Geometry: Perimeter and Area
Practice 24
Many sports require a rectangular field of play which is a specific length and width. Use the
information given in the problems below to compute the perimeter and area of each field of play.
Reminder
• The perimeter of a rectangle is computed by adding the length and width and
multiplying by 2.
• The area of a rectangle is computed by multiplying the length times the width.
Remember: P = (l + w) x 2 and A = l x w
1. An NFL playing field (not counting the end zones) is 300 feet long and 160 feet wide.
What is the perimeter? __________________ What is the area? __________________
2. An NBA basketball court is 94 feet long and 50 feet wide.
What is the perimeter? __________________ What is the area? __________________
3. A major league baseball diamond is a square 90 feet long on each side.
What is the perimeter? __________________ What is the area? __________________
4. An ice hockey rink is 100 feet wide and 200 feet long.
What is the perimeter? __________________ What is the area? __________________
5. A field hockey playing area is 100 yards long and 60 yards wide.
What is the perimeter? __________________ What is the area? __________________
6. A softball diamond is a square 65 feet long on each side.
What is the perimeter? __________________ What is the area? __________________
7. A soccer field is 73 meters wide and 100 meters long.
What is the perimeter? __________________ What is the area? __________________
8. The playing area of a Canadian football field (not counting the end zones) is 110 yards long and
65 yards wide.
What is the perimeter? __________________ What is the area? __________________
27
Geometry: Area
Practice 25
Lawn Magic is a business run by three sixth grade friends who earn money mowing their neighbors’
lawns. They charge by the square foot so they need to know the area of each lawn they mow. Help
Lawn Magic compute the area in square feet of each lawn described below.
Formulas to Remember
• Area of a rectangle = base times height
(or length times width)
• Area of a parallelogram = base times height
• Area of a triangle = base times height divided by 2.
1. Lawn Magic did your neighbor’s lawn which is a rectangular shape 12 feet high and 20 feet long
at the base. What is the area? ________________ square feet
2. Lawn Magic mowed Mr. Crick’s parallelogram-shaped lawn which has a height of 15 feet and a
base of 30 feet What is the area? ________________ square feet
3. Mr. Ford’s lawn is a parallelogram with a height of 23 feet and a base of 45 feet What is the area
Lawn Magic will mow? ________________ square feet
4. Mrs. Jopp’s lawn is triangular with a height of 12 feet and a base of 40 feet What is the area that
Lawn Magic will mow? ________________ square feet
5. Lawn Magic mowed Mr. Lee’s front lawn which is a rectangle 43 feet high and 97 feet at the
base. What is the area they mowed? ________________ square feet
6. Mr. Dapper’s back lawn is a triangle with a height of 33 feet and a base of 70 feet What is the
area? ________________ square feet
7. Mrs. Smith’s side lawn is a parallelogram 22.4 feet high and 30 feet at the base. What is the area
Lawn Magic will mow? ________________ square feet
8. Lawn Magic mowed Ms. Brown’s front lawn, a triangle 12.5 feet high and 14 feet at the base.
What is the area they mowed? ________________ square feet
9. What is the area of a triangular lawn 16.6 feet high and 12 feet at the
base? ________________ square feet
10. What is the area of a square lawn 22 feet on each side? ________________ square feet
28
Answer Key
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
no
5 m.p.h.
20 m.p.h.
the scale doesn’t
go 0 to 70
start at 0/use a
different scale
1995
1998
10 thousand dollars
the scale is
distorted, starts
at 40
25 thousand
dollars
scale starts at 40
thousand dollars
starts at 0 and go
to 70
Page 27
1. 920 feet
48,000 feet2
2. 288 feet
4,700 feet2
3. 360 feet
8,100 feet2
4. 600 feet
20,000 feet2
5. 320 yd.
6,000 yd.2
6. 260 feet
4,225 feet2
7. 346 m
7,300 m2
8. 350 yd.
7,150 yd.2
Page 28
1. 240 feet2
2. 450 feet2.
3. 1,035 feet2
4. 240 feet2
5. 4,171 feet2
6. 1,155 feet2
7. 672 feet2
8. 87.5 feet2
9. 99.6 feet2
10. 484 feet2
Page 29
1. C = πd
C = 3.14 x 9
28.26 centimeters
2. C = πd
C = 3.14 x 23
72.22 centimeters
3. C = 2πr
C = 2 x 3.14 x 2
12.56 centimeters
(cont.)
