity

a. The corresponding angles of similar figures are __________.

b. The corresponding sides of similar figures are __________.

�ABC � �DEF

c. The measure of �F is _____ .

d. The measure of �B is _____ .

e. The measure of �E is _____ .

f. length of AC = =

length of DF

g. length of DE = _____

h. length of BC = _____

Name __________________________________ Date ___________________

36

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

B

CD

E

FA

15

208

10

36°

37

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Slides (Translations)

a. Which pair of triangles shows a slide? Pair ______

1. 2.

3. 4.

b. Translate the figure 6 units right and6 units down.

c. Translate the figure4 units left and 5 units up.

Name __________________________________ Date ___________________

38

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Slides (Translations)

a. Translate the figure

5 units left.

b. Slide the figure 4 spaces

left and 1 space up.

c. Slide the figure 6 spaces

right and 3 spaces down.

39

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Flips (Reflections)

a. Which pair of triangles shows a flip? Pair ______

1. 2.

3. 4.

b. Reflect the figure

across the given line of

reflection.

c. Reflect the triangle

across the given line

of reflection.

Name __________________________________ Date ___________________

40

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Flips (Reflections)

a. Flip the figure using the

given line of reflection.

b. Reflect the figure

across the given line

of reflection.

c. Flip the figure using the

given line of reflection.

41

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Turns (Rotations)

a. Which pair of triangles shows a turn? Pair ______

1. 2.

3. 4.

b. Which of the following figures is a 90° rotation of figure A? ___

A 1 2 3

c. What are the three types of transformation that do not

change the shape or size of a figure?

__________ __________ __________

d. How many degrees in a full rotation? _____

e. In a rotation, the figure turns around a ________ or _________ .

Name __________________________________ Date ___________________

42

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Turns (Rotations)a. Draw a figure with rotational symmetry.

b. Rotate the figure around the given point of rotation clockwise

90° (quarter turn), 180°(half turn), and 270°(three-quarter turn).

Perimeter

a. Find the perimeter of the figure.

b. This figure is a regular pentagon.

If one side is 4 feet long, what is

the perimeter?

c. Find the perimeter of the triangle.

d. Find the perimeter of the rectangle.

e. Find the perimeter of the square.

43

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

2 c

m

3.3 cm

2 cm

1 cm

1.3 cm 1 cm

5.94

6.4

33 ft

12 ft

7 in

Name __________________________________ Date ___________________

44

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Perimetera. Find the perimeter of the

parallelogram.

Find the missing measurements in each table.

30

20

RECTANGLE length width perimeter

b. 4 ft 2 ft _____

c. _____ 3 in 16 in

d. 6.5 m 4.1 m _____

Triangle side 1 side 2 side 3 perimeter

h. 3 ft 4 ft 5 ft _____

i. _____ 10 in 13 in 29 in

j. 5.7 miles 4.1 miles 4.9 miles _____

SQUARE side perimeter

e. 6 m _____

f. _____ 12 mm

g. 3.2 cm _____

45

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Area: Rectangles and Squares

a. Find the area of the rectangle.

Remember, area is the number of

square units needed to cover a figure.

b. To find the area of a rectangle, you can multiply the

__________ by the __________.

c. To find the area of a square you can multiply the length of

a __________ by itself.

Find the missing measurements in each table.

99 uunniittss

77 uunniittss

RECTANGLE length width area

d. 8 mm 5 mm _____

e. 9 cm 6 cm _____

f. 12 in 3 in _____

g. _____ 8 in 40 in2

SQUARE side length area

h. 9 cm _____

i. 14 in _____

j. _____ 64 in2

Area: Rectangles and SquaresFind the area of the composite figures using the information

you are given.

a. Area of total figure = area of section a + area of section b

Area of total figure = (6 � 7) + (6 � 15)

Area of total figure =

b. Find the area of the same figure

using different sections (sections c and d).

c. Find the area of the composite figure.

Name __________________________________ Date ___________________

46

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

a

b

c

d

6

7

6

15

7

8

6

12

10

6

5

3

Area: Parallelograms

a. To find the area of a parallelogram, multiply the __________ by

the __________.

