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Lesson 13.1 Skills Practice
Name ________________________________________________________ Date _________________________
The Language of GeometrySketching, Drawing, Naming, and Sorting Basic Geometric Figures
VocabularySketch an example of each geometric figure.
1. triangle 2. quadrilateral 3. square 4. rectangle 5. polygon
6. scalene triangle 7. equilateraltriangle
8. regular polygon 9. irregularpolygon
10. pentagon
11. equiangulartriangle
12. hexagon 13. isoscelestriangle
14. nonagon 15. kite
16. obtuse triangle 17. acutetriangle
18. octagon 19. rhombus 20. trapezoid
21. right triangle 22. heptagon 23. parallelogram 24. decagon 25. isoscelestrapezoid
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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.
28. In a quadrilateral, are sides that do not share a common endpoint.
29. A(n) 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, are sides that share a common endpoint.
33. When you a geometric figure, the figure is created without the use of
tools.
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Lesson 13.1 Skills Practice page 3
Name ________________________________________________________ Date _________________________
Problem SetName each polygon and list its sides and angles.
1.
Sample answer.
Name of Polygon: quadrilateral MTFD
Sides: MT, TF, FD, and DM
Angles: /M (or /DMT ), /T (or /MTF ),
/F (or /TFD), and /D (or FDM )
2.
Name of Polygon:
Sides:
Angles:
3.
Name of Polygon:
Sides:
Angles:
4.
Name of Polygon:
Sides:
Angles:
F
DM
T
TQ
WZ
BR
XM
H K
S C
GY
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Lesson 13.1 Skills Practice page 4
5.
Name of Polygon:
Sides:
Angles:
6.
Name of Polygon:
Sides:
Angles:
N
W
P
T
RX B
M
EZ
T XW
JA
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Lesson 13.1 Skills Practice page 5
Name ________________________________________________________ Date _________________________
Sort the given polygons into the appropriate categories.
BC
D
H
KJ
A
E F G
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:
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Chapter 13 Skills Practice • 725
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Lesson 13.2 Skills Practice
Name ________________________________________________________ Date _________________________
Weaving a RugArea and Perimeter of Rectangles and Squares
Problem SetCalculate the perimeter of each given rectangle. Each square on the grid represents a square that
is 1 foot long and 1 foot wide.
1. 2.
Perimeter 5 2(12) 1 2(8)
5 24 1 16 5 40 feet
3. 4.
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Lesson 13.2 Skills Practice page 2
5. 6.
Calculate the perimeter of each given rectangle.
7.
3 in.
5 in.
8. 2 in.
9 in.
P 5 2(5) 1 2(3) 5 10 1 6 5 16 in.
9.
4 m
2 m
10.
12 m
8 m
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Lesson 13.2 Skills Practice page 3
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11. 12.
Calculate the area of each given rectangle. Each grid square is 1 foot long and 1 foot wide.
13. 14.
Area 5 6(13) 5 78 square feet
15. 16.
8 ft
4.5 ft
9.5 m
9.5 m
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Lesson 13.2 Skills Practice page 4
17. 18.
Calculate the area of each given rectangle.
19.3 cm
11 cm
20. 4 cm
7 cm
A 5 11(3) 5 33 cm2
21.
2.5 m
1.75 m
22.
11.2 m
2.3 m
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Lesson 13.2 Skills Practice page 5
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23. 14 ft
14 ft
24. 12 in.
12 in.
In each rectangle, the length, width, or area is unknown. Calculate the value of the unknown measure.
25.
Length: 4 ft
Area: 12 ft2
26.
Length: 7 ft
Area: 35 ft2
A 5 lw
12 5 4w
3 5 w
The width is 3 feet.
27.
6 yd
2 yd
28.
5 yd
13 yd
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Lesson 13.2 Skills Practice page 6
29.
Area: 30 in.2 Width: 4 in.
30.
Area: 65 m2 Width: 5 m
Calculate the missing measures using the given measure for each square.
31. Side length: 6 feet 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
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Lesson 13.2 Skills Practice page 7
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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
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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.
43.
8 m
8 m
8 m
8 m 8 m
A 5 24 (8) 1 8 (8)
5 192 1 64
5 256 m2
44.