4. C = πd
C = 3.14 x 2
6.28 centimeters
5. C = πd
C = 3.14 x 2.6
8.164 centimeters
6. C = 2πr
C = 2 x 3.14 x 12
75.36 inches
7. C = 2πr
C = 2 x 3.14 x 2
12.56 inches
8. C = 2πr
C = 2 x 3.14 x 3
18.84 centimeters
Page 30
1. A = πr2
A = 3 x 3 x 3.14
28.26 cm2
2. A = πr2
A = 3.14 x 8 x 8
200.96 inches2
3. A = πr2
A = 3.14 x 6 x 6
113.04 cm2
4. A = πr2
A = 3.14 x 7 x 7
153.86
millimeters2
5. A = πr2
A = 3.14 x 9 x 9
254.34
millimeters2
6. A = πr2
A = 3.14 x 2 x 2
12.56 feet2
7. A = πr2
A = 3.14 x 4 x 4
50.24 feet2
8. A = πr2
A = 3.14 x 4.5 x
4.5
63.585 cm2
9. A = πr2
A = 3.14 x 3.5 x
3.5
38.465 cm2
10. A = πr2
A = 3.14 x 1.15 x
1.15
4.15265 cm2
Page 31
1. 216 inches3
2. 27 cm3
3. 729 inches3
4. 8 inches3
5. 125 inches3
6. 900 cubic puzzles
7. 192 cubic
magnifying glasses
8. 1,000 cm3 blocks
9. 120 games
10. 1,728 cubic puzzles
Page 33
1. library
2. town hall
3. gas station
4. (-11, 1)
5. (4, -4)
6. (-5, -9)
7. park
8. (-10, -7)
9. (-9, 5)
10. general store
11. drug store
12. III
13. I
14. II
Page 34
1. 3/10
2. 4/15
3. 9/50
4. 11/16
5. 1/2
6.
7.
8.
9.
10.
3/40
2/3
8/45
2/5
1/27
Page 35
1. n = 35 – 12
n = 23
2. 23 + n = 41
n = 18
3. n – 29 = 61
n = 90
4. 36 + n = 53
n = 17
5. 19 + n = 43
n = 24
6. n/4 = 12
n = 48
7. n x 12 = 96
n=8
8. n/8 = 11
n = 88
9. n x 19 = 190
n = 10
10. 42/n = 6
n=7
Page 36
1. 5:4 or 5/4
2. 4:5 or 4/5
3. 2:5 or 2/5
4. 5:2 or 5/2
5. 3:5 or 3/5
6. 5:3 or 5/3
7. 4:3 or 4/3
8.
9.
10.
11.
12.
13.
14.
15.
3:4 or 3/4
2:3 or 2/3
3:2 or 3/2
7:5 or 7/5
5:7 or 5/7
3:7 or 3/7
7:3 or 7/3
12:2 or 12/2 or 6:1
or 6/1
16. 2:12 or 2/12 or 1:6
or 1/6
17. 3:7 or 3/7
18. 7:3 or 7/3
Page 37
1. 1:4 :: 20:n
n = 80 feet
2. 1:2 :: 25:n
n = 50 feet
3. 3:15 :: 9:n
n = 45 m
4. 4:1 :: 100:n
n = 25 stories
5. 3:10 :: 33:n
n = 110 yd.
6. 3:10 :: 15:n
n = 50 m
7. 5:3 :: n:30
n = 50 inches
8. 7:2 :: 42:n or
2:7 :: n:42
n = 12 inches
Page 38
1. 528
9
59 (58.67)
2. 911
11
83 (82.8)
3. 1,160
13
89 (89.2)
4. 138
10
14 (13.8)
5. 63
12
5 (5.25)
6. 175
13
13 (13.46)
7. 109
16
7 (6.8)
Page 39
1. (46, 47, 48, 49, 50,
52, 52, 52, 53, 54,
2.
3.
4.
5.
56)
52
52
(47, 49, 55, 56, 57,
58, 59, 59, 59, 60,
60, 61, 63)
59
59
(57, 59, 59, 60, 61,
61, 63, 63, 65, 66)
59, 61, 63
61
(47, 49, 49, 49, 51,
52, 53, 54, 55, 57,
59)
49
52
(39, 40, 44, 44, 45,
48, 50, 55, 57, 57,
58, 60, 60, 61)
44, 57, 60
52.5
Page 40
1. C
2. D
3. B
4. A
5. A
6.
7.