Find the area of each parallelogram.

b. Area = __________ c. Area = __________

d. Area = __________ e. Area = __________

47

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

7

16

10

10

12

6

90

200

Name __________________________________ Date ___________________

48

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Area: Parallelograms

Find the area of each parallelogram.

a. Area = __________ b. Area = __________

Complete the following table.

0.8 mm

1.6 mm

6 in

15 in

PARALLELOGRAM base height area

c. 17 m 20 m _____

d. 3.5 cm 8 cm _____

e. 1/2 in 3/4 in _____

f. 62 ft 12 ft _____

g. 3 in _____ 27 in2

h. _____ 4 in 16 in2

Area: Triangles

a. �ABC was copied, turned, and pushed up against itself.

What new shape was formed?

b. The area of �ABC is _____ the area of the new parallelogram.

c. To find the area of a triangle, multiply ___ � ______ � ______.

d. The height of a triangle is a __________ line segment from the

__________ to the __________ across from it.

Find the area of each triangle.

e. Area = __________ f. Area = __________

49

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

A

B

C

20

20

20

62

Name __________________________________ Date ___________________

50

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Area: Triangles

Find the area of each triangle.

a. Area = __________ b. Area = _______

Complete the following table.

7

10

9.2

ft

11.5 ft

TRIANGLE base height area

c. 11 m 12 m _____

d. 1.2 cm 8 cm _____

e. 1/2 in 3/4 in _____

f. 100 ft 12 ft _____

g. 3 in _____ 9 in2

h. _____ 2 in 20 in2

51

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Circle Measurementsa. Circumference is the __________ of a circle.

b. The decimal 3.14 and the fraction 22/7 are both used to

approximate the infinite decimal that is known as _____.

c. The formula for the circumference of a circle is C = ______.

d. The formula for the area of a circle is A = ______.

e. The symbol _____ means “approximately equal to.”

f. Find the circumference of a circle

with a diameter of 42 feet. (Hint: Use 22/7 for �)

C �� __________

g. Find the area of a circle

with a diameter of 42 feet.

A �� __________

42 ft

Name __________________________________ Date ___________________

52

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Circle MeasurementFind the circumference and area for each circle.

a. C = �d A = �r2 b.C �� 22

7(21) A �� 22

7(10

12)2

C �� A �� 227

(1012)(10

12)

A ��

c. Find the circumference and area of a circle with a radius

of 2 feet. Use � = 3.14.

d. Use � = 3.14 for this problem. Barney the dog is on a 15 ft.

chain that is staked into the ground. If he runs around in the

biggest circle he can one time, how far does he run?

e. Using the information from the last problem, how much room

does Barney have to play when he is on his chain?

d = 21 m r = 3.5 m

Nets and Surface Area

a. Find the surface area of the rectangular prism. Remember, surface area is the total area of all of the faces.

Surface Area = 2(area front face) + 2(area side face) + 2(area top face)Surface Area = 2(w � h) + 2(l � h) + 2(l � w)Surface Area = 2(6 � 3) + 2(5 � 3) + 2(5 � 6)Surface Area =

b. Find the surface area of the rectangular prism.

c. What is the surface area of a cube with a side length of 10 cm?

53

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

65

312 in

9 in

11 i

n

Name __________________________________ Date ___________________

54

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Nets and Surface AreaUse nets to help find the surface area of the following figures.

a. Find the surface area of this cylinder. Use � = 22/7.

The net has already been drawn for you.

b. Draw a net to find the surface area of a cube with a

side length of 6 units.

rr == 77 iinn

hh == 1122 iinn

Volume Prisms

a. Volume is the amount of __________ something occupies.

b. Volume is measured in __________ units.

c. To find the volume of a rectangular prism,

multiply __________ � __________ � __________.

d. To find the volume of any prism, multiply ________ � ________.

e. Find the volume of the rectangular prism.

f. What is the volume of a cube with a side length of 3 feet?

g. What is the volume of a triangular prism with a height

of 22 inches and base with an area of 12 square inches?

