How to with Geometry 5

5
How to
Facts to Know
• • • • • • • • • • • • • • • Solve Word Problems
with Geometry
Basic Geometric Formulas
Perimeter
• Perimeter is the length around a closed shape.
It is computed by adding the length of all
the sides of the figure.
• The formula for finding the perimeter of
rectangles and other parallelograms is
P = (l + w) x 2 or P = 2 l + 2 w
Area
The area of a flat surface is a measure of how much space is covered by that surface. Area is measured
in square units.
• Area of a Rectangle
The area of a rectangle is computed by
multiplying the width of one side times the
length of the adjoining side.
A=lxw
• Area of a Triangle
A triangle is always one half of a rectangle
or a parallelogram. The area of a triangle is
computed by multiplying 1/2 of the base
times the height of a triangle.
A = 1– b x h
2
The area of a rectangle can also be
determined by multiplying the base
times the height.
A=bxh
• Area of a Parallelogram
The area of a parallelogram is computed by
multiplying the base times the height.
A=bxh
• Area of a Circle
To find the area of a circle, multiply π (3.14)
times the radius times the radius again.
2
A=πr
Circumference
The circumference is the distance around a circle.
To find the circumference of a circle, multiply π
(which always equals 3.14) times the diameter or
multiply 2 times π (3.14) times the radius.
C = π d or C = 2 π r
Volume
• The formula for finding the volume of a rectangular prism, such as a box, is to multiply the length
times the width times the height. V = l x w x h
• The formula for finding the volume of a cylinder is to multiply π (3.14) times the radius squared
2
times the height. V = π x r x h
• Volume is always computed in cubic units. Use cubic inches or centimeters when determining
volume for small prisms and cylinders, and cubic feet or meters for larger ones.
21
1
Practice
• • • • • Recalling Information About Lines
and Geometry
Directions: Using the information on pages 5 and 6, choose the answer to each question.
1. Geometry comes from two Greek words meaning
a. “round” and “equal.”
b. “center” and “to measure.”
c. “earth” and “center.”
d. “earth” and “to measure.”
2. The difference between plane geometry and solid geometry is:
e. one is flat and the other is round.
f. plane is easier than solid.
g. plane has two dimensions and solid has three.
h. plane has three dimensions and solid has two.
3. A quadrilateral is a shape with
a. sides.
b. four straight sides.
c. three or more sides.
d. long sides.
4. A polygon is a shape with
e. curved sides.
f. irregular sides.
g. four straight sides.
h. three or more sides.
5. The beginning and end of a line segment are
a. capital letters.
b. points.
c. line segments that never end.
d. arrows.
6. What kind of shape is this?
e. polygon
f. quadrilateral
g. regular
h. line segment
7. What kind of shape is this?
a. triangle
b. quadrilateral
c. regular
d. line segment
7
▲
●
Pages 7 and 8
1. d
2. g
3. b
4. h
5. b
6. e
7. b
8. e
9. a
10. f
11. c
12. g
13. d
14. f
Pages 12 and 13
1. b
2. f
3. a
4. f
5. b
6. g
7. d
8. e
9. b
10. e
11. c
12. h
Page 17
1. 80°
2. 80°
3. 100°
4. 15°
5.
g
6.
f
7. 110°
8. 70°
9. 70°
10. 180°
11. 360°
12. 30°
13. 30°
14. 150°
15. 30°
■
• • • • • • • • • • • • • • • • • • • • • • Answer Key
6. parallelogram
7. 120 ft.
8. 36 ft.
9. 2.75 ft.
10. 7 ft.
11. 45 ft.
12. 14 ft.
Pages 36 and 37
1. 120 ft.2
2. 48 ft.2
3. 400 yds.2
4. 110.25 in.2, 176 in.2
5. 40 ft.2
6. 14.625 ft.2
7. 12 ft.2
8. 6 in.2
9. 6 ft.2
10. 21.85 ft.2
11. 37.1 ft.2
12. 117 in.2
Pages 40 and 41
1. 385 in.3
2. 125 in.3
3. 2,154 in.3
4. 565.2 in.3
5. 400 ft.3
6. 79.507 ft.3
7. 1,846.32 ft.3
8. 427⁄8 ft.3 or 42.875 ft.3
Pages 42 and 43
1. 21 m; 9.5 m2
2. 12 m; 9 m2
3. 36 m; 81 m2
4. 162 m
5. 13.72 m; 4.64 m2
6. 155 cm
7. 25.6 m; 40.87 m2
8. 195 m
9. 84 ft.2
10. 336 ft.2
11. 4 quarts
12. 13.58 m2
13. 43,560 ft.2
14. 4,840 yards2
15. 1.10 acres
Pages 20 and 21
1. radius
2. diameter
3. chord
4. circumference
5. 4 ft.
