1. wide. What is the area of the field?
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. Use A = w and find the third value.
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 = 35 m, w = 7 m
3. A = 25 cm2, = 2.5 cm = 7.2 ft, w = 7.2 ft
Check Skills You’ll Need
10-1

3. Area: Parallelograms Solutions 1. A = w 2. A = w 54 = 6 A = 35 • 7
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 = ft2
10-1

4. Find the area of the rectangle.
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 and 1.5.
= 6 Simplify.
The area of the rectangle is 6 m2.
Quick Check
10-1

5. Find the area of each parallelogram.
Area: Parallelograms
PRE-ALGEBRA LESSON 10-1
Find the area of each parallelogram. a. b.
A = bh area formula
A = bh
= (8)(2) Substitute.
= (2.5)(6)
= 16 Simplify.
= 15
The area is 16 m2.
The area is 15 in.2.
Quick Check
10-1

6. 3. a rectangle with a base of 50 cm and a height of 5 cm 40 cm2
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
1 2
Find the area of a rectangle that is ft wide and twice as high.
24 ft2
1 2
10-2

8. Area: Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
(For help, go to Lesson 5-4.)
Find each product.
1. • • 14 • 6
3. • 5 • • 2 • 8 1 2 1 2 1 2 1 2 1 2
Check Skills You’ll Need
10-2

9. Area: Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Solutions
1. • • 14 • 6
• 168 = • 147 • 6
7 • 6 = 42
3. • 5 • • 2 • 8
• 75 = • • 8
• • 82
5 • 2 = 10 1 2 1 2 1 21 1 21 1 2 1 2 1 2 1 2 1 2 1 2 5 2 1 21 5 21
10-2

10. Area: Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Find the area of the triangle.
A = bh Use the formula for area of a triangle. 1 2
= • 13 • 6 Replace b with 13 and h with 6. 1 2
= 39 Simplify.
The area is 39 in.2.
Quick Check
10-2

11. Area: Triangles and Trapezoids
PRE-ALGEBRA LESSON 10-2
Find the area of the figure.
Area of triangle
A = bh 1 2
= • 45 • 20
= 450
Area of rectangle
A = bh
= 45 • 30
= 1,350
Add to find the total: ,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.
A = h(b1 + b2)
Use the formula for the area of a trapezoid. 1 2
A = • 3( )
Replace h with 3, b1 with 31, and b2 with 40. 1 2
= • 3(71)
Simplify. 1 2
= • 213 1 2 =
Quick Check
The area of the cross section is 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. Explain how this pattern works. (15,873  7)  2 = (222,222)
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. 1. 3.14 • 42 2. 3.14 • 52 Area: Circles Simplify each expression.
PRE-ALGEBRA LESSON 10-3
(For help, go to Lesson 4-7.)
Simplify each expression.
• • 52
• • 0.52
Check Skills You’ll Need
10-3

16. 1. 3.14 • 42 2. 3.14 • 52 Area: Circles Solutions
PRE-ALGEBRA LESSON 10-3
Solutions
• • 52
= 3.14 • 4 • 4 = 3.14 • 5 • 5
= = 78.5
• • 0.52
= 3.14 • 9 • 9 = 3.14 • 0.5 • 0.5
= = 0.785
10-3

17. Find the exact area of a circle with diameter 20 in.
Area: Circles
PRE-ALGEBRA LESSON 10-3
Find the exact area of a circle with diameter 20 in.
A = r 2
= (10)2 r = d; r = 10 1 2
= Simplify.
The area is in.2.
Quick Check
10-3

18. The area of the region is about 7,850 mi2.
Area: Circles
PRE-ALGEBRA LESSON 10-3
A TV station’s weather radar can detect precipitation in a circular region having a diameter of 100 mi. Find the area of the region.
A = r 2
= (50)2 r = d; r = 50 1 2
= 2,500 exact area
(2,500)(3.14) Use 3.14 for .
= 7,850 approximate area
The area of the region is about 7,850 mi2.
Quick Check
10-3

19. Area of region that is one fourth of a circle: area of circle = r 2
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.
Area of region that is one fourth of a circle:
area of circle = r 2
area of quarter circle = r 2
A (3.14)(15)2 Replace with 3.14 and r with 15.
= ft2 1 4
10-3

20. Area of region that is a rectangle: area of rectangle = bh
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.
1,302 ÷ Divide to find the number of pounds of seed.
You need to buy one 3-lb bag of grass seed.
Quick Check
10-3

21. 1. Find the exact area of a circle with diameter 32 in.
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.
in.2
20 ft2
160 ft2
10-3

22. Find the area of a square 15.7 mm on each side.
Space Figures
PRE-ALGEBRA LESSON 10-4
Find the area of a square 15.7 mm on each side.
mm2
10-4

23. Judging by appearance, classify each polygon. 1. 2.
Space Figures
PRE-ALGEBRA LESSON 10-4
(For help, go to Lesson 9-3.)
Judging by appearance, classify each polygon.
Check Skills You’ll Need
10-4

24. Space Figures Solutions 1. triangle 2. square 3. rectangle 4. hexagon
PRE-ALGEBRA LESSON 10-4
Solutions
1. triangle 2. square
3. rectangle 4. hexagon
10-4