8.
9.
10.
C
B
D
B
D
Page 41
1. B
2. D
3. C
4. A
5. D
6.
7.
8.
9.
10.
A
C
A
B
C
Page 42
1. A
2. B
3. C
4. B
5. D
6.
7.
8.
9.
10.
B
D
C
A
D
Page 43
1. C
2. C
3. B
4. D
5. D
6.
7.
8.
9.
10.
B
A
D
B
C
Page 44
1. C
2. C
3. A
4. B
5. D
6.
7.
8.
9.
10.
A
C
B
D
C
Page 45
1. C
2. A
3. B
6. C
7. A
8. B
48
Unit 7: Polynomials
Name _____________________________________
Area of Shaded Region
Directions: Find the area of each shaded region in simplest terms.
165
Appendix B: Answer Keys
Guided Practice Book Answers
(cont.)
67
Area
6.7
Name _________________________________________
Date ___________________
Directions: Use the formulas to calculate both the area and perimeter for each rectangle.
Think about the best way to record each answer, whether inches, square inches, feet, square
feet, yards, or square yards. Complete the table below.
1.
15 ft.
2.
32 in.
3.
12 yds.
32 in.
9 ft.
8 in.
5.
19 yds.
44 m
4.
56 in.
44 m
6.
106 yds.
27 yds.
7. A rectangle has a long side of 7.4 in. and a short side of 4 in. Find its perimeter and
area.
8. A square wall has sides measuring 19 yds. What is the perimeter and what area do the
bricks cover?
area
perimeter
1
2
3
4
5
6
7
8
63
Answer Key
Student Pages
Page 53
Page 63
1. 1 m = 100 cm, 1 kg = 1,000 g,
1 cm = 10 mm
2. 1 km = 1,000 m, 1 ton = 1,000 kg,
1 L = 1,000 mL
3. 1 km = 100,000 cm, 1t = 1,000,000 g,
1 L = 1,000 cm
4. To convert cm to km, we divide by
1,000.
5. To convert g to kg, we divide by
1,000.
6. To convert mL to L, we divide by
1,000.
7. 25 km
8. 740 cm
9. 9,600 g
10. 0.72 m
11. 140 mm
12. 0.180 kg
13. 8,600 g
14. 716.542 tons
15. 9,210 kg
16. 16,240 mL
17. 1.21 m
18. 5,100 mL
19. 8 cups
20. 4 pints
21. 2 quarts
22. 12 gallon
23. 6000 pounds
24. 6000 pounds
25. 2640 feet
26. 2640 feet
1.
2.
3.
4.
5.
6.
7.
8.
Area
135 sq. ft.
1,024 sq. in.
228 sq. yards
1,936 sq. m
448 sq. in.
2,862 sq. yards
29.6 sq. in.
361 sq. yards
Page 69
Answers will vary.
Page 75
1.
2.
3.
4.
5.
6.
7.
8.
1,368.1 cm2
110.8 in.2
244.9 m2
420 yards2
655.2 ft.2
2.4 yards2
967.1 m2
483.7 in.2
Page 81
Part A
1. 10 units cubed
2. 9 units cubed
3. 28 units cubed
4. 48 units cubed
5. 1,443 mm cubed
6. 705 mm cubed
7. 807 in. cubed
8. 13 ft.
9. 3 in.
10. 9 in. cubed
120
Perimeter
48 ft.
128 in.
62 yards
176 m
128 in.
266 yards
22.8 in.
76 yards
2
Practice • • • • • • • • • • • • • • Computing Perimeters
of Rectangles
To compute the perimeter of a rectangle, add the length and the width and then multiply by 2.
12.5 cm
12.5 cm + 3.3 cm = 15.8 cm
15.8 cm x 2 = 31.6 cm
P = 31.6 cm
3.3 cm
Directions: Use the information on page 9 to compute the perimeters of these rectangles.
Remember to label the unit of measurement—inches, feet, yards, centimeters, meters—in your answers.
2.
1.
6.7 cm
9.8 cm
2.4 cm
3.3 cm
P = _______
P = _______
3.
4 1– cm
2
5 1– ft.
4
4.
2 1– cm
4
3 ft.
P = _______
5.
P = _______
5 1– in.
8
6.
2 1– in.
2
1 cm
6—
16
3 1– cm
8
P = _______
P = _______
Directions: Use a ruler and the information on pages 5 and 9 to help you measure and compute the
perimeters of these rectangles.