55

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

65

3

Name __________________________________ Date ___________________

56

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Volume: Prisms

Find the volume of each prism.

a. Volume = __________ b. Volume = __________

c. Joe is picking strawberries. His containers are rectangular

prisms that are 5 inches wide, 5 inches long and 4 inches high.

How much does each container hold?

d. A moving van is 36 feet long, 10 feet wide and 12 feet high.

What is the volume of space inside?

8 in

5 in

6 in.

7 cm

7 cm

7 cm

57

Name __________________________________ Date ___________________

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Volume: Cylinders and Cones

a. The volume of a cylinder has the same formula as the volume

for any __________.

b. The formula for the volume of a cylinder is ________ � ________.

c. Find the volume of the cylinder.

Use � = 3.14. (Hint: Find the area

of the circular base first.)

d. A tube has a diameter of 1 inch. If the tube is 12 inches long,

what is the volume of the tube? Use � = 3.14.

e. Mac’s favorite mug is a cylinder that has a base area of

10 square inches and a height of 6 inches. How much coffee

can be put in his mug?

r = 5 cm

h = 10 cm

Name __________________________________ Date ___________________

58

© Enslow Publishers, Inc. Sheets are reproducible for educational use only.

Volume: Cylinders and Cones

a. The volume of a circular cone is _____ the volume of a cylinder

with the same base area and height. (Hint: It’s a fraction.)

b. Find the volume of a circular cone with a diameter of 6 inches

and a height of 15 inches. Use � = 3.14.

Complete the following table. Use 3.14 for �. Round your answers

to the nearest hundredth.

SSoolliiddRRaaddiiuussooff bbaassee

HHeeiigghhttAArreeaa ooff

bbaasseeVVoolluummee

c. cylinder 4 cm 8 cm

d. cone 4 cm 8 cm

e. cylinder 6 mm 12 mm

f. cone 6 mm 12 mm

g. cylinder 9 in 10 in

h. cone 9 in 10 in

AAnnsswweerrss

PPooiinnttss,, LLiinneess aanndd PPllaanneessPage 3: a. ppooiinnttss AA,, BB,, CC,, aanndd DD; b. lliinnee AABB,, lliinnee CCDD,, aanndd lliinnee mm; c. ppllaannee ((aannyy tthhrreeee ppooiinnttss)); d. lliinnee mm; e. lliinnee AABB oorr lliinnee pp; f. lliinnee CCDD;g. lliinnee AABB,, lliinnee CCDD,, lliinnee nn,, aanndd lliinnee pp; h. ppooiinnttss AA,, BB,, CC,, aanndd DD;; i.ppllaannee ((aannyy tthhrreeee ppooiinnttss)); j. lliinnee nn

Page 4: a. AA,, CC,, EE,, aanndd GG; b. AACC,, EEGG,, aanndd mm; c. ppllaannee ((aannyy tthhrreeee ppooiinnttss)); d. EEGG; e. mm; f. oobblliiqquuee; g. lliinnee; h. ppooiinntt; i. ppllaannee; j. oobblliiqquuee; k.vveerrttiiccaall; l. hhoorriizzoonnttaall

RRaayyss aanndd LLiinnee SSeeggmmeennttssPage 5: a. PPoossssiibbllee aannsswweerrss:: rraayy PPRR,, rraayy MMNN,, rraayy NNMM,, rraayy RRPP,, rraayy TTRR,, rraayy TTNN,, rraayy TTMM,, rraayy TTPP; b. PPoossssiibbllee aannsswweerrss:: lliinnee sseeggmmeennttPPTT,, lliinnee sseeggmmeenntt TTRR,, lliinnee sseeggmmeenntt PPRR,, lliinnee sseeggmmeenntt MMNN,, lliinnee sseeggmmeenntt MMTT,, lliinnee sseeggmmeenntt TTNN; c. aa lliinnee sseeggmmeenntt; d. ttwwoo; e. PPoossssiibbllee aannsswweerrss:: lliinnee sseeggmmeenntt AATT,, lliinnee sseeggmmeenntt KKTT,, lliinnee sseeggmmeenntt KKSS,, lliinnee sseeggmmeenntt AAKK,, lliinnee sseeggmmeenntt TTSS; f. PPoossssiibblleeaannsswweerrss:: rraayy TTKK,, rraayy SSKK,, rraayy TTSS,, aanndd rraayy KKSS; g. NNoo; h. YYeess; i. YYeess

