Course 1 Student Skills Practice Chapter 13

Lesson 13.1
Skills Practice
Name________________________________________________________ Date _________________________
The Language of Geometry
Sketching, Drawing, Naming, and Sorting Basic Geometric Figures
Vocabulary
Sketch an example of each geometric figure.
1. triangle
3. square
4. rectangle
5. polygon
6. scalene triangle
7. equilateral
triangle
8. regular polygon
9. irregular
polygon
10. pentagon
11. equiangular
triangle
12. hexagon
13. isosceles
triangle
14. nonagon
15. kite
16. obtuse triangle
17. acute
triangle
18. octagon
19. rhombus
20. trapezoid
21. right triangle
22. heptagon
23. parallelogram
24. decagon
25. isosceles
trapezoid
Chapter 13 Skills Practice • 719
Lesson 13.1
Skills Practice
page 2
Write the term that best completes each statement.
26. When you
a geometric figure, the figure is created with the use of tools
such as a ruler, a straightedge, a compass, or a protractor.
27. A(n)
is a tool used to create arcs or circles.
29. A(n)
are sides that do not share a common endpoint.
is a ruler with no numbers.
30. When you
a geometric figure, the figure is created using only a compass
and a straightedge.
31. A(n)
can be used to approximate the measure of an angle.
32. In a polygon,
33. When you
are sides that share a common endpoint.
a geometric figure, the figure is created without the use of
tools.
720 • Chapter 13 Skills Practice
Lesson 13.1
Skills Practice
page 3
Name________________________________________________________ Date _________________________
Problem Set
Name each polygon and list its sides and angles.
1.
F
2.
Q
T
T
M
Z
D
R
Sides: MT, TF, FD, and DM
Angles: /M (or /DMT ), /T (or /MTF ),
/F (or /TFD), and /D (or FDM )
3.
W
Name of Polygon:
Sides:
Angles:
4.
H
B
K
Y
G
S
M
Name of Polygon:
Sides:
Angles:
C
X
Name of Polygon:
Sides:
Angles:
Chapter 13 Skills Practice • 721
Lesson 13.1
5.
Skills Practice
page 4
6.
P
W
T
Z
X
R
T
Name of Polygon:
Sides:
Angles:
N
X
M
E
B
A
J
W
Name of Polygon:
Sides:
Angles:
722 • Chapter 13 Skills Practice
Lesson 13.1
Skills Practice
page 5
Name________________________________________________________ Date _________________________
Sort the given polygons into the appropriate categories.
A
C
B
F
E
D
G
J
H
K
7. Regular polygons: C, F, H, and K
Irregular polygons: A, B, D, E, G, and J
8. Polygons with at least one right angle:
Polygons with no right angles:
9. Polygons with at least one pair of congruent sides:
Polygons with no congruent sides:
10. Polygons with at least one obtuse angle:
Polygons with no obtuse angles:
11. Polygons with at least one pair of opposite sides parallel:
Polygons with no opposite sides parallel:
12. Polygons with at least one acute angle:
Polygons with no acute angles:
Chapter 13 Skills Practice • 723
724 • Chapter 13 Skills Practice
Lesson 13.2
Skills Practice
Name________________________________________________________ Date _________________________
Weaving a Rug
Area and Perimeter of Rectangles and Squares
Problem Set
Calculate the perimeter of each given rectangle. Each square on the grid represents a square that
is 1 foot long and 1 foot wide.
2.
1.
Perimeter 5 2(12) 1 2(8)
5 24 1 16 5 40 feet
4.
3.
Chapter 13 Skills Practice • 725
Lesson 13.2
Skills Practice
5.
page 2
6.
Calculate the perimeter of each given rectangle.
8.
7.
2 in.
3 in.
9 in.
5 in.
P 5 2(5) 1 2(3) 5 10 1 6 5 16 in.
9.
10.
12 m
2m
8m
726 • Chapter 13 Skills Practice
4m
Lesson 13.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
11. 12. 4.5 ft
9.5 m
9.5 m
8 ft
Calculate the area of each given rectangle. Each grid square is 1 foot long and 1 foot wide.
