lesson perimeter & area of rectangles 6-1 & … · find the perimeter of each figure. a. p...

Copyright © by Holt, Rinehart and Winston. 109 Holt Pre-AlgebraAll rights reserved.

Perimeter & Area of Rectangles & Parallelograms pp. 280–2826-1

LESSON

Vocabulary

perimeter (p. 280)

area (p. 281)

Additional Examples

Example 1

Find the perimeter of each figure.

A.

P � � � � Add all side lengths.

� units

or P � 2b � 2h Perimeter of rectangle

� 2( ) � 2( ) Substitute for b and for h.

� 28 � 10 � units

B.

P � � � �

� units

16

20

5

14

LESSON 6-1 CONTINUED


Example 2

Graph the figure with the given vertices. Then find the area of the figure.

(�1, �2), (2, �2), (2, 3), (�1, 3)

A � bh Area of a rectangle

� � Substitute for b and for h.

� units2

Try This

1. Find the perimeter of the figure.

2. Graph the figure with the given vertices.Then find the area of the figure.

(�1, �1), (3, �1), (5, 3), (1, 3)

x

y

6

11

x

y


Perimeter and Area of Triangles and Trapezoids pp. 285–2866-2

LESSON

Additional Examples

Example 1

Find the perimeter of each figure.

A.

P � � � Add all sides.

� units

B.

P � � � � Add all sides.

� units

Example 2

Graph and find the area of each figure with thegiven vertices.

A. (�2, 2), (4, 2), (0, 5)

A � �12� bh of a triangle

� �12� � � Substitute for b and h.

� units2

17

11

8 6

10

4 7

x

y



B. (�1, �2), (5, �2), (5, 2), (�1, 6)

A � �12�h(b1 � b2) Area of a

� �12� � ( � ) Substitute for h, b1, and b2.

� units2

Try This

1. Find the perimeter of the figure.

2. Graph and find the area of the figure with thegiven vertices.

(�2, �1), (0, 5), (3, 5), (5, �1)

x

y

16

22

6 5

x

y


The Pythagorean Theorempp. 290–2916-3

LESSON

Vocabulary

Pythagorean Theorem (p. 290)

legs (p. 290)

hypotenuse (p. 290)

Additional Examples

Example 1

Find the length of the hypotenuse.

a2 � b2 � c 2 Theorem

2

�

2

� c 2 Substitute for a and b.

� � c 2 Simplify powers.

� c 2

� c Solve for c ; c � �c 2� .

� c

5

c4



Example 2

Solve for the unknown side in the right triangle.

a2 � b2 � c 2 Theorem

2

� b2 � Substitute for a and c.

� b2 � Simplify powers.

� �

b2 �

b � �576� � 24

Try This

1. Find the length of the hypotenuse.

2. Solve for the unknown side in the right triangle.

7

b25

7

c5

4

b12


Circlespp. 294–2956-4

LESSON

Vocabulary

circle (p. 294)

radius (p. 294)

diameter (p. 294)

circumference (p. 294)

Additional Examples

Example 1

Find the circumference of each circle, both in terms of � and to thenearest tenth. Use 3.14 for �.

A. circle with a radius of 4 m

C � 2�r

� 2�( )

� � m � m

B. circle with a diameter of 3.3 ft

C � �d

� �( )

� � ft � ft



Example 2

Find the area of each circle, both in terms of � and to the nearest tenth.Use 3.14 for �.

A. circle with a radius of 4 in.

A � �r 2 � �(2

)

� � in2 � in2

B. circle with a diameter of 3.3 m

A � �r 2 � �(2

) �d2� �

� � m2 � m2

Try This

1. Find the circumference of the circle, both in terms of � and to thenearest tenth. Use 3.14 for �.

circle with a diameter of 4.25 in.

2. Find the area of each circle, both in terms of � and to the nearesttenth. Use 3.14 for �.

circle with a radius of 8 cm


Drawing Three-Dimensional Figurespp. 302–3036-5

LESSON

Vocabulary

face (p. 302)

edge (p. 302)

vertex (p. 302)

perspective (p. 303)

vanishing point (p. 303)

horizon line (p. 303)

Additional Examples

Example 1

Use isometric dot paper to sketch a rectangular box that is 5 units long, 3units deep and 2 units tall.