7. a math book cover
length ___________
width ___________
P=
___________
9. a paperback book cover
length ___________
width ___________
P=
___________
8. a sheet of paper
length ___________
width ___________
P=
___________
10. a desk
length ___________
width ___________
P=
___________
10
2
Practice
• • • • • • • • • • • • • • Computing Perimeters
of Regular Polygons
To compute the perimeter of a regular polygon,
in which all sides are equal, multiply the length
of one side by the number of sides.
4.9 m
Directions: Compute the perimeter of each of the
regular polygons illustrated below. Remember to
label the unit of measurement—inches, feet, yards,
centimeters, meters—in your answer.
1.
5.2 cm
4.9 m x 4 = 19.6 m
2 1– in.
4
2.
3 1– ft.
8
6.1 m
3.
4.
9.3 m
5.
8 yd.
6.
22.9 cm
7.
11.7 m
8.
11
2
Practice • • • • • Computing Perimeters of Irregular
Polygons and Circumferences of Circles
To compute the perimeter of an irregular polygon, add the lengths of the sides.
4.7 m
3.5 m
2.8 m
6.3 m
P = 4.7 m + 3.5 m + 6.3 m + 2.8 m = 17.3 m
Directions: Use the information on pages 5 and 9 to help you compute the perimeters of these
polygons. Remember to label the unit of measurement—inches, feet, yards, centimeters, meters—in
your answer.
1. P = ______
2. P = ______
4.3 m
8.4 m
4.1 m
2.9 m
7.3 m
6.9 m
7.8 m
3. P = ______
5 in.
4. P = ______
6 1– in.
2
4 1– ft.
2
5 1– ft.
2
3 ft.
8 1– in.
2
5 ft.
2 1– ft.
2
6 in.
Directions: Use the information on page 9 to help you compute the circumferences of these circles.
(C = 2πr or C = πd)
5.
6.
r=4m
•
r = 6 in.
•
C = _________
7.
C = _________
8.
d = 10 cm
d=7m
C = _________
C = _________
12
3
How to
• • • • • • • • • • • • • • • • • • • • Compute Area
Facts to Know
Area of a Rectangle
The area of a rectangle is computed by multiplying the length
times the width.
2 cm
A=lxw
A = 2 cm x 6 cm
A = 12 cm2
6 cm
The formula is written: A = l x w (Area = length times
width) or A = b x h (Area = base times height).
The answer is given in square units. They are usually
abbreviated like this: 4 sq. m or 4 m2.
Example: This rectangle is 6 centimeters long and 2
centimeters wide.
Area of a Parallelogram
The area of a parallelogram is computed by multiplying the
base times the height.
The formula is written: A = b x h or Area = base times height.
Example: This parallelogram has a base of 12 cm and a
height of 3 cm.
3 cm
A=bxh
A = 12 cm x 3 cm
A = 36 cm2
12 cm
Area of a Triangle
The area of a triangle is computed by multiplying 1– times the base
2
times the height.
A triangle is always one half of a rectangle or parallelogram.
bxh
The formula is written: A = 1– (b x h) or
2
2
Example: This triangle has a base of 10 cm and a height
of 4 cm.
Area of a Circle
The area of a circle is computed by multiplying pi (which is
approximately 3.14) times the radius times itself.
4 cm
10 cm
A=1
– (b x h)
2
A=1
– x 10 cm x 4 cm
2
A = 20 cm2
Example: This circle has a radius of 4 cm.
r = 4 cm
•
A = πr2 (Area = pi x the radius x the radius)
A = 3.14 x 4 cm x 4 cm
A = 50.24 cm2
13
3
Practice • • • • Computing the Areas of Rectangles
and Parallelograms
parallelogram
rectangle
All rectangles are also parallelograms. They
have two pairs of parallel sides.
The formula for the area of a rectangle is
A = l x w or A = b x h
w
The formula for the area of a parallelogram is A = bh
h
b
l
Directions: Use the information on page 13 to compute the areas of these rectangles and
parallelograms. Remember to indicate the unit—square feet, square meters, square inches, etc.—with
the answer.
1.
2.
18 yd.
A = _______
A = _______
7 yd.
8.2 m
5m
3.
4.
3.2 m
1.9 m
9 cm
A = _______
A = _______
7.5 cm
6.
3 1– in.
4
A = _______
5.
8 1– ft.
2
5 in.
A = _______
4 ft.
75 mm
8.
7.