13.
14.
16.
Area 5 6(13) 5 78 square feet
15.
Chapter 13 Skills Practice • 727
Lesson 13.2
Skills Practice
17.
page 4
18.
Calculate the area of each given rectangle.
19.
3 cm
20.
4 cm
11 cm
7 cm
A 5 11(3) 5 33 cm
2
21.
22.
2.5 m
11.2 m
2.3 m
728 • Chapter 13 Skills Practice
1.75 m
Lesson 13.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
23.
14 ft
24.
12 in.
14 ft
12 in.
In each rectangle, the length, width, or area is unknown. Calculate the value of the unknown measure.
25.
26.
Area: 12 ft2
Area: 35 ft2
Length: 4 ft
Length: 7 ft
A 5 lw
12 5 4w
35w
The width is 3 feet.
27.
28.
5 yd
6 yd
2 yd
13 yd
Chapter 13 Skills Practice • 729
Lesson 13.2
Skills Practice
29.
page 6
30.
Area: 30 in.2
Area: 65 m2
Width: 4 in.
Width: 5 m
Calculate the missing measures using the given measure for each square.
32. Side length: 18 centimeters
Area: 36 square feet
Area:
Perimeter: 24 feet
Perimeter:
33. Side length:
34. Side length:
Area: 16 square inches
Area:
Perimeter:
Perimeter: 36 meters
35. Side Length: 5.5 inches
36. Side Length:
Area:
Area: 400 square meters
Perimeter:
Perimeter:
Calculate the perimeter and area of a rectangle or square whose dimensions are double
the dimensions of each given rectangle or square.
37. A rectangle with a perimeter of 14 meters and an area of 10 square meters
The rectangle whose dimensions are doubled will have the following perimeter and area.
Perimeter 5 2 (14)
5 28 meters
Area 5 4 (10)
5 40 square meters
730 • Chapter 13 Skills Practice
31. Side length: 6 feet
Lesson 13.2
Skills Practice
page 7
Name________________________________________________________ Date _________________________
38. A rectangle with a perimeter of 30 feet and an area of 54 square feet
39. A square with a perimeter of 60 meters and an area of 225 square meters
40. A square with a perimeter of 14 inches and an area of 12.25 square inches
41. A rectangle with a perimeter of 42 meters and an area of 20 square meters
Chapter 13 Skills Practice • 731
Lesson 13.2
Skills Practice
page 8
42. A square with a perimeter of 72 feet and an area of 324 square feet
Calculate the area of each composite figure.
44.
8m
43.
11 ft
2 ft
8m
8m
6 ft
8m
8m
4 ft
A 5 24 (8) 1 8 (8)
5 192 1 64
5 256 m2
46.
5 in.
8 ft
5 ft
8 in.
14 in.
9 ft
14 in.
6 in.
6 in.
10 ft
6 ft
5 in.
5 in.
732 • Chapter 13 Skills Practice
6 ft
18 ft
45.
Lesson 13.2
Skills Practice
page 9
Name________________________________________________________ Date _________________________
47.
48.
5m
7m
4m
7m
7m
5m
7m
16 m
14 m
4m
5m
16 m
49.
50.
20 ft
7 ft
7 ft
6m
6 ft
3.5 m
4m
8 ft
6m
8m
6m
6m
3.5 m
4m
6m
6 ft
20 ft
Chapter 13 Skills Practice • 733
734 • Chapter 13 Skills Practice
Lesson 13.3
Skills Practice
Name________________________________________________________ Date _________________________
Boundary Lines
Area of Parallelograms and Triangles
Vocabulary
Define each term in your own words.
1. altitude of a parallelogram
2. height of a parallelogram
3. altitude of a triangle
4. height of a triangle
Chapter 13 Skills Practice • 735
Lesson 13.3
Skills Practice
page 2
Problem Set
Calculate the area of each given parallelogram. Each square on the grid represents a square that
is 1 centimeter long and 1 centimeter wide.