Step 1: Lightly draw the edges of the bottom face. It willlook like a parallelogram.

units by units

Step 2: Lightly draw the vertical line segments from thevertices of the base.

units high

Step 3: Lightly draw the top face by connecting the vertical lines to form aparallelogram.

units by units



Step 4: Darken the lines. Use lines for the edges that are

visible and lines for the edges that are hidden.

Example 2

Sketch a one-point perspective drawing of a cube.

Step 1: Draw a square. This will be the front face.

Label the A through D.

Step 2: Mark a point V

above your square, and draw a dashed line from each vertexto V.

Step 3: Choose a point G on BV�� and draw a smaller squarethat has G as one of its vertices.

Step 4: Darken the visible edges, and draw dashed segments

for the hidden edges. Erase the point and the lines

connecting it to the vertices.

Try This

1. Use isometric dot paper to sketch a rectangular box that is 4 unitslong, 2 units deep and 3 units tall.

GB

D C

A


Volume of Prisms and Cylinderspp. 307–3096-6

LESSON

Vocabulary

prism (p. 307)

cylinder (p. 307)

Additional Examples

Example 1

Find the volume of each figure to the nearest tenth.

A. A rectangular prism with base 2 cm by 5 cm and height 3 cm.

B � � � cm2 Area of

V � Bh of a prism

� �

� cm3

B.B � �(

2

) � � in2 of base

V � Bh Volume of a

� � �

� � � in3

12 in.

4 in.



Example 4

Find the volume of the barn.

� �

V � (40)(50)(15) � �12�(40)(10)(50)

� �

� ft3

The volume is 40,000 ft3.

Try This

1. Find the volume of the figure to the nearest tenth.

2. Find the volume of the figure.

Volume oftriangular prism

Volume ofrectangular prism

Volume of barn

40 ft50 ft

15 ft10 ft

15 cm

8 cm

8 ft3 ft

4 ft

5 ft


Volume of Pyramids and Conespp. 312–3136-7

LESSON

Vocabulary

pyramid (p. 312)

cone (p. 312)

Additional Examples

Example 1

Find the volume of each figure.

A.B � �

12�( � ) � cm 2

V � �13� � � V � �

13�Bh

V � cm3

B.B � �(

2

) � � in2

V � �13� � � � V � �

13�Bh

V � � � in3 Use 3.14 for .3 in.

10 in.

4 cm

6 cm

7 cm



Example 2

A cone has a radius of 3 ft. and a height of 4 ft. Explain whether triplingthe height would have the same effect on the volume of the cone astripling the radius.

When the height of the cone is tripled, the volume is . When

the radius is tripled, the volume becomes times the original volume.

Try This

1. Find the volume of the figure.

2. A cone has a radius of 2 m and a height of 5 m. Explain whetherdoubling the height would have the same effect on the volume of thecone as doubling the radius.

V � �13��r2h V � �

13��r2(3h) V � �

13��(3r)2h

� �13��(32)4 � �

13��(32)(3 � 4) � �

13��(3 � 3)2(4)

� � �

OriginalDimensions Triple the Height Triple the Radius

3 m

7 m


Surface Area of Prisms and Cylinderspp. 316–3176-8

LESSON

Vocabulary

surface area (p. 316)

lateral face (p. 316)

lateral surface (p. 316)

Additional Examples

Example 1

Find the surface area of each figure.

A.

S � 2�r 2 � 2�rh

� 2�(2

) � 2�( )( )

� � in2 � in2

B.

S � 2B � P � 2( � � ) � ( )( )

� ft2

10 ft3 ft

8 ft

5 ft

5 ft

6 in.

4 in.



Example 2

A cylinder has diameter 8 in. and height 3 in. Explain whether tripling theheight would have the same effect on the surface area as tripling the radius.

They have the same effect. Tripling the radius would

increase the surface area than tripling the height.

Try This

1. Find the surface area of the figure.

2. A cylinder has diameter 6 in. and height 2 in. Explain whether doublingthe height would have the same effect on the surface area as doublingthe radius.