2 ft
4 ft
6 ft
11 ft
45.
6 in.6 in.
5 in.
5 in.
5 in.
8 in.14 in.14 in.
46.
9 ft
6 ft
6 ft
10 ft 18 ft
5 ft
8 ft
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Lesson 13.2 Skills Practice page 9
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47. 5 m
4 m5 m
4 m
16 m5 m
48. 7 m 7 m
7 m
14 m
7 m
16 m
49.
6 ft
6 ft
8 ft
7 ft7 ft
20 ft
20 ft 50. 6 m
8 m
6 m4 m
3.5 m 3.5 m
6 m
6 m
4 m
6 m
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Chapter 13 Skills Practice • 735
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Lesson 13.3 Skills Practice
Name ________________________________________________________ Date _________________________
Boundary LinesArea of Parallelograms and Triangles
VocabularyDefine 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
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Lesson 13.3 Skills Practice page 2
Problem SetCalculate the area of each given parallelogram. Each square on the grid represents a square that
is 1 centimeter long and 1 centimeter wide.
1. 2.
Area 5 6(9) 5 54 square centimeters
3. 4.
5. 6.
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Lesson 13.3 Skills Practice page 3
Name ________________________________________________________ Date _________________________
Calculate the area of each parallelogram.
7.4 mi
8 mi
8.
11 mi
6 mi
A 5 8(4) 5 32 mi2
9.
32 yd
14 yd
10.
16 yd
7 yd
In each given parallelogram, the base, height, or area is unknown. Calculate the value of
the unknown measure.
11.
8 in.
8.5 in.
12.
4.5 ft
20 ft
A 5 8.5(8) 5 68 in.2
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Lesson 13.3 Skills Practice page 4
13.
Area: 63 m2
9 m
14. Area: 36 m2
18 m
15.Area: 96 ft2
12 ft
16.
Area: 286 ft2
22 ft
17.
12 ft
15 ft
18.
Area: 138 m2
9.2 m
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Lesson 13.3 Skills Practice page 5
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The base of each triangle is labeled. Draw a segment that represents the height of the triangle.
19.
b
h
20.
b
21.
b
22.
b
23.
b
24.
b
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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.
25. 26.
Area 5 1 __ 2 (12)(8) 5 48 square feet
27. 28.
29. 30.
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Lesson 13.3 Skills Practice page 7
Name ________________________________________________________ Date _________________________
Calculate the area of each given triangle.
31.
8 in.
6 in. 32.
7 ft
7 ft
A 5 1 __ 2
(6)(8) 5 1 __ 2 (48) 5 24 in.2
33.
11 mm
20 mm
34.
4 m
4.5 m
35.
7.5 in
18 in
36.
12 m
14 m
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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
15 m
38.2 ft
3 ft
A 5 1 __ 2
bh
30 5 1 __ 2
(15)h
60 5 15h
4 5 h
The height of the triangle is 4 meters.
39.
Area: 35 sq. in.
10 in.
40.
3 yd
Area: 6 sq. yd
41.
8 ft
Area: 88 sq ft 42.
6 in.Area: 31.5 sq in.
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Lesson 13.3 Skills Practice page 9
Name ________________________________________________________ Date _________________________
Calculate the area of each shaded region.
43. The figure is composed of 2 triangles.
9 m
15 m
20 m
The area of the large triangle is: The area of the small triangle is:
A 5 1 __ 2 bh A 5 1 __
2 bh
5 1 __ 2
(20)(15) 5 1 __ 2
(20)(9)
5 150 m2 5 90 m2
The shaded area 5 150 2 90 5 60 m2
44. The figure is composed of a parallelogram and a triangle.
10 yd
5 yd 2 yd
7 yd
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Lesson 13.3 Skills Practice page 10
45. The figure is composed of 2 triangles.
6 m
14 m
16 m
46. The figure is composed of a parallelogram and a triangle.
8 ft
9 ft
3 ft
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Lesson 13.3 Skills Practice page 11
Name ________________________________________________________ Date _________________________
47. The figure is composed of 2 triangles.
6 in.
12 in.
8 in.
3 in.