Page 6: a-b. CChheecckk ddrraawwiinnggss; c. PPoossssiibbllee aannsswweerrss:: rraayy AADD,, rraayy TTDD,,rraayy AATT,, aanndd rraayy DDTT; d. PPoossssiibbllee aannsswweerrss:: lliinnee sseeggmmeenntt RRAA,, lliinneesseeggmmeenntt RREE,, lliinnee sseeggmmeenntt AAEE,, lliinnee sseeggmmeenntt RRLL,, lliinnee sseeggmmeenntt EELL,,lliinnee sseeggmmeenntt AALL; e. rraayy KKRR; f. rraayy PPLL aanndd rraayy PPTT; g. 33

LLiinnee RReellaattiioonnsshhiippssPage 7: a. ppooiinntt RR; b. ppeerrppeennddiiccuullaarr; c. ppaarraalllleell; d. sskkeeww; e. ppeerrppeennddiiccuullaarr; f. ppaarraalllleell

Page 8: a. lliinnee BBLL; b. ppeerrppeennddiiccuullaarr; c. ppaarraalllleell; d. iinntteerrsseeccttiioonn;

e. ppeerrppeennddiiccuullaarr; f. lliinnee JJUU �� �� lliinnee SSTT; g. ppeerrppeennddiiccuullaarr

AAnngglleessPage 9: a. ��BB,, ��AABBCC,, ��22 oorr ��CCBBAA; b. ppooiinntt BB; c. rraayy BBAA aanndd rraayy BBCC; d. YYeess; e. ��55; f. ��RRTTSS oorr ��SSTTRR; g. ��11 iiss oobbttuussee..; h. ��22 iissaaccuuttee..; i. ��SSTTUU iiss ssttrraaiigghhtt..

Page 10: a. aaccuuttee; b. oobbttuussee; c. rriigghhtt; d. ssttrraaiigghhtt; e. rreefflleexx; f-i. CChheecckkddrraawwiinnggss..

59

. . . .

AAnnggllee RReellaattiioonnsshhiippssPage 11: a. aaddjjaacceenntt; b. 118800°°; c. 9900°°; d. ccoonnggrruueenntt; e. ��22 aanndd ��44; f. ��11 aanndd ��33; g. ��77 aanndd ��88; h. ��55 aanndd ��66

Page 12: a. ��22 aanndd ��33; b. ��22 aanndd ��44; c. 114433°°; d. 6677°°; e. 6655°°; f. 9900°°;g. 4455°°

AAnngglleess ooff IInntteerrsseeccttiinngg LLiinneessPage 13: a. ��11 aanndd ��22,, ��11 aanndd ��33,, ��22 aanndd ��44,, oorr ��33 aanndd ��44; b. ��11aanndd ��44,, ��22 aanndd ��33; c. ssuupppplleemmeennttaarryy; d. ccoonnggrruueenntt; e. lliinneeaarr ppaaiirrss;f. ppooiinntt ooff iinntteerrsseeccttiioonn; g. 336600°°; h. iinntteerrsseeccttiinngg; i. 118800°°; j. vveerrttiiccaallaanngglleess

Page 14: a. 110077°°; b. 110077°°; c. 7733°°; d. ��55 aanndd ��88,, ��66 aanndd ��77; e. ��55aanndd ��66,, ��66 aanndd ��88,, ��55 aanndd ��77,, ��77 aanndd ��88; f. 111133°°; g. 6677°°

PPllaannee FFiigguurreessPage 15: a. NNoo; b. cc; c. aa; d. ff; e. 33; f. dd; g. bb; h. ff; i. 88; j. 1100; k. 55,, 55; l. ssiiddeess; m. vveerrtteexx