6. 6 in.
7. 9 ft.
8. 8 1⁄2 in.
9. 13⁄4 in.
10. 110 ft.
11. 20.41 miles
12. 5 1⁄2 yds.
13. 452.16 ft.2
14. 615.44 in.2
15. 314 ft.2
Page 25
1. acute
2. equilateral
3. right
4. isosceles
5. obtuse
6. scalene
7. acute
8. isosceles
9. acute
10. scalene
11. acute
12. equilateral
Page 29
1. 60°
2. acute and scalene
3. 60°
4. acute and equilateral
5.
D = 55°
F = 55°
6. 50°
7. c = 2.5''
8. b = 12'
Pages 32 and 33
1. parallelogram
2. trapezoid
3. rhombus
4. rectangle
5. trapezoid
48
16. 3,780,000 pounds
17. A = 5,024 cm2
C = 251 cm
18. 16.75 minutes
19. r = 50 cm
A = 7,850 cm2
C = 314 cm
time = 20.93 min
20. r = 30 cm
A = 2,826 cm2
C = 188.4 cm
time = 12.56 min
Pages 44 and 45
1. 32 cm2 = 1,024 cm2
2. P = 2(4s) = 16 cm
3. P = 4(4s) = 32 cm
4. A = 4(1 x w) = 16 cm2
5. A = 16(1 x w) = 64 cm2
6. 50°
7. Let side of square A =
1 cm
Let the side of square
B = 4 cm
Area square A = 1 cm
Area square B = 16 cm
The area of square B
is 16 times greater
than the area of
square A.
8. Area of rectangle =
70 cm x 30 cm =
2,100 cm2
2,100 cm2 + 600 cm2
= 2,700 cm2
30 x 2,700 cm2 =
81,000 cm2 of wood
9. Yes, they have the
same area. Since you
multiply the base and
height, and these two
parallelograms use
the same numbers, so
it doesn’t matter
which is the base and
which is the height.
5
Practice
Geometry at Home
• • • • • • • • • • • • • Solving Word Problems
with Geometry
Geometry is a very important aspect of math around the home. Houses and property are measured in
geometric terms. Floor and wall coverings, heating systems, and the water supply all have a geometric
component.
For this practice page, you need to know the following:
• Wallpaper is sold in double rolls totaling 44 square feet.
• Carpeting is priced by the square yard.
• There are 9 square feet in 1 square yard.
• You cannot buy partial rolls of carpeting or wallpaper.
Directions: Use the formulas and information on page 21 and the information above to help you solve
these word problems.
1. Your mother said you can have new carpeting in your room if you compute the amount of
carpeting needed and the cost. The length of your room is 18 1– feet and the width is 17 feet.
2
The cost of one medium grade of carpeting is $20.00 per square yard.
A. Compute the number of square feet in the room: __________________
B. Convert square feet to square yards (divide by 9): _________________
C. Compute the cost of carpeting needed (multiply by $20.00): _________
2. You want to cover one wall of your room with neon-colored wallpaper that costs $25.00 for a
double roll containing 44 square feet. The wall is 18 1– feet long and 10 feet high.
2
A. Compute the area of your wall in square feet. _________________
B. Determine how many rolls of wallpaper you need: _____________
C. Compute the cost of the wallpaper: _________________________
3. Your friend decided to paint the walls and the ceiling of her room with a lovely lavender paint.
One gallon of this paint will cover only 400 square feet and costs $17.99 a gallon. These are the
dimensions of her room:
• Wall 1—21 1– feet long and 11 1– feet high
• Wall 3—21 1– feet long and 11 1– feet high
4
2
4
2
• Wall 2—20 feet long and 11 1– feet high
• Wall 4—20 feet long and 11 1– feet high
2
2
• Ceiling—21 1– feet long and 20 feet wide
4
A. Compute the area of each wall and ceiling in square feet.
Wall 1 ______ Wall 2 ______ Wall 3 ______ Wall 4 ______ Ceiling _________
B. Compute the total area in square feet: _________________________________
C. Determine how many gallons of paint are needed: _______________________
D. Compute the total cost of the paint: ___________________________________
22
5
Practice
Neighborhood Jobs
• • • • • • • • • Solving More Word Problems
with Geometry
You need money to supplement your allowance. You decide to pick up some jobs at home and in the
neighborhood so you can buy some necessities such as a scooter, a mountain bike, and a boom box.