A = _______
92 m
100 mm
A = _______
40 m
14
3
Practice
• • • • • • Computing the Areas of Triangles
This is the formula for computing the area of a triangle:
A=1
– b x h (or) A = b x h
2
2
A=1
–x8x4
2
A = 16 m2
4m
8m
Directions: Use the information on page 13 to compute the areas of these triangles. Remember to
indicate the unit—square feet, square meters, square inches, etc.—with the answer.
1. A = _____
2. A = _____
6 ft.
9 yd.
10 yd.
8 ft.
3. A = _____
4. A = _____
5.3 cm
6.6 cm
8.4 cm
4.4 cm
5. A = _____
6. A = _____
27 in.
9.1 m
30 in.
10.8 m
7. A = _____
8. A = _____
11.3 cm
9.5 m
20.6 cm
18.2 m
15
• • • • • • • • • • • • • • • • • • • • • • 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°
7
How to
Facts to Know
• • • • • • • • • • • • Understand Quadrangles
A quadrilateral is the name given to a plane figure with four straight sides. In other words, it’s a foursided polygon. Quadrilaterals are also called quadrangles. Quadrangles have four straight sides and
four angles.
Kinds of Quadrangles
A
• Square
A square has four sides, all the same length.
It has four right angles and two pairs of
parallel sides.
— —
— —
AB || CD and AC || BD
C
4''
4''
4''
B
E
• Rectangle
A rectangle has equal opposite sides. It has
four right angles and two pairs of parallel
sides.
— —
— —
EF || GH and EG || FH
D
4''
F
7''
4''
4''
G
B
• Rhombus
A rhombus has four equal sides like a square.
It has two pairs of parallel sides. It has equal
opposite angles.
— —
— —
AB || CD and AC || BD
• Parallelogram
A parallelogram has equal opposite sides like
a rectangle. It has two pairs of parallel sides.
It has equal opposite angles. A rhombus is a
kind of parallelogram.
— —
— —
MO || NP and MN || OP
H
7''
2''
2''
A
D
2''
2''
C
M
O
4''
2''
N
A
• Trapezoid
A trapezoid has only one pair of parallel
sides.
— —
AB || CD
P
4''
2''
4''
C
30
2''
B
5''
6''
D
7
How to
Facts to Know (cont.)
• • • • • • • • • • • • Understand Quadrangles
Finding Perimeter
Perimeter is the distance around a figure.
To find the perimeter of a triangle, a quadrilateral, or a polygon—a figure with three sides or more—
you add the lengths of the sides.
5'
4' + 5' + 7' = 16'
The perimeter of the triangle is 16'.
4'
7'
5''
6'' + 5'' + 4'' + 9'' = 24''
The perimeter of this trapezoid is 24''.
6''
4''
9''
3 ft.
3 ft.
3 ft.
3 ft. + 3 ft. + 3 ft. + 3 ft. = 12 ft.
The perimeter of this square is 12 ft.
3 ft.
There are formulas for finding perimeter, but sometimes just adding up the sides is faster.
• For the perimeter of a square: P (Perimeter) = 4s (side). For the square above, enter the numbers
in the formula, P = 4(3 ft.) or 12 ft.
• For the perimeter of a rectangle or parallelogram:
P (Perimeter) = 2w (width) + 21 (length). Let’s say
you knew the lengths of two sides of a rectangle.
5 ft.
You could use the formula:
P = 2(5 ft.) + 2(14 ft.), which is 38 ft.
14 ft.
31
7
Practice
• • • • • • • • • • • Identifying and Finding the
Perimeter of Quadrangles
Directions: Read the clues and answer the questions.
1. It has 2 pairs of equal opposite sides like
a rectangle.
It has two pairs of parallel sides.
It has 2 pairs of equal opposite angles.
What kind of quadrangle is it?
_________________________________
2. It has one pair parallel sides.
What kind of quadrangle is it?
____________________________
Directions: Identify the following quadrangles.
5'
100°
80°
8''
5'
5'
5''
5''
100°
80°
8''
5'
3. _________________________________
4. _________________________________
5''
110°
3''
8''
4''
140°
40°
70°
7''
6''
130°
130°
50°
50°
6''
8''
5. _________________________________
6. _________________________________
32
7
Practice
• • • • • • • • • • • Identifying and Finding the
Perimeter of Quadrangles
Directions: Find the perimeter.
30 ft.
7. ______________________
8. ______________________
7 ft.
11 ft.