Page 16: a-f. CChheecckk ddrraawwiinnggss

TTrriiaanngglleessPage 17: a. ��KKLLMM ((oorr LLMMKK,, MMKKLL,, LLKKMM,, KKMMLL,, oorr MMLLKK)); b. 118800°°; c. ccoonnggrruueenntt; d. ccoonnggrruueenntt; e. aaccuuttee; f. 9900°°; g. ggrreeaatteerr tthhaann 9900°°; h. eeqquuiillaatteerraall; i. iissoosscceelleess; j. ssccaalleennee

Page 18: a. 6633°°; b. 3300°°; c. 6644°°; d. 9900°°; e. 2200°°; f. eeqquuiiaanngguullaarr aannddeeqquuiillaatteerraall; g. rriigghhtt aanndd ssccaalleennee; h. oobbttuussee aanndd ssccaalleennee; i. rriigghhtt aannddiissoosscceelleess

QQuuaaddrriillaatteerraallssPage 19: a. qquuaaddrriillaatteerraall; b. BB; c. AA,, BB,, aanndd DD; d. CC; e. ttrraappeezzooiidd; f. NNoo; g. NNoo; h. YYeess; i. YYeess; j. YYeess; k. qquuaaddrriillaatteerraall,, ppaarraalllleellooggrraamm,,rreeccttaannggllee,, aanndd ssqquuaarree

Page 20: a. aaddjjaacceenntt,, ccoonnggrruueenntt; b. ccoonnggrruueenntt; c. ccoonnggrruueenntt; d.ccoonnggrruueenntt; e-f. CChheecckk ddrraawwiinnggss; g. 9966°°; h. 7744°°; i. 1177°°; j. 111111°°

60

CCiirrcclleessPage 21: a. cceenntteerr; b. lliinnee sseeggmmeenntt BBCC; c. lliinnee sseeggmmeenntt OOAA,, lliinneesseeggmmeenntt OOBB,, oorr lliinnee sseeggmmeenntt OOCC; d. cceennttrraall; e. cchhoorrdd; f. vveerrtteexx; g. mmiinnoorr; h. aarrcc AACC,, aarrcc AABB,, oorr aarrcc BBCC; i. mmiinnoorr; j. mmaajjoorr; k. 1100 mm; l. ddiiaammeetteerr; m. sseemmiicciirrccllee PPMMNN

Page 22: a. OO; b. ��CCOODD oorr ��AAOOCC; c. cchhoorrdd; d. ddiiaammeetteerr; e. rraaddiiuuss;f. 33; g. 33; h. 11; i. mmiinnoorr; j. mmaajjoorr; k. sseemmiicciirrccllee; l. cceenntteerr; m. 77..22 mmmm; n. 3366 ccmm; o. 1111 ffeeeett; p. 55..88 mm; q. 11//22 iinn

PPrriissmmssPage 23: a. AA,, CC,, DD,, EE,, FF,, aanndd HH; b. AA,, DD,, EE,, aanndd HH; c. AA,, DD,, aanndd HH; d. 66; e. 22; f. 1122; g. 88; h. rreeccttaanngguullaarr pprriissmm

Page 24: a. DD; b. 88; c. 1188; d. 1122; e. 66,, 1122,, 88; f. 77,, 1155,, 1100; g. 1111,, 2277,, 1188; h. 1144,, 3366,, 2244

PPyyrraammiiddssPage 25: a. qquuaaddrriillaatteerraall; b. llaatteerraall ffaaccee; c. eeddggee; d. aappeexx; e. 55; f. qquuaaddrriillaatteerraall AABBCCDD; g. oonnee; h. ttrriiaanngguullaarr; i. 1177; j. 1100

Page 26: a. ppeennttaaggoonn; b. 55; c. 1100; d. aappeexx; e. ttrriiaannggllee; f. ��AABBXX,,��BBCCXX,, ��CCDDXX,, ��DDEEXX,, ��EEAAXX; g. 44,, 66,, 44; h. 1111,, 2200,, 1111; i. 1133,, 2244,, 1133; j. 2211,, 4400,, 2211

CCoonneess aanndd CCyylliinnddeerrssPage 27: a. oonnee; b. ppeerrppeennddiiccuullaarr; c. cceenntteerr; d. hheeiigghhtt; e. aappeexx; f. ccyylliinnddeerr; g. rreeccttaannggllee; h. cciirrccllee oorr oovvaall; i. hheeiigghhtt; j. oonnee; k. ttwwoo

Page 28: a. rreeccttaannggllee; b. cciirrccllee oorr oovvaall; c. zzeerroo; d. hheeiigghhtt; e. nnoo; f. AAnnsswweerrss wwiillll vvaarryy..; g. AAnnsswweerrss wwiillll vvaarryy..