Directions: Use the formulas and information on page 21 to help you solve these word problems.
1. Your dad agrees to pay you for mowing the
front and back lawn. He will pay you $0.01
a square foot. The front lawn is 62 feet long
and 38 feet wide.
5. A neighbor down the street offers to pay you
$0.15 a square foot to paint his fence which
is 103 feet long and 6.25 feet high. He will
supply the paint.
A. What is the square footage? _________
B. How much will you be paid? ________
A. What is the square footage? __________
B. How much will you be paid? _________
2. Your dad will pay you $0.03 a linear foot for
trimming the edge of this lawn.
6. Your favorite uncle offers to pay you $0.18 a
square foot to paint his board fence. It is
8 1– feet high and 26 feet long.
2
A. What is the square footage? __________
B. How much will you be paid? _________
A. What is the perimeter of the lawn? ____
B. How much will you be paid? _________
3. The back lawn is shaped like a
parallelogram. The base is 36 feet and the
height is 31 feet.
7. A neighboring mother wants you to paint a
dodge ball court with a 6-foot radius on her
driveway.
A. What is the square footage? __________
B. How much will you be paid? _________
A. What is the circumference of the court?
__________
B. What is the area in square feet of the
court? _________
4. Your next-door neighbor offers to pay you
the same price for edging and mowing his
circular lawn which has a radius of 5.5 feet.
A. What is the circumference of the lawn?
__________
B. How much will you be paid for edging?
__________
C. What is the area of the lawn in square
feet? _________
D. How much will you be paid for mowing
it? ___________
Extension
• Measure and compute the perimeter and area
of your lawn.
• Measure and compute the perimeter and area
of a neighbor’s lawn.
23
5
Practice
• • • • • • • • • • • • • • • • • Solving Even More
Word Problems with Geometry
Directions: Use the formulas and information on page 21 to help you solve these word problems.
1. You decide to start your own sidewalk business after school selling candy bars. The candy bars
come packed in cartons which are 1 foot long, 1 foot wide, and 1 foot high (a cubic foot). How
many of these cartons could you pack into your closet which is 5 feet long, 4 feet wide, and
12 feet high? _______________
2. Your bedroom is 20 feet wide, 18 1– feet long, and 11 feet high. How many cubic feet of space are
2
in your bedroom? __________________
3. The circular top of your water heater has a radius of 9 inches. The height of the cylinder is
8 feet 5 inches. How many cubic inches of water will the water heater hold? _________________
4. A can of cleanser has a radius of 4.5 cm and a height of 22.3 cm. How many cubic centimeters of
cleanser will the can hold? _______________
5. A closet in your parent’s bedroom is 9 1– feet long, 3 1– feet wide, and 12 feet high. How many
4
3
cubic feet of space does it have? _______________
6. This is a diagram of the living room in a house. Compute the number of cubic feet in the room.
(Hint: Do the problem in two sections.) _______________
51 feet
36 1
– feet
The height of the ceiling is 10 feet.
2
16 1
– feet
2
28 feet
7. A city water tower is 83 feet high with a radius of 25 feet. How many cubic feet of water can be
stored in the tower? ________________
8. A cubic foot of water weighs 62.38 pounds. What is the weight of the water that can be stored in
the water tower in problem #7? _______________
9. One cubic foot of water equals 7.48 gallons. How many gallons of water can be stored in the
water tower in problem #7? _______________
10. How many cubic inches of water will fit into a hose which is 50 feet long and has a radius of
1– inch? _________________
2
11. One silo or elevator for storing grain has a radius of 15 feet and is 120 feet high. How many
cubic feet of grain can be stored in it? _______________
24
• • • • • • • • • • • • • • • • • • • • • • Answer Key
Page 6
5. 405 in.2
1. 5 11⁄16"
6. 49.14 m2
2. 2 5⁄16"
7. 116.39 cm2
3. 6 3/4"
8. 86.45 m2
4. 6 7/16"
Page 16
5.–18. Answers will vary.
1. 50.24 m2
Pages 7 and 8
2. 78.5 cm2
Answers will vary.