15 cm

3 cm

S � 2�r2 � 2�rh S � 2�r2 � 2�r(3h) S � 2�(3r)2 � 2�(3r)h� 2�(4)2 � 2�(4)(3) � 2�(4)2 � 2�(4)(9) � 2�(12)2 � 2�(12)(3)

� 56� in2 � � 104� in2 � � 360� in2 �

OriginalDimensions Triple the Height Triple the Radius


Surface Area of Pyramids and Conespp. 320–3216-9

LESSON

Vocabulary

slant height (p. 320)

regular pyramid (p. 320)

right cone (p. 320)

Additional Examples

Example 1

Find the surface area of each figure.

A. S � B � �12�Pl

� ( � ) � �12�( )( )

� ft2

B. S � �r 2 � �r l

� �(2

) � �( )( )

� � � cm2

6 cm

3 cm

2.4 ft

3 ft

2.4 ft



Example 2

A cone has diameter 8 in. and slant height 3 in. Explain whether triplingthe slant height would have the same effect on the surface area astripling the radius.

They have the same effect. Tripling the radius would

increase the surface area than tripling the slant height.

Try This

1. Find the surface area of the figure.

2. A cone has diameter 9 in. and a slant height 2 in. Explain whethertripling the slant height would have the same effect on the surface areaas tripling the radius.

S � �r2 � �rl S � �r2 � �r(3l) S � �(3r)2 � �(3r)l� �(4)2 � �(4)(3) � �(4)2 � �(4)(9) � �(12)2 � �(12)(3)

� 28� in2 � � 52� in2 � � 180� in2 �

Original Triple the Dimensions Slant Height Triple the Radius

5 m

3 m3 m


Spherespp. 324–3256-10

LESSON

Vocabulary

sphere (p. 324)

hemisphere (p. 324)

great circle (p. 324)

Additional Examples

Example 1

Find the volume of a sphere with radius 9 cm, both in terms of � and tothe nearest tenth of a unit.

V � ��43��r 3 of a sphere

� ��43��(

3

) Substitute for r.

� � cm3 � cm3

Example 2

Find the surface area, both in terms of � and to thenearest tenth of a unit.

S � 4�r 2 area of a sphere

� 4�(2

) Substitute for r.

� � in2 � in2

3 in.



Example 3

Compare the volume and surface area of a sphere with radius 42 cm withthose of a rectangular prism measuring 44 � 84 � 84 cm.

The sphere and the prism have approximately the same ,

but the prism has a surface area.

Try This

1. Find the volume of a sphere with radius 3 cm, both in terms of � and tothe nearest tenth of a unit.

2. The moon has a radius of 1,738 km. Find the surface area, both interms of � and to the nearest tenth.

Sphere:

V � ��43��r 3 � ��

43��(

3

)

� ��43��

272��

� cm3

S � 4�r 2 � 4�(2

)

� �

� ��272��

� cm2

Rectangular Prism:

V � lwh

� ( )( )( )

� cm3

S � 2lw � 2lh � 2wh

� 2( )( ) �

2( )( ) �

2( ) ( )

� cm2

Chapter 6Vocabulary Chain

EXAMPLE TERM

circumference

EXAMPLE TERM

perimeter

EXAMPLE TERM

hypotenuse

EXAMPLE TERM

Pythagorean Theorem

EXAMPLE TERM

surface area

Directions1. Write an example and an explanation in words, numbers, and algebra for each term.

2. Cut out each vocabulary strip and fold in thirds.

3. Punch a hole in the corner of each folded vocabulary strip, and string them togetherto create your vocabulary chain.

Developed in cooperation with The Bag Ladies. 129 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. All rights reserved.

Chapter 6Vocabulary Chain

WORDS ALGEBRA

WORDS ALGEBRA

WORDS ALGEBRA

WORDS ALGEBRA

WORDS ALGEBRA

NUMBERS

NUMBERS

NUMBERS

NUMBERS

NUMBERS

Developed in cooperation with The Bag Ladies. 130 Holt Pre-AlgebraCopyright © by Holt, Rinehart and Winston. All rights reserved.

lesson perimeter & area of rectangles 6-1 & … · find the perimeter of each figure. a. p...

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