2.
1.
Area 5 6(9) 5 54 square centimeters
4.
5.
6.
3.
736 • Chapter 13 Skills Practice
Lesson 13.3
Skills Practice
page 3
Name________________________________________________________ Date _________________________
Calculate the area of each parallelogram.
7.
8.
4 mi
6 mi
8 mi
11 mi
A 5 8(4) 5 32 mi2
9.
10.
16 yd
32 yd
7 yd
14 yd
In each given parallelogram, the base, height, or area is unknown. Calculate the value of
the unknown measure.
12.
11.
4.5 ft
8 in.
20 ft
8.5 in.
A 5 8.5(8) 5 68 in.2
Chapter 13 Skills Practice • 737
Lesson 13.3
Skills Practice
13.
page 4
14.
Area: 36 m2
18 m
Area: 63 m2
9m
15.
16.
Area: 96 ft2
Area: 286 ft2
12 ft
22 ft
18.
Area: 138 m2
12 ft
15 ft
738 • Chapter 13 Skills Practice
9.2 m
17. Lesson 13.3
Skills Practice
page 5
Name________________________________________________________ Date _________________________
The base of each triangle is labeled. Draw a segment that represents the height of the triangle.
19.
20.
b
h
b
21.
22.
b
b
23.
b
24.
b
Chapter 13 Skills Practice • 739
Lesson 13.3
Skills Practice
page 6
Calculate the area of each given triangle. Each square on the grid represents a square that is 1 foot
long and 1 foot wide.
26.
25.
1(12)(8) 5 48 square feet
Area 5 __
2
28.
29.
30.
27.
740 • Chapter 13 Skills Practice
Lesson 13.3
Skills Practice
page 7
Name________________________________________________________ Date _________________________
Calculate the area of each given triangle.
31.
6 in.
32.
7 ft
8 in.
7 ft
1(6)(8) 5 __
1(48) 5 24 in.2
A 5 __
2
2
33.
34.
4.5 m
4m
20 mm
11 mm
35.
36.
7.5 in
12 m
18 in
14 m
Chapter 13 Skills Practice • 741
Lesson 13.3
Skills Practice
page 8
In each given triangle, the base, height, or area is unknown. Calculate the value of
the unknown measure.
37.
Area: 30 sq. m
38.
2 ft
15 m
3 ft
1 bh
A 5 __
2
1 (15)h
30 5 __
2
60 5 15h
45h
The height of the triangle is 4 meters.
39.
40.
3 yd
10 in.
Area: 6 sq. yd
41.
42.
Area: 88 sq ft
8 ft
742 • Chapter 13 Skills Practice
6 in.
Area: 31.5 sq in.
Area: 35 sq. in.
Lesson 13.3
Skills Practice
page 9
Name________________________________________________________ Date _________________________
Calculate the area of each shaded region.
43. The figure is composed of 2 triangles.
15 m
9m
20 m
The area of the large triangle is:
The area of the small triangle is:
1 bh
A 5 __
2
1 (20)(15)
5 __
2
5 150 m2
1 bh
A 5 __
2
1
__
5 (20)(9)
2
5 90 m2
The shaded area 5 150 2 90 5 60 m2
44. The figure is composed of a parallelogram and a triangle.
7 yd
10 yd
5 yd
2 yd
Chapter 13 Skills Practice • 743
Lesson 13.3
Skills Practice
page 10
45. The figure is composed of 2 triangles.
6m
16 m
14 m
46. The figure is composed of a parallelogram and a triangle.
3 ft
9 ft
744 • Chapter 13 Skills Practice
8 ft
Lesson 13.3
Skills Practice
page 11
Name________________________________________________________ Date _________________________
47. The figure is composed of 2 triangles.
6 in.
8 in.
3 in.
12 in.