3. 314 cm2
4. 452.16 cm2
Page 10
5. 1,256 cm2
1. 18.2 cm
6. 615.44 ft.2
2. 26.2 cm
7. 706.5 in.2
3. 131⁄2 cm
8. 1,962.5 m2
4. 161⁄2 ft.
5. 151⁄4 in.
Page 18
6. 183⁄8 cm.
1. 105 m3
7.–10. Answers will vary.
2. 720 ft.3
3. 343 cm3
Page 11
4. 165 in.3
1. 15.6 cm
5. 240 yd.3
2. 111⁄4 in.
6. 67.032 m3
3. 24.4 m
7. 92.736 m3
4. 183⁄4 ft.
8. 694.512 cm3
5. 74.4 m
9. 1,728 ft.3
6. 64 yd.
10. 86 6/8 ft.3
7. 137.4 cm
8. 105.3 m
Page 19
1. 351.68 m3
Page 12
2. 169.56 cm3
1. 19.1 m
3. 282.6 cm3
2. 22.6 m
4. 18.84 in.3
3. 26 in.
5. 50,240 cm3
4. 201⁄2 ft.
6. 1,538.6 ft.3
5. 25.12 m
6. 37.68 in.
Pages 20–23
7. 31.4 cm
Answers will vary.
8. 21.98 m
Page 24
Page 14
1. 6 lbs. 4 oz.
2
1. 41 m
2. 1 ton 300 lbs.
2. 126 yd.2
3. 4,000 cassettes
3. 67.5 cm2
4. 100 pills
4. 6.08 m2
5. 100,000 pills
2
5. 34 ft.
6. 2,000 dictionaries
6. 16 1/4 in.2
7. 12,000 staplers
7. 3,680 m2
8. 100 people
8. 7,500 mm2
9. 500 mg or 1/2 g
10. 220 kg
Page 15
11. 4,400 kg
1. 24 ft.2
12. 2,200 clips
2. 45 yd.2
13. 6,400 calculators
3. 11.66 cm2
14. 40 cameras
4. 27.72 cm2
Page 26
1. 8 fl. oz.
2. 16 fl. oz.
3. 32 fl. oz.
4. 48 fl. oz.
5. 64 fl. oz.
6. 72 fl. oz.
7. 32 fl. oz.
8. 64 fl. oz.
9. 160 fl. oz.
10. 96 fl. oz.
11. 4 qt.
12. 16 qt.
13. 128 fl. oz.
14. 60 qt.
15. 1,920 fl. oz.
16. 16 fl. oz.
17. 48 fl. oz.
18. 112 fl. oz.
19. 40 pints
20. 176 cups
21. 120 pints
22. 1,280 fl. oz.
23. 34 cups
24. 176 fl. oz.
25. 344 fl. oz.
Page 27
1. 30 mL
2. 240 mL
3. 1,000 mL
4. 960 mL
5. 40 mL
6. 480 mL
7. 3,840 mL
8. 3.84 L
9. 38.4 L
10. 69.1 L
11. 960 L
12. 96 L
13. 96 L
14. 1920
15. 360 L
Page 28
1. 2 qt.
2. 12 mL
3. 80 mL
4. 336 mL
5. 50 pennies
6. 432 mL
47
7.
8.
9.
10.
11.
12.
24 fl. oz.
384 mL
128 quarters
19.2 L
8 times
48 cups
Page 30
1. 40° acute
2. 120° obtuse
3. 180° straight
4. 90° right
5. 50° acute
6. 130° obtuse
7. 250° reflex
8. 215° reflex
9. 90° right
10. 80° acute
Page 31
1. <BAC = 100°
1. <CBA = 35°
1. <ACB = 45°
1. ▲ABC = 180°
2. <CDE = 50°
1. <ECD = 70°
1. <DEC = 60°
1. ▲DEC = 180°
3. <LMN = 90°
1. <MNL = 30°
1. <MLN = 60°
1. ▲LMN = 180°
4. <MNO = 25°
1. <OMN = 65°
1. <MON = 90°
1. ▲MNO = 180°
5. <XYZ = 60°
1. <ZXY = 60°
1. <YZX = 60°
1. ▲XYZ = 180°
6. <WPO = 154°
1. <POW = 11°
1. <PWO = 15°
1. ▲WPO = 180°
? ? ?