SSpphheerreessPage 29: a. zzeerroo; b. oonnee; c. cciirrccllee; d. cceenntteerr; e. nnoo; f. AA sspphheerree iiss aassoolliidd ffiigguurree ((tthhrreeee--ddiimmeennssiioonnaall)) aanndd aa cciirrccllee iiss aa ppllaannee ffiigguurree ((ttwwoo--ddiimmeennssiioonnaall)); g. AAnnsswweerrss wwiillll vvaarryy..

Page 30: a. ccuubbee; b. sspphheerree; c. ppeennttaaggoonnaall ppyyrraammiidd; d. ttrriiaanngguullaarrpprriissmm; e. ppaarraalllleellooggrraamm; f. ccoonnee

61

LLiinnee SSyymmmmeettrryyPage 31: a. b.

c. AAnnsswweerrss wwiillll vvaarryy..; d. 00,, 11,, 33,, aanndd 88

Page 32:

a. FF; b. BB; c. CC; d. AA,, DD,, aanndd EE; e. EE

CCoonnggrruueenncceePage 33: a. lliinnee sseeggmmeenntt XXYY; b. lliinnee sseeggmmeenntt YYZZ; c. lliinnee sseeggmmeennttZZXX; d. ��XX; e. ��YY; f. ��ZZ; g. lliinnee sseeggmmeenntt BBEE; h. lliinnee sseeggmmeenntt EEAA; i. lliinnee sseeggmmeenntt AARR; j. lliinnee sseeggmmeenntt RRBB; k. ��BB; l. ��EE; m. ��AA; n. ��RR

Page 34: a. lliinnee sseeggmmeenntt CCOO; b. lliinnee sseeggmmeenntt JJRR; c. ��YY; d. ��GG; e. lliinnee sseeggmmeenntt YYCC; f. lliinnee sseeggmmeenntt NNLL,, 99 ccmm; g. lliinnee sseeggmmeenntt FFEE,,1166 ccmm; h. ��FF,, 6600°°; i. ��MM,, 3300°°

SSiimmiillaarriittyyPage 35: a. AAWW BBXX CCYY DDZZ; b. BBXX; c. lleennggtthh ooff AABB//lleennggtthh ooff WWXX ==1144//2288 == 11//22,, lleennggtthh ooff BBCC//lleennggtthh ooff XXYY == 2200//4400 == 11//22,, lleennggtthh ooffCCDD//lleennggtthh ooff YYZZ == 1144//2288 == 11//22;; lleennggtthh ooff DDAA//lleennggtthh ooff ZZWW ==2200//4400 == 11//22; d. YYeess; e. sshhaappee,, ssiizzee

Page 36: a. ccoonnggrruueenntt; b. pprrooppoorrttiioonnaall; c. 3366°°; d. 5544°°; e. 5544°°; f.2200//88 == 55//22; g. 66; h. 2255

62

Infinite

SSlliiddeess ((TTrraannssllaattiioonnss))Page 37: a. 11; b. c.

Page 38: a. b. c.

FFlliippss ((RReefflleeccttiioonnss))Page 39: a. 33; b. c.

Page 40: a. b. c.

TTuurrnnss ((RRoottaattiioonnss))Page 41: a. 22; b. 11; c. ttrraannssllaattiioonnss ((sslliiddeess)),, rreefflleeccttiioonnss ((fflliippss)),, aannddrroottaattiioonnss ((ttuurrnnss)); d. 336600°°; e. ttuurrnn cceenntteerr oorr cceenntteerr ooff rroottaattiioonn

Page 42: a. CChheecckk ssttuuddeenntt ddrraawwiinnggss.. b.