48. The figure is composed of 2 parallelograms and 1 triangle.
22 m
9m
9m
3m
Chapter 13 Skills Practice • 745
746 • Chapter 13 Skills Practice
Lesson 13.4
Skills Practice
Name________________________________________________________ Date _________________________
The Keystone Effect
Area of Trapezoids
Vocabulary
Explain how the set of terms are related.
1. legs of a trapezoid and bases of a trapezoid
2. altitude of a trapezoid and height of a trapezoid
Problem Set
Calculate the area of each given trapezoid. Each square on the grid represents a square that is 1 inch
long and 1 inch wide.
2.
1.
1(8 1 4) 5
A 5 __
2
1(12)(5)
5 __
2
5 30
The area of the trapezoid is 30 square inches.
Chapter 13 Skills Practice • 747
Lesson 13.4
Skills Practice
page 2
3.
4.
5.
6.
Calculate the area of each trapezoid with the given dimensions, where h represents the height, b1
represents the length of a base, and b2 represents the length of the other base.
8. h 5 6, b1 5 5, b2 5 3
1 (4 1 3)2 5 __
1 (7)(2) 5 7
A 5 __
2
2
The area is 7 square units.
9. h 5 3, b1 5 11, b2 5 7
748 • Chapter 13 Skills Practice
10. h 5 5, b1 5 9, b2 5 1
7. h 5 2, b1 5 4, b2 5 3
Lesson 13.4
Skills Practice
page 3
Name________________________________________________________ Date _________________________
1, b 5 10, b 5 14
11. h 5 __
2
2 1
2 , b 5 __
4
12. h 5 4, b1 5 __
3 2 3
In each given trapezoid, the length of one base, the height, or the area is unknown. Calculate
the value of the unknown measure.
13.
4 feet
14.
3 centimeters
Area: 8 square centimeters
2 centimeters
3 feet
2 feet
1(2 1 4)3 5 __
1(6)(3) 5 9
A 5 __
2
2
The trapezoid has an area of
9 square feet.
Area: 5 square feet 15.
16.
5 yards Area: 25 square yards
3 feet
1 feet
8 yards
Chapter 13 Skills Practice • 749
Lesson 13.4
17.
Skills Practice
2 millimeters
page 4
18.
15 yards
4 millimeters
Area: 70 square yards
5 yards
Area: 14 square millimeters
19.
Area: 13.5 square inches
20.
13 feet
3 inches
5 feet
3 inches
22 feet
22.
21.
7 meters
5 yards
8 yards
Area: 98 square meters
2 yards
13 meters
750 • Chapter 13 Skills Practice
Lesson 13.4
Skills Practice
page 5
Name________________________________________________________ Date _________________________
Use the given information to answer each question.
23. The side of a staircase has the shape of a trapezoid with the dimensions shown in
the diagram. You want to paint this side of the staircase. How many square feet will
you need to cover with paint?
13 feet
11 feet
26 feet
1(b 1 b )h
A 5 __
2
2 1
1
__
A 5 (26 1 13)11
2
A 5 214.5
You will need to cover 214.5 square feet with paint.
24. Yvonne cut a picture into the shape of a trapezoid to place into her scrapbook. The picture is
shown. What is the area of the picture?
5 in.
4 in.
7 in.
Chapter 13 Skills Practice • 751
Lesson 13.4
Skills Practice
page 6
25. A mosaic on a CD cover is in the shape of an isosceles trapezoid with the
dimensions shown in the diagram. The artist needs to tell the production
company the area of the mosaic. How many square inches is the mosaic?
4 inches
4 inches
3 inches
26. The planning committee submitted a plan to the town architect to revitalize the town square.
Their plan includes a new flagpole with a concrete base in the shape of a trapezoid. The base
of the trapezoid and its dimensions are shown. What is the area of the base proposed by the
planning committee?
4 feet
7 feet
5 feet
752 • Chapter 13 Skills Practice
Lesson 13.4
Skills Practice
page 7
Name________________________________________________________ Date _________________________
27. An aeronautical engineering student has painted a rocket-shaped design on her T-shirt.
The design is composed of a triangle, a rectangle, and a trapezoid. How many square
inches is the design?