Page 6
1. change
subtraction
$2.12
2. money spent
multiplication
$36.64
3. split evenly
division
28 cards
4. amount needed
subtraction
$10.33
5. total cost
addition
$129.17
6. how much saved
subtraction
$2.21
7. total cost
multiplication
$41.58
Page 7
1. change
subtraction
$16.11
2. % discount
multiplication
$59.80
3. total cost
addition
$50.73
4. times as much
multiplication
$5,325
5. average
division
11.03 miles
6. total cost
addition
$1,342.97
7. times as much
multiplication
$350.10
8. total
addition
125.3 miles
Page 8
1. how much change
subtraction
$8.05
• • • • • • • • • • • • • • • • • • • • • • Answer Key
2. how much saved
subtraction
$6.95
3. product
multiplication
$113.85
4. how much left
subtraction
$25.41
5. split evenly
division
$1.59
6. share evenly
division
27 CDs
7. discount
multiplication
$3.19
8. difference
subtraction
$3.11
Page 12
1. multiplication
$22.68
2. addition
$8.97
3. multiplication
$59.67
4. addition
$13.46
5. division
$17.04
6. subtraction
$2.70
Challenge:
$70.20; 1 large
cola, 1 Double Bean
Burrito, 1 Tornado
Taco; $0.39
Page 14
1. 7/12 miles
2. 5/12 miles
3. 2 2/3 miles
4. 1/3 mile
5. 1 1/6 miles
6. 8 miles
7. 1 1/4 miles
8. 4 5/18 miles
9. 1/2 mile
10. 26 2/3 miles
Page 10
1. addition
$34.42
2. subtraction
$2.55
3. subtraction
$7.50
4. addition
$40.47
5. subtraction
$3.50
6. addition
$78.41
7. addition
Answers will vary.
Extension: Answers will
vary.
Page 15
1. 3/4 pizza
2. 10 cups
3. 3 3/4 pizzas
4. 1 1/2 pizzas
5. 1/2 pizza
6. 1/10 cake
7. 15/16 cake
8. 14 cups
9. 5/8 pizza
10. 81 ounces
11. 338 ounces
12. 1 1/2 ounces
Page 11
1. multiplication
$45.00
2. division
$3.75
3. multiplication
$126.50
4. multiplication
$99.80
5. multiplication
$119.25
6. division
$1.79
Challenge: $11.25; $8.75
Extension: 4 2/3 pizzas
Page 16
1. 33 3/4 miles
2. 39/40 mile
46
3. 7/10 mile
4. 1/2 lb.
5. 14 2/3 miles
6. 9 lbs.
7. 4 5/3 miles
8. 1 13/40 sec.
9. 12 3/8 miles
10. 7 17/24 miles
Extension: Answers will
vary.
Page 18
1. $62.29; $237.71
2. $77.50; $160.21
3. $11.88; $148.33
4. $7.46; $29.82;
$118.51
5. $57.94; $60.57
6. $10.00; $60.00;
$0.57
7. $299.43
8. no
Page 19
1. 60%
2. 24 shots
3. 71% or 71.4%
4. 17 shots
5. 89% or 89.3%
6. 19 shots
7. 94% or 94.4%
8. 65% or 64.7%
9. 64% or 63.9%
10. 4 shots
Challenge: Answers will
vary.
Page 20
1. 0.625 gallons
2. 25.2 lbs.
3. 4.4 oz.
4. 43.2 lbs.
5. 2.4 qts.
6. 114.7 lbs.
7. 19.5 lbs.
8. 3.75 or 3 3/4 times
9. 56% or 55.6%
10. 41%
Page 22
1. A. 314.5 sq. ft.
B. 34.9 or
35 sq. yd.
• • • • • • • • • • • • • • • • • • • • • • Answer Key
? ? ?
C. $698.00 or
$700.00
2. A. 185 sq. ft.
B. 5 rolls
C. $125
3. A. 244 3/8 sq. ft.
230 sq. ft.;
244 3/8 sq. ft.;
230 sq. ft.;
425 sq. ft.
B. 1,373 3/4 sq. ft.
or 1,374 sq. ft.
C. 4 gallons
D. $71.96
Page 23
1. A.
B.
2. A.
B.
3. A.
B.
4. A.
B.
C.
D.
5. A.
B.
6. A.
B.
7. A.
B.
2,356 sq. ft.
$23.56
200 ft.
$6.00
1,116 sq. ft.
$11.16
34.54 ft.
$1.04
94.99 sq. ft.
$0.95
643.75 sq. ft.
$96.56
221 sq. ft.
$39.78
37.68 ft.
113.04 sq. ft.
Extension: Answers will
vary.