63

PPeerriimmeetteerrPage 43: a. 1100..66 ccmm; b. 2200 ffeeeett; c. 1166..33 uunniittss; d. 9900 ffeeeett; e. 2288 iinn

Page 44: a. 110000 uunniittss; b. 1122 fftt; c. 55 iinn; d. 2211..22 mm; e. 2244 mm; f. 33 mmmm; g. 1122..88 ccmm; h. 1122 fftt; i. 66 iinn; j. 1144..77 mmiilleess

AArreeaa:: RReeccttaanngglleess aanndd SSqquuaarreessPage 45: a. 6633 uunniitt22; b. lleennggtthh,, wwiiddtthh; c. ssiiddee; d. 4400 mmmm22; e. 5544 ccmm22;f. 3366 iinn22; g. 55 iinn; h. 8811 ccmm22; i. 119966 iinn22; j. 88 iinn

Page 46: a. 113322 uunniittss22; b. 113322 uunniittss22; c. 7755 uunniittss22

AArreeaa:: PPaarraalllleellooggrraammssPage 47: a. bbaassee,, hheeiigghhtt; b. 111122 uunniittss22; c. 110000 uunniittss22; d. 7722 uunniittss22; e. 1188,,000000 uunniittss22

Page 48: a. 11..2288 mmmm22; b. 9900 iinn22; c. 334400 mm22; d. 2288 ccmm22; e. 33//88 iinn22; f. 774444 fftt22; g. 99 iinn; h. 44 iinn

AArreeaa:: TTrriiaanngglleess

Page 49: a. aa ppaarraalllleellooggrraamm; b. hhaallff; c. 11//22,, bbaassee,, hheeiigghhtt;

d. ppeerrppeennddiiccuullaarr,, bbaassee,, vveerrtteexx; e. 220000 uunniittss22; f. 662200 uunniittss 22

Page 50: a. 3355 uunniittss 22; b. 5522..99 fftt22; c. 6666 mm22; d. 44..88 ccmm22; e. 33//1166 iinn22; f. 660000 fftt22; g. 66 iinn; h. 2200 iinn

CCiirrccllee MMeeaassuurreemmeennttss

Page 51: a. ppeerriimmeetteerr; b. ppii,, oorr �; c. �dd; d. �rr22; e. ��; f. 113322 fftt;

g. 11,,338866 fftt22

Page 52: a. 6666 mm, 334466 11//22 mm22; b. 2222 mm,, 3388 11//22 mm22; c. 1122..5566 fftt,,

1122..5566 fftt22; d. 9944..22 fftt; e. 770066..55 fftt22

NNeettss aanndd SSuurrffaaccee AArreeaa

Page 53: a. 112266 uunniittss22; b. 667788 iinn22; c. 660000 ccmm22

Page 54: a. 883366 iinn22; b. 221166 uunniittss22

64

VVoolluummee:: PPrriissmmss

Page 55: a. ssppaaccee; b. ccuubbiicc c. lleennggtthh,, wwiiddtthh,, hheeiigghhtt; d. bbaassee aarreeaa,,hheeiigghhtt; e. 9900 uunniitt33; f. 2277 fftt33; g. 226644 iinn33

Page 56: a. 224400 iinn33; b. 334433 ccmm33; c. 110000 iinn33; d. 44,,332200 fftt33

VVoolluummee:: CCyylliinnddeerrss aanndd CCoonneessPage 57: a. pprriissmm; b. bbaassee aarreeaa,, hheeiigghhtt; c. 778855 ccmm33; d. 99..4422 iinn33; e. 6600 iinn33

Page 58: a. 11//33; b. 114411..33 iinn33; c. 5500..2244 ccmm22,, 440011..9922 ccmm33; d. 5500..2244 ccmm22,,113333..9977 ccmm33; e. 111133..0044 mmmm22,, 11,,335566..4488 mmmm33 f. 111133..0044 mmmm22,, 445522..1166 mmmm33; g. 225544..3344 iinn22,, 22,,554433..44 iinn33; h. 225544..3344 iinn22,, 884477..88 iinn33

65