48. The figure is composed of 2 parallelograms and 1 triangle.
9 m
9 m
3 m
22 m
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Chapter 13 Skills Practice • 747
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The Keystone EffectArea of Trapezoids
VocabularyExplain 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 SetCalculate the area of each given trapezoid. Each square on the grid represents a square that is 1 inch
long and 1 inch wide.
1. 2.
A 5 1 __ 2 (8 1 4) 5
5 1 __ 2
(12)(5)
5 30
The area of the trapezoid is 30 square inches.
Lesson 13.4 Skills Practice
Name ________________________________________________________ Date _________________________
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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.
7. h 5 2, b1 5 4, b2 5 3 8. h 5 6, b1 5 5, b2 5 3
A 5 1 __ 2 (4 1 3)2 5 1 __
2 (7)(2) 5 7
The area is 7 square units.
9. h 5 3, b1 5 11, b2 5 7 10. h 5 5, b1 5 9, b2 5 1
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Lesson 13.4 Skills Practice page 3
Name ________________________________________________________ Date _________________________
11. h 5 1 __ 2
, b1 5 10, b2 5 14 12. h 5 4, b1 5 2 __ 3 , b2 5 4 __
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
3 feet
2 feet
14. 3 centimeters Area: 8 square centimeters
2 centimeters
A 5 1 __ 2 (2 1 4)3 5 1 __
2 (6)(3) 5 9
The trapezoid has an area of
9 square feet.
15. Area: 5 square feet
3 feet
1 feet
16.5 yards
8 yards
Area: 25 square yards
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Lesson 13.4 Skills Practice page 4
17. 2 millimeters
4 millimeters
Area: 14 square millimeters
18. 15 yards
Area: 70 square yards
5 yards
19. Area: 13.5 square inches
3 inches
3 inches
20. 13 feet
5 feet
22 feet
21.
5 yards 2 yards 8 yards
22. 13 meters
7 meters
Area: 98 square meters
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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?
26 feet
13 feet
11 feet
A 5 1 __ 2 (b1 1 b2)h
A 5 1 __ 2 (26 1 13)11
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.
7 in.4 in.
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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?
5 feet4 feet
7 feet
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Lesson 13.4 Skills Practice page 7
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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?
3 in.
6 in.
4 in.
4 in.
9 in.
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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?
8 cm
14 cm
25 cm
12 cm
10 cm
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Lesson 13.5 Skills Practice
Name ________________________________________________________ Date _________________________
Go Fly a KiteArea of Rhombi and Kites
Problem SetCalculate 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.
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Lesson 13.5 Skills Practice page 2
3. The polygon is a rhombus. 4. The polygon is a kite.
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Lesson 13.5 Skills Practice page 3
Name ________________________________________________________ Date _________________________
5. The polygon is a kite. 6. The polygon is a kite.
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Lesson 13.5 Skills Practice page 4
Calculate the area of each given rhombus or kite.
7. The polygon is a rhombus.
13 in.
15 in.
A 5 bh
5 15 (13)
5 195
The area of the rhombus is 195 square
inches.
8. The polygon is a rhombus.
8.5 m
7 m
9. The polygon is a rhombus.
12 yd
11 yd
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Lesson 13.5 Skills Practice page 5
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10. In the given kite, AE 5 6 ft, CE 5 6 ft, BE 5 9 ft, and DE 5 15 ft.
E
B
D
CA
11. In the given kite, JK 5 3 meters, FK 5 7 meters, GK 5 12 meters, and HK 5 7 meters.
KGJ
H
F
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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.
ZTR
W
S
Calculate the area of each shaded region.
13. The figure is composed of 2 congruent rhombi.
16 ft
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.
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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.
C
A
F
E
B
GD
Lesson 13.5 Skills Practice page 7
Name ________________________________________________________ Date _________________________
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Lesson 13.5 Skills Practice page 8
15. The figure is composed of a trapezoid and a rhombus.
8.5 in.
11 in.
10 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.
M
Q
N
S TRP
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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.
C
A
EB D
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Lesson 13.5 Skills Practice page 10
18. The figure is composed of 2 congruent triangles and a rhombus.
4 in.
4 in.5 in.
4 in.
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Street SignsArea