Page 24
1. 240 cartons
2. 4,070 cu. ft.
3. 25,688.34 cu. in.
4. 1,417.95 cu. cm
5. 370 cu. ft.
6. 14,820 cu. ft.
7. 162,887.5 cu. ft.
8. 10,160,922 lb.
9. 1,218,398.5 gallons
10. 471 cu. in.
11. 84,780 cu.ft.
Page 26
1. $45.60
2. $34.13
3. $104.65
4.
5.
6.
7.
8.
9.
$43.51
$32.95
$29.25
$36.86
$30,555.64
Monday and
Tuesday = Saturday
10. $17,111.16
11. $12,473.53
4.
5.
6.
7.
Page 27
1. $101.47
2. $12.27
3. You could buy the
DVD player;
$179.67
$5.96 change
4. $786.15
5. The traditional
machine/phone is
$11.24 cheaper.
6. $19.20
7. $49.76
8. Boom Box City
$25.46 less
9. $16.30
10. 25%
8.
0 quarters,
2 half dollars
6, 9, 12, 15, 18
300, 350, 400, 450,
500
3 footballs, 6 tennis
balls, 3 baseballs, 2
basketballs
Jack is 26 years
old; Dad is 52 years
old
Marie is 22 years
old; Mother is 44
years old
Page 31
1. $360.00
2. 2,700 beads
3. 240 total
16 skirts
32 jeans
64 shorts
128 blouses
4. $372.00 total
Elaine $12.00
Christina $24.00
Alyse $48.00
Doreen $96.00
Melissa $192.00
5. James 2 years old
Raymond 3 years
old
Brett 4 1/2 years
old
John 6 years old
Robert 11 years old
Page 28
1. 22.86 miles per day
2. 4 hr. 24 min.
3. 3 hr. 20 min.
4. 40 m.p.h.
5. 1 mile per minute
6. $21.00
7. $3.20
8. $0.82
9. $46.74
Page 32
1. 3 hr. 2 min.
2. 31 games
3. 81 times
4. 30 names
5. 20 points on 8th
game; 35 points on
14th game
6. 35 players are 13
years old
Page 30
1. 6 tops/4 skorts
2. 3 pennies, 3
nickels, 0 dimes, 3
quarters,
3. A. 1 penny, 0
nickels,
4 dimes,
4 quarters,
0 half dollars
B. 1 penny, 4
nickels,
2 dimes,
Page 34
1. n = 36–23
n = 13
13 years old
2. n = (4 x 15) + 2
47
n = 62
62 CDs
3. n = 216–122
n = 94
94 lb.
4. n = 25 x .60
n = 15
15 shots
5. n = 22 – 7
n = 15
15 minutes
6. n = 1,145 – 316
n = 829
829 words
7. n = 88 x 3/4
n = 66
66 minutes
Extension: Answers will
vary.
Page 35
1. n + (n + 28) = 50
2n + 28 = 50
n = 11
Mother is 39 years
old.
Sarah is 11 years
old.
2. n + (n + 140)= 336
2n + 140= 336
n = 98
Joe weighs 98 lbs.
Dad weighs 238
lbs.
3. n + 4n + 22 = 122
n = 25
Melissa has $25.00.
Christina has $97.00.
4. n + 2n = 669
3n = 669
n = 223
John read 223
words.
Joseph read 446
words.
5. n + 4n = 15
5n = 15
n=3
Nicholas is 3 years
old.
Norman is 12 years
old.
10
Word
Problems
• • • • • • • • • • • • • • • • Real Life Geometry
The students at Wood Hill Elementary were surprised one day in gym class when the coach
handed out a math test.
“What’s going on?” they asked.
“Good athletes have to be good students, too,” said the coach. “You don’t want to be
disqualified from a team because of poor grades. Answer these questions.” He gave them
each sheet of paper.