4 in.
9 in.
3 in.
4 in.
6 in.
Chapter 13 Skills Practice • 753
Lesson 13.4
Skills Practice
page 8
28. An advertising company has designed its new logo. The logo is composed of two trapezoids.
What is the area of the shaded region?
25 cm
10 cm
8 cm
12 cm
14 cm
754 • Chapter 13 Skills Practice
Lesson 13.5
Skills Practice
Name________________________________________________________ Date _________________________
Go Fly a Kite
Area of Rhombi and Kites
Problem Set
Calculate the area of each given rhombus or kite. Each square on the grid represents a square
that is 1 foot long and 1 foot wide.
1. The polygon is a rhombus.
2. The polygon is a rhombus.
A 5 bh
5 10 (8)
5 80
The area of the rhombus is 80 square feet.
Chapter 13 Skills Practice • 755
Lesson 13.5
Skills Practice
4. The polygon is a kite.
3. The polygon is a rhombus.
page 2
756 • Chapter 13 Skills Practice
Lesson 13.5
Skills Practice
page 3
Name________________________________________________________ Date _________________________
6. The polygon is a kite.
5. The polygon is a kite.
Chapter 13 Skills Practice • 757
Lesson 13.5
Skills Practice
page 4
Calculate the area of each given rhombus or kite.
7. The polygon is a rhombus.
8. The polygon is a rhombus.
15 in.
7m
13 in.
8.5 m
A 5 bh
5 15 (13)
5 195
The area of the rhombus is 195 square
inches.
9. The polygon is a rhombus.
12 yd
11 yd
758 • Chapter 13 Skills Practice
Lesson 13.5
Skills Practice
page 5
Name________________________________________________________ Date _________________________
10. In the given kite, AE 5 6 ft, CE 5 6 ft, BE 5 9 ft, and DE 5 15 ft.
B
E
A
C
D
11. In the given kite, JK 5 3 meters, FK 5 7 meters, GK 5 12 meters, and HK 5 7 meters.
F
K
J
G
H
Chapter 13 Skills Practice • 759
Lesson 13.5
Skills Practice
page 6
12. In the given kite, SZ 5 WZ 5 10 yards, TZ 5 12 yards, and RZ 5 32 yards.
S
Z
R
T
W
Calculate the area of each shaded region.
13. The figure is composed of 2 congruent rhombi.
20 ft
The area of 1 rhombus is:
A 5 bh
5 20 (16)
5 320 square feet
The area of the figure is 2(320) 5 640 square feet.
760 • Chapter 13 Skills Practice
16 ft
Lesson 13.5
Skills Practice
page 7
Name________________________________________________________ Date _________________________
14. The figure is composed of a kite and a square.
Given: AG 5 7 meters, BG 5 FG 5 8 meters, DG 5 13.5 meters, and CE 5 9 meters.
B
C
G
A
D
E
F
Chapter 13 Skills Practice • 761
Lesson 13.5
Skills Practice
page 8
15. The figure is composed of a trapezoid and a rhombus.
10 in.
8.5 in.
11 in.
24 in.
16. The figure is composed of 2 kites.
Given: MR 5 RS 5 5 feet, ST 5 PT 5 10 feet, and NS 5 QS 5 12 feet.
N
R
S
T
Q
762 • Chapter 13 Skills Practice
P
M
Lesson 13.5
Skills Practice
page 9
Name________________________________________________________ Date _________________________
17. The figure is composed of a square and a kite.
Given: AE 5 9 inches, BE 5 DE 5 7 inches, and CE 5 15 inches.
A
E
B
D
C
Chapter 13 Skills Practice • 763
Lesson 13.5
Skills Practice
page 10
18. The figure is composed of 2 congruent triangles and a rhombus.
4 in.
5 in.
4 in.
4 in.
764 • Chapter 13 Skills Practice
Lesson 13.6
Skills Practice
Name________________________________________________________ Date _________________________
Street Signs
Area of Regular Polygons
Vocabulary
Draw an example of each given term.