9. A parallelogram has a perimeter of 13 feet. Its length is 3.75 feet. What is its width? __________
10. A square has a perimeter of 28 feet. What is the length of one side? _______________________
11. Grandma’s garden has sides of 15 ft., 10 ft., 8 ft., and 12 ft.
How much fencing does she need to keep the rabbits out? ________________________________
12. Myra’s poster of the Rockin’ Jellybeans measures 4 ft. by 3 ft.
How much frame does she need to go around it?________________________________________
33
8
How to
Facts to Know
• • • • • • • • • • • Find the Areas of Different
Geometric Shapes
Area is the amount of space on a flat surface. Area is measured in square units: square inches, square
feet, square miles, etc. Think of a surface covered with square tiles. In the drawing below, each tile is
1 square inch.
19 in.
9 in.
If you counted them all, you would find there are 171 square inches in this 19 in. by 9 in. rectangle.
But there’s a simpler way to arrive at the total number of square inches.
Finding the Area of Rectangles
In the rectangle above, there are 9 rows of 19 square inches. A shortcut is to multiply 9 in. x 19 in.,
which would give you 171 square inches.
The formula for finding the area of a rectangle is A (area) = l (length) x w (width).
4 ft.
Here’s an example using the formula:
A=lxw
A = 4 ft. x 3 ft.
A = 12 ft.2
3 ft.
So, the area is 12 sq. ft.
Always remember to add square or sq. in the answer to an area problem.
Finding the Area of Squares
A square is a quadrilateral with four equal sides. The formula to find the area is even simpler:
A (area) = s (side) x s (side) or A = s2.
5 ft.
Using the formula,
A=sxs
A = 5 ft. x 5 ft.
A = 25 ft.2
5 ft.
So, the area of the square is 25 sq. ft.
34
8
How to
• • • • • • • • • • • Find the Areas of Different
Geometric Shapes
Facts to Know (cont.)
Finding the Area of Triangles
To find the area of a triangle, you need to know the base and the height. The base can be any side of
the triangle. The height of a triangle is its altitude.
The altitude is a line that is perpendicular to
the base and extends from the angle
opposite the base.
altitude
Perpendicular lines form right (90°) angles.
base
To find the area, the height or altitude must be given so that you can put the numbers into the formula,
A (area) = 1– b (base) x h (height) or A = 1– bh.
2
2
10 ft.
1
Here’s an example using the formula: A = – x 10 x 8
(base)
2
A = 1– (80)
2
A = 40
8 ft.
(height)
So, the area of the triangle is 40 sq. ft.
Finding the Area of Parallelograms
You use the same logic for finding the area of a triangle to find the area of a parallelogram. To find the
area, the height must be given in the problem.
The formula is A (area) = b (base) x h (height) or A = bh.
9 ft.
(base)
Using the formula,
A=9x5
A = 45
So, the area of the
parallelogram is 45 sq. ft.
5 ft.
(height)
35
8
Practice
• • • • • • • • • Finding the Areas of Different
Geometric Shapes
Directions: Answer the questions.
1. The high jump pit is a rectangle 12 feet long and 10 feet wide.
What is the area? _______________
2. Ingrid is purchasing a rectangular rug that measures 6 ft. by 8 ft.
How many square feet of floor space will it cover? _________________________
3. A baseball field has 20 yards between bases. The Izaac Walton Ball Club wants to buy a tarp that
will cover the field at night.
How big will the tarp have to be? ________________
4. What is the area of the square below? ______ What is the area of the rectangle below? _______
10.5 in.
22''
8''
5. Ingrid’s first rug was too small. So, she bought a 8 ft. by 10 ft. rug instead. It’s going to go in a
10 ft. by 12 ft. room. How much floor space won’t be covered by the rug? __________________
10 ft.
8 ft.
12 ft.
10 ft.
rug
room
6. Find the area of a rectangle that has a length of 6.5 ft. and a width of 2.25 ft. ________________
36
8
Practice
• • • • • • • • • Finding the Areas of Different
Geometric Shapes
Directions: Find the area of each triangle.
7.
5'
5'
Area = ________________
3'
8'
8.
6''
Area = ________________
2''
4.25''
3''
9.
5'
3'
Area = ________________
4'
Directions: Find the area of each parallelogram.
10.
Area = ________________
2.3'
9.5'
11.
Area = ________________
5.3'
7'
12.
Area = ________________
6.5''
18''
37
▲
●
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.