1. The volleyball net is 1 m wide and 9.50 m long. What are the perimeter and the area of the net?
perimeter = ____________ area = ____________
2. The service area in volleyball is 3 m long and 3 m wide.
What is the perimeter and the area of the service area? perimeter = ____________
area = ____________
3. The volleyball court is 18 m long and 9 m wide. It is divided into two halves. What are the
perimeter and the area of each half? perimeter = ____________ area = ____________
4. Tiffany runs 3 times around the volleyball court. How far does she run? ____________
5. The badminton net is 0.76 m wide and 6.10 m long. What are the perimeter and area of the net?
perimeter = ____________ area = ____________
6. The badminton net is 1.55 m high (1 m = 100 cm). What is its height in centimeters?
____________
7. The badminton court is 13.40 m long and 6.10 m wide. It is divided into two halves. What is the
perimeter of each half? ____________ How many square meters of material would it take to
cover one half? ____________
8. Dan runs 5 times around the badminton court. How far does he run? ____________
Ira has agreed to do a project for his father in exchange for a new snowboard this winter. Ira
needs to paint the garden shed in his backyard. His father needs to buy the paint for the
shed and has asked Ira to measure the size of each wall to determine the amount of paint
he should purchase. There are four walls to the shed.
9. After measuring the walls, Ira has determined that each wall is 7 feet high and 12 feet long. What
is the area of each wall? ____________
10. What is the total area of the walls around the shed? ____________
11. If a quart of paint covers 100 square feet, how many quarts of paint must Ira’s father purchase?
____________
12. Dan O’Leary has decided to plant a garden. He wants to make it 10.1 m long and 4.2 m wide.
However, in order to keep the rabbits out, Dan needs a fence surrounding the garden. He decides
to make the fence 11.2 m long and 5.0 m wide. What is the area between the fence and the
garden? ____________
(Hint: Find the area for the garden. Then, find the area of the space surrounded by the fence.)
42
10
Word
Problems
• • • • • • • • • • • • • • • • Real Life Geometry
The rod is an old unit of measurement of length. A rod is 16 1/2 feet long. A square rod is
a square plot of ground. Each side of the plot is 16 1/2 feet long. An acre is 160 square
rods.
13. How many square feet are in one acre? ____________
14. How many square yards are in one acre? ____________
15. A football field is 160 feet wide and 300 feet from goal line to goal line. What is the area of the
football field in acres? (round to the nearest hundredth) ____________
16. Mr. Anderson is a farmer. He has a 300-acre field. He expects to harvest about 225 bushels of
corn per acre. A bushel of corn weighs about 56 pounds. How many pounds of corn would Tom
get from his field? ____________
Mr. Peterson is a math teacher. Dinner at his house is
unusual. One night, after a pizza was delivered, he
posed the following questions to his hungry family.
“Before we eat this delicious pizza, let’s answer a few
interesting questions,” he said. Everyone groaned. “The
radius of a regular pizza is 40 cm. Now, listen closely to
my questions.”
17. Find the area and the circumference of the pizza.
area = _______ circumference = _______
18. If an ant walked 1 cm in 4 seconds, how long would it take for the ant to walk the
circumference? ____________
19. Repeat question #18 assuming the radius of the pizza is increased by 25%. Find the following
measurements:
radius = _______
area = _______
circumference = _______
ant’s time = _______
20. Repeat question #18 assuming the radius of the pizza is decreased by 25%. Find the following
measurements:
radius = _______
area = _______
circumference = _______
ant’s time = _______
43
11
• • • • • • • • • • • • Carpenters and Pyramids
Brain
Teasers
Directions: Answer these brain teaser questions.
1. Four strips of paneling 40 cm long and 4 cm wide are arranged to form a square, like a picture
frame. (Note: The ends of the strip of paneling will overlap.)
What is the area of the inner square in square cm? ____________
It’s “Challenge Day” in Mr. Peterson’s math class. “Take out a sheet of paper,” he says. “Now,
draw a 2 cm x 2 cm square. Listen closely.
2. What is the equation for finding the perimeter of a square that is twice the size of the original
square? _________________________
3. What is the equation for finding the perimeter of a square that is four times the size of the original
square? _________________________
4. What is the equation for finding the area of a square that is twice the size of the original
square? _________________________
5. What is the equation for finding the area of a square that is four times the size of the original
square? _________________________
6. In the following diagram of the front view of the Great Pyramid, the measure of PRQ is 120°
degrees, and the measure of PST is 110° degrees.
What is the measure of
RPS in degrees? _________________________
P
Q
R
(Hint: The sum of the angles in a triangle is
180 degrees. A straight line is 180 degrees.
Use the known angles to find the unknown
angles. See Unit 3 on supplementary angles
to help you solve the problem.)
S
T
7. One side of square B is four times the length of one side of square A. How many times greater is
the area of square B than the area of square A? _________________________
B
A
44
11
Brain
Teasers
• • • • • • • • • • • • Carpenters and Pyramids
8. Two carpenters decided to design desks for students at James Hart Junior High. The dimensions
of the desks are as shown. How much wood in cm2 would they need for 30 desks? __________
70 cm
30 cm
20 cm
20 cm
(Hint: What is the area of one desk? Find the area of each part and add all the areas to find the
total area. If there are 30 desks, how much wood in square centimeters is needed?)
