Area: Parallelograms

1
Area Parallelograms
PRE-ALGEBRA LESSON 10-1
It takes 126 ft of fence to enclose a field that
is twice as long as it is wide. What is the area
of the field?
882 ft2
10-1
2
Area Parallelograms
PRE-ALGEBRA LESSON 10-1
(For help, go to Lesson 3-4.)
Use A w and find the third value. 1. A
54 in.2, w 6 in. 2. 35 m, w 7 m 3. A
25 cm2, 2.5 cm 4. 7.2 ft, w 7.2 ft
Check Skills Youll Need
10-1
3
Area Parallelograms
PRE-ALGEBRA LESSON 10-1
Solutions 1. A w 2. A w 54 6 A
35 7 9 in. A 245 m2 3. A
w 4. A w 25 2.5w A 7.2 7.2 w 10
cm A 51.84 ft2
10-1
4
Area Parallelograms
PRE-ALGEBRA LESSON 10-1
Find the area of the rectangle.
Step 1 Change the units so that they are the
same. 150 cm 1.5 m Change 150 centimeters
to meters.
Step 2 Find the area.
A bh Use the formula for area of a
rectangle.
(4)(1.5) Replace b and h with the
dimensions 4 and 1.5.
6 Simplify.
The area of the rectangle is 6 m2.
Quick Check
10-1
5
Area Parallelograms
PRE-ALGEBRA LESSON 10-1
Find the area of each parallelogram.
a.
b.
The area is 16 m2.
The area is 15 in.2.
Quick Check
10-1
6
Area Parallelograms
PRE-ALGEBRA LESSON 10-1
Find each area. 1. rectangle
ABFE 2. parallelogram ACFD 3. a
rectangle with a base of 50 cm and a height of 5
cm
40 cm2
48 cm2
250 cm2
10-1
7
Area Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Find the area of a rectangle that is 3 ft
wide and twice as high.
10-2
8
Area Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
(For help, go to Lesson 5-4.)
Find each product. 1. 16 2. 14
6 3. 5 15 4. 2 8
Check Skills Youll Need
10-2
9
Area Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Solutions 1. 16 2. 14 6
168 8 147 6 7  6
42 3. 5 15 4. 2 8
75 37 8
82 5 2 10
1 21
1 21
1 21
5 21
10-2
10
Area Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Find the area of the triangle.
39 Simplify.
Quick Check
The area is 39 in.2.
10-2
11
Area Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Find the area of the figure.
Add to find the total 450 1,350 1,800.
Quick Check
The area of the figure is 1,800 cm2.
10-2
12
Area Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Suppose that, through the years, a layer of silt
and mud settled in the bottom of the Erie Canal.
Below is the resulting cross section of the
canal. Find the area of the trapezoidal cross
section.
106.5
Quick Check
The area of the cross section is 106.5 ft2.
10-2
13
Area Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Find each area. 1. trapezoid
PQRU 2. triangle PTU 3. triangle
QRS 4. trapezoid PQSU
192 ft2
20 ft2
28 ft2
164 ft2
10-2
14
Area Circles
PRE-ALGEBRA LESSON 10-3
Explain how this pattern works. (15,873 ? 7) ? 2
(222,222) (15,873 ? 7) ? 3
(333,333) (15,873 ? 7) ? 4 (444,444)
because (15,873 ? 7) ? 1 (111,111)
10-3
15
Area Circles
PRE-ALGEBRA LESSON 10-3
(For help, go to Lesson 4-7.)
Simplify each expression. 1. 3.14 42 2. 3.14
52 3. 3.14 92 4. 3.14 0.52
Check Skills Youll Need
10-3
16
Area Circles
PRE-ALGEBRA LESSON 10-3
Solutions 1. 3.14 42 2. 3.14 52 3.14
4 4 3.14 5 5 50.24
78.5 3. 3.14 92 4. 3.14 0.52 3.14 9
9 3.14 0.5 0.5 254.34 0.785
10-3
17
Area Circles
PRE-ALGEBRA LESSON 10-3
Find the exact area of a circle with diameter 20
in.
Quick Check
10-3
18
Area Circles
PRE-ALGEBRA LESSON 10-3
A TV stations weather radar can detect
precipitation in a circular region having a
diameter of 100 mi. Find the area of the region.
7,850 approximate area
The area of the region is about 7,850 mi2.
Quick Check
10-3
19
Area Circles
PRE-ALGEBRA LESSON 10-3
A pound of grass seed covers approximately 675
ft2. Find the area of the lawn below. Then find
the number of bags of grass seed you need to buy
to cover the lawn. Grass seed comes in 3-lb bags.
10-3
20
Area Circles
PRE-ALGEBRA LESSON 10-3
(continued)
Area of region that is a rectangle area of
rectangle bh A 45 25 Replace b with 45 and
h with 25. 1,125 ft2
The area of the lawn is about 177 ft2 1,125 ft2
1,302 ft2.