25. For each figure describe the bases and name the figure.
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. Name the space figure you can form from each net.
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. Describe the base(s) and name each solid. 1. 2.
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 You’ll 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.
Find the area of each rectangle in the net.
Draw and label a net.
= 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 1 Find the lateral area.
L.A. = ph Use the formula for lateral area.
= ( ) p = and h = 20
= 440
Step 2 Find the surface area.
S.A. = L.A. + 2B
= (5 • 6) L.A. = 440 and B = 5 • 6 =
= 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.
Step 1 Find the lateral area.
L.A. = rh Use the formula for lateral area.
2(3.14)(8)(15)
754
Step 2 Find the surface area.
S.A. = L.A B Use the formula for surface area.
= L.A ( r 2)
(3.14)(8)2
1,156
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 ) (12 ) + (15 )
3. (24 ) + (3 ) (32 ) + (14 ) 2 3 1 2 3 4 2 5 1 6 1 3 5 8 1 7
Check Skills You’ll Need
10-6

37. Surface Area: Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Solutions
• • • •
= =
= 10 = 15
• • • •
= =
= 5 = 22 2 31 1 21 3 41 2 51
123
153 1 61 1 31 5 81 1 71
142
10-6

38. Surface Area: Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Find the surface area of the square pyramid.
Step 1 L.A. = p Use the formula for lateral area. 1 2
= • 20 • 8 = p = 4(5) and = 8.
Step 2 S.A. = L.A. + B
= Lateral area = 80 and B = 52.
= = 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.
Step 1 L.A. = r Use the formula for lateral area.
3.14(3)(7) r = 3 and = 7. =
Step 2 S.A. = L.A. + B Use the formula for surface area.
(3) L.A and B = (3)2. = =
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 Earth’s approximate surface area to the nearest 1,000 mi2? Assume that Earth is a sphere.
S.A. = r 2 Use the formula for surface area.
4(3.14)(3,963)2 r ,963
= 197,259, Multiply.
197,259,000 Round to nearest 1,000.
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 area—a 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.
Check Skills You’ll Need
10-7

44. Volume: Prisms and Cylinders
PRE-ALGEBRA LESSON 10-7
Solutions
= (82)( ) = (122)( )
= 64(3.14) = 144(3.14)
201 cm cm2
3. r = d 1 2
1. A = r2
2. A = r2 1 2
= (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.
= 63 • B = • 9 • 14 = 63 cm2 1 2
= 1, 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.
V = r 2h B = r 2
3.14 • 3.42 • Replace r with 3.4, and h with 16.
= 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, ft3
800 cm3
10-7

48. Problem Solving Strategy: Make a Model
PRE-ALGEBRA LESSON 10-8
1 2
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?
1 3
23 ft2
2 3
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 You’ll Need
10-8

50. Problem Solving Strategy: Make a Model
PRE-ALGEBRA LESSON 10-8
Solutions
Answers may vary. Samples: 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.
not to scale
10-8

52. Problem Solving Strategy: Make a Model
PRE-ALGEBRA LESSON 10-8
(continued)
not to scale
Measure your models to find approximate radii.
Radius of 10-in. high can in.
Radius of 8-in. high can in.
V = r 2h
(3.14)(1.32)(10)
53.1 in.3
(3.14)(1.62)(8)
64.3 in.3
Find the volumes.
The volume of the can with height 8 in. is greater.
Quick Check
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 
b  2
c. 
3 4
1 2 1
7 8
1 8
1 6 2
7 16
1 7
2 5
2 35
10-9

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) (3.14)(0.5)3 1 3 1 3 4 3 4 3
Check Skills You’ll Need
10-9

56. Volume: Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Solutions
1. (3.14)(22)(5) = (3.14)(4)(5) (42)(6) = (16)(6)
= (62.8) = (96)
= = 32
3. (3.14)(23) = (3.14)(8) (3.14)(0.5)3 = (3.14)(0.125)
= (25.12) = (0.3925)
= = 0.523 1 3 1 3 1 3 1 3 1 3 1 3 4 3 4 3 1 3 4 3 4 3 4 3
10-9

57. Volume: Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Find the volume of the cone.
V = Bh Use the formula for volume. 1 3
V = r 2h B = r 2 1 3
(3.14)(2)2(12) Replace r with 2 and h with 12. 1 3
= Simplify.
Quick Check
The volume of the cone is about 50 in.3.
10-9

58. Volume: Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Find the volume of the square pyramid.
V = Bh Use the formula for volume. 1 3
V = s 2h B = s2 1 3
= (8)2(12) Replace s with 8 and h with 12. 1 3
= Simplify.
Quick Check
The volume of the pyramid is 256 in.3.
10-9

59. Volume: Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-9
Earth has an average radius of 3,963 mi. What is Earth’s approximate volume to the nearest 1,000,000 mi3? Assume that Earth is a sphere.
V = r Use the volume formula. 4 3
(3.14)(3,963)3 Replace r with 3,963. 4 3
260,579,713,159 Simplify.
The volume of the Earth is about 260,580,000,000 mi3.
Quick Check
10-9

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