9. Do these parallelograms have the same area? How do you know? __________________________
_______________________________________________________________________________
_______________________________________________________________________________
2 cm
5 cm
2 cm
5 cm
(Hint: Review the formula for finding the area of a parallelogram.)
45
▲
●
Pages 7 and 8
1. d
2. g
3. b
4. h
5. b
6. e
7. b
8. e
9. a
10. f
11. c
12. g
13. d
14. f
Pages 12 and 13
1. b
2. f
3. a
4. f
5. b
6. g
7. d
8. e
9. b
10. e
11. c
12. h
Page 17
1. 80°
2. 80°
3. 100°
4. 15°
5.
g
6.
f
7. 110°
8. 70°
9. 70°
10. 180°
11. 360°
12. 30°
13. 30°
14. 150°
15. 30°
■
• • • • • • • • • • • • • • • • • • • • • • Answer Key
6. parallelogram
7. 120 ft.
8. 36 ft.
9. 2.75 ft.
10. 7 ft.
11. 45 ft.
12. 14 ft.
Pages 36 and 37
1. 120 ft.2
2. 48 ft.2
3. 400 yds.2
4. 110.25 in.2, 176 in.2
5. 40 ft.2
6. 14.625 ft.2
7. 12 ft.2
8. 6 in.2
9. 6 ft.2
10. 21.85 ft.2
11. 37.1 ft.2
12. 117 in.2
Pages 40 and 41
1. 385 in.3
2. 125 in.3
3. 2,154 in.3
4. 565.2 in.3
5. 400 ft.3
6. 79.507 ft.3
7. 1,846.32 ft.3
8. 427⁄8 ft.3 or 42.875 ft.3
Pages 42 and 43
1. 21 m; 9.5 m2
2. 12 m; 9 m2
3. 36 m; 81 m2
4. 162 m
5. 13.72 m; 4.64 m2
6. 155 cm
7. 25.6 m; 40.87 m2
8. 195 m
9. 84 ft.2
10. 336 ft.2
11. 4 quarts
12. 13.58 m2
13. 43,560 ft.2
14. 4,840 yards2
15. 1.10 acres
Pages 20 and 21
1. radius
2. diameter
3. chord
4. circumference
5. 4 ft.
6. 6 in.
7. 9 ft.
8. 8 1⁄2 in.
9. 13⁄4 in.
10. 110 ft.
11. 20.41 miles
12. 5 1⁄2 yds.
13. 452.16 ft.2
14. 615.44 in.2
15. 314 ft.2
Page 25
1. acute
2. equilateral
3. right
4. isosceles
5. obtuse
6. scalene
7. acute
8. isosceles
9. acute
10. scalene
11. acute
12. equilateral
Page 29
1. 60°
2. acute and scalene
3. 60°
4. acute and equilateral
5.
D = 55°
F = 55°
6. 50°
7. c = 2.5''
8. b = 12'
Pages 32 and 33
1. parallelogram
2. trapezoid
3. rhombus
4. rectangle
5. trapezoid
48
16. 3,780,000 pounds
17. A = 5,024 cm2
C = 251 cm
18. 16.75 minutes
19. r = 50 cm
A = 7,850 cm2
C = 314 cm
time = 20.93 min
20. r = 30 cm
A = 2,826 cm2
C = 188.4 cm
time = 12.56 min
Pages 44 and 45
1. 32 cm2 = 1,024 cm2
2. P = 2(4s) = 16 cm
3. P = 4(4s) = 32 cm
4. A = 4(1 x w) = 16 cm2
5. A = 16(1 x w) = 64 cm2
6. 50°
7. Let side of square A =
1 cm
Let the side of square
B = 4 cm
Area square A = 1 cm
Area square B = 16 cm
The area of square B
is 16 times greater
than the area of
square A.
8. Area of rectangle =
70 cm x 30 cm =
2,100 cm2
2,100 cm2 + 600 cm2
= 2,700 cm2
30 x 2,700 cm2 =
81,000 cm2 of wood
9. Yes, they have the
same area. Since you
multiply the base and
height, and these two
parallelograms use
the same numbers, so
it doesn’t matter
which is the base and
which is the height.