You need to buy one 3-lb bag of grass seed.
Quick Check
10-3
21
Area Circles
PRE-ALGEBRA LESSON 10-3
Find the area. 1. Find the exact area of a
circle with diameter 32 in. 2. A
5-ft-diameter round table is in a 12 ft-by-15 ft
room. a. What is the area covered by the table?
Round to the nearest unit. b. What is the
area of the rest of the room? Round to the
nearest unit.
20 ft2
160 ft2
10-3
22
Space Figures
PRE-ALGEBRA LESSON 10-4
Find the area of a square 15.7 mm on each side.
246.49 mm2
10-4
23
Space Figures
PRE-ALGEBRA LESSON 10-4
(For help, go to Lesson 9-3.)
Judging by appearance, classify each
polygon. 1. 2. 3. 4.
Check Skills Youll Need
10-4
24
Space Figures
PRE-ALGEBRA LESSON 10-4
Solutions 1. triangle 2. square 3. rectangle
4. hexagon
10-4
25
Space Figures
PRE-ALGEBRA LESSON 10-4
For each figure describe the bases and name the
figure.
a.
b.
The bases are circles.
The bases are rectangles.
The figure is a cylinder.
The figure is a rectangular prism.
Quick Check
10-4
26
Space Figures
PRE-ALGEBRA LESSON 10-4
Name the space figure you can form from each net.
a.
b.
With two hexagonal bases and rectangular sides,
you can form a hexagonal prism.
With a rectangular base and triangular sides, you
can form a rectangular pyramid.
Quick Check
10-4
27
Space Figures
PRE-ALGEBRA LESSON 10-4
Describe the base(s) and name each
solid. 1. 2. 3. Name the solid you
can form from this net.
circular base cone
triangular bases triangular prism
octagonal pyramid
10-4
28
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
A prism has 7 faces and 10 vertices. How many
edges does the prism have?
15
10-5
29
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
(For help, go to Lesson 9-6.)
Find the circumference of each circle with the
given radius or diameter. 1. r 5 in. 2. r
4.2 cm 3. d 8 ft 4. d 6.8 in.
Check Skills Youll Need
10-5
30
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Solutions 1. C 2 r 2. C 2 r C
2(3.14)(5 in.) C 2(3.14)(4.2 cm) C 31.4
in. C 26.4 cm 3. C d 4. C d C
(3.14)(8 ft) C (3.14)(6.8 in.) C 25.1
ft C 21.3 in.
10-5
31
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of the rectangular prism
using a net.
Draw and label a net.
60 60 150 90 150 90 600 Add the
areas.
Quick Check
The surface area is 600 cm2.
10-5
32
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of the rectangular prism.
Step 2 Find the surface area. S.A. L.A. 2B
440 2(5 6) L.A. 440 and B
5 6 440 60 500
Quick Check
The surface area of the rectangular prism is 500
in.2.
10-5
33
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of the cylindrical water
tank.
Quick Check
The surface area of the water tank is about 1,156
ft2.
10-5
34
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of each figure rounded to
the nearest whole unit. 1. triangular prism
with base perimeter 24 cm, base area 24 cm2, and
height 15 cm 2. rectangular prism with base
perimeter 30 cm, base area 50 cm2, and height
150 cm 3. cylindrical candle with radius 2
cm and height 16 cm
408 cm2
4,600 cm2
about 226 cm2
10-5
35
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Give the number of faces, edges, and vertices of
a rectangular prism.
6 faces, 12 edges, 8 vertices
10-6
36
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
(For help, go to Lesson 5-4.)
Use the Order of Operations to simplify each
expression. 1. (9 ) (8 ) 2.
(12 ) (15 ) 3. (24 ) (3
) 4. (32 ) (14 )
Check Skills Youll Need
10-6
37
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Solutions 1. 93 84 2.
6 4 9
6 10 15 3. 244
31 4. 324
4 20 2 5 22
2 31
3 41
2 51
1 61
1 71
1 31
5 81
10-6
38
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Find the surface area of the square pyramid.
Step 2 S.A. L.A. B
80 52 Lateral area 80 and B
52. 80 25 105
Quick Check
The surface area of the pyramid is 105 m2.
10-6
39
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Find the surface area of the cone.
Quick Check
The surface area of the cone is about 94 m2.
10-6
40
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Earth has an average radius of 3,963 mi. What is
Earths approximate surface area to the nearest
1,000 mi2? Assume that Earth is a sphere.
197,259,434.64 Multiply.
Quick Check
The surface area of Earth is about 197,259,000
mi2.
10-6
41
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Find the surface area of each space figure. Round
to the nearest whole unit. 1. a square pyramid
with base edge 80 m and slant height 100 m
2. a cone with slant height 22 cm and
radius 7 cm 3. a sphere with radius 12 cm
22,400 m2
about 637 cm2
about 1,809 cm2
10-6
42
Volume Prisms and Cylinders
PRE-ALGEBRA LESSON 10-7
Use graph paper. Design and draw a diagram to
determine which has the greater areaa square
with sides 10 cm or a circle with a diameter 10
cm?