1. congruent polygons
2. apothem
Problem Set
Determine whether each polygon is a regular polygon.
2.
1.
The polygon is not a regular polygon.
Chapter 13 Skills Practice • 765
Lesson 13.6 Skills Practice
3.
5 cm
120°
120°
5.
3 ft
4 inches
110°
5 cm
120°
100°
6.
135°
135°
135°
135°
100°
3 ft
110°
70°
7 inches
3 ft
3 ft
4 inches
70°
5 cm
120°
5 cm
110°
4 inches
120°
5 cm
120°
4.
5 cm
120°
page 2
135°
110°
135°
135°
3 ft
135°
7.
8.
9.
10.
11.
766 • Chapter 13 Skills Practice
12.
Draw an apothem of each given figure.
Lesson 13.6
Skills Practice
page 3
Name________________________________________________________ Date _________________________
Write a formula for the area of each regular polygon. State the area in terms of
an apothem a of the polygon.
13. regular octagon with side h
1 ha 8 5 4 ha
A 5 __
2
14. regular hexagon with side c
15. regular nonagon with side b
16. regular decagon with side d
17. regular pentagon with side length g
18. regular heptagon with side length t
(
)
Calculate the area of each regular polygon.
19.
20.
8 cm
12 ft
6.3 cm
8.3 ft
1(8)(6.3)(6)
A 5 __
2
A 5 151.2
The area is 151.2 square centimeters.
Chapter 13 Skills Practice • 767
Lesson 13.6
Skills Practice
21.
page 4
22.
10 yd
20 km
24.1 km
10.4 yd
24.
23.
4 in.
15 in.
7.5 in.
4.3 in.
26.
25.
12 m
2m
6m
Use the given information to calculate the area of each regular polygon.
27. A regular decagon has a side length of 26 yards and an apothem length of
40 yards. What is the area of the regular decagon?
1 (26)(40)(10)
A 5 __
2
5 5200
The area of the regular decagon is 5200 square yards.
768 • Chapter 13 Skills Practice
1m
Lesson 13.6
Skills Practice
page 5
Name________________________________________________________ Date _________________________
28. A regular 15-gon has a side length of 10 feet and an apothem length of 23.5 feet.
What is the area of the regular 15-gon?
29. A regular 12-gon has a side length of 11 meters and an apothem length of
20.5 meters. What is the area of the regular 12-gon?
30. A regular octagon has a perimeter of 36 millimeters and an apothem length of
5.4 millimeters. What is the area of the regular octagon?
31. A regular pentagon has a perimeter of 625 centimeters and an apothem length
of 86 centimeters. What is the area of the regular pentagon?
32. A regular 20-gon has a perimeter of 1000 inches and an apothem length of
157.8 inches. What is the area of the regular 20-gon?
Chapter 13 Skills Practice • 769
Lesson 13.6
Skills Practice
page 6
Calculate the area of each shaded region.
33. The figure is composed of a regular pentagon and a square.
13 in.
20 in.
9 in.
The area of the square is:
The area of the pentagon is:
A 5 s2
1 la n
A 5 __
2
1
__
5 (13)(9)(5)
2
5 292.50 square inches
( )
5 (20)2
5 400 square inches
The area of the shaded region is 400 2 292.50 5
107.50 square inches.
34. The figure is composed of a regular hexagon and a square.
10 ft
11 ft
8.7 ft
770 • Chapter 13 Skills Practice
Lesson 13.6
Skills Practice
page 7
Name________________________________________________________ Date _________________________
35. The figure is composed of a regular pentagon and 2 congruent trapezoids.
14 cm
10 cm
13.3 cm
9.7 cm
19 cm
36. The figure is half of a regular octagon.
12 in.
14.5 in.
Chapter 13 Skills Practice • 771
Lesson 13.6
Skills Practice
page 8
37. The figure is composed of 2 regular pentagons.
15 m
10 m
6.9 m
10.3 m
38. The figure is composed of 4 congruent regular hexagons.
22 ft