Draw a circle within the square to prove that the
square has the greater area.
10-7
43
Volume Prisms and Cylinders
PRE-ALGEBRA LESSON 10-7
(For help, go to Lesson 10-3.)
Find the area of each circle. 1. 2. 3.
Check Skills Youll Need
10-7
44
Volume Prisms and Cylinders
PRE-ALGEBRA LESSON 10-7
Solutions (82)( ) (122)(
) 64(3.14) 144(3.14)
201 cm2 452.2 cm2
(20) 10 A r2 (102)( )
100(3.14) 314 cm2
10-7
45
Volume Prisms and Cylinders
PRE-ALGEBRA LESSON 10-7
Find the volume of the triangular prism.
V Bh Use the formula for volume.
1,260 Simplify.
The volume is 1,260 cm3.
Quick Check
10-7
46
Volume Prisms and Cylinders
PRE-ALGEBRA LESSON 10-7
Find the volume of the juice can, to the nearest
cubic centimeter.
V Bh Use the formula for volume.
580.7744 Simplify.
Quick Check
The volume is about 581 cm3.
10-7
47
Volume Prisms and Cylinders
PRE-ALGEBRA LESSON 10-7
Find the volume of each space figure. 1.
rectangular prism with base 12 m by 14 m and
height 50 m 2. cylindrical pool with
diameter 24 ft and height 4 ft 3. right
triangular prism with base legs 8 cm and 10 cm
and height 20 cm
8,400 m3
about 1,808.64 ft3
800 cm3
10-7
48
Problem Solving Strategy Make a Model
PRE-ALGEBRA LESSON 10-8
A roll of wallpaper is 24 in. wide. You used all
but 4 ft of one roll. Another roll has 7 ft
of wallpaper on it. What is the total area you
can cover with the remaining wallpaper?
10-8
49
Problem Solving Strategy Make a Model
PRE-ALGEBRA LESSON 10-8
(For help, go to Lesson 9-3.)
Draw each figure described below. 1. a
rectangle with small squares drawn in each
corner 2. a rectangle divided into eight
congruent rectangles 3. two parallelograms
that have different shapes but the same perimeter
Check Skills Youll Need
10-8
50
Problem Solving Strategy Make a Model
PRE-ALGEBRA LESSON 10-8
Solutions Answers may vary. Samples 1.
2. 3.
10-8
51
Problem Solving Strategy Make a Model
PRE-ALGEBRA LESSON 10-8
A can company rolls rectangular pieces of metal
that measure 8 in. by 10 in. to make the sides of
cans. Which height, 8 in. or 10 in., will make
the can with the greater volume?
Build two cans using 8 in.-by-10 in. pieces of
paper. You do not need to make the bases, just
the sides.
10-8
52
Problem Solving Strategy Make a Model
PRE-ALGEBRA LESSON 10-8
(continued)
not to scale
Quick Check
The volume of the can with height 8 in. is
greater.
10-8
53
Problem Solving Strategy Make a Model
PRE-ALGEBRA LESSON 10-8
Solve. 1. You cut square corners from a piece
of cardboard that has dimensions 32 cm by 40
cm. You then fold the cardboard to create a box
with no lid. To the nearest centimeter, what are
the dimensions of the box that will have the
greatest volume?
20 cm by 28 cm by 6 cm
10-8
54
Volume Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9

• Multiply. Write each answer in simplest form.
• a. 3 ?
• b. 1 ? 2
• c. ?

12
55
Volume Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
(For help, go to Lesson 5-4.)
Multiply. 1. (3.14)(2)2(5) 2.
(4)2(6) 3. (3.14)(2)3 4. (3.14)(0.5)3
Check Skills Youll Need
56
Volume Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Solutions 1. (3.14)(22)(5)
(3.14)(4)(5) 2. (42)(6) (16)(6)
(62.8)
(96) 20.93
32 3. (3.14)(23) (3.14)(8) 4.
(3.14)(0.5)3 (3.14)(0.125)
(25.12)
(0.3925) 33.493
0.523
57
Volume Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Find the volume of the cone.
50.24 Simplify.
Quick Check
The volume of the cone is about 50 in.3.
58
Volume Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Find the volume of the square pyramid.
256 Simplify.
Quick Check
The volume of the pyramid is 256 in.3.
59
Volume Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Earth has an average radius of 3,963 mi. What is
Earths approximate volume to the nearest
1,000,000 mi3? Assume that Earth is a sphere.
The volume of the Earth is about 260,580,000,000
mi3.
Quick Check
60
Volume Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Find the volume of each space figure to the
nearest unit. 1. a cone with diameter 9 cm and
height 12 cm 2. a square pyramid with base
edges 12 m and height 18 m 3. a basketball
with diameter 10 in.
about 254 cm2
864 m3
about 523 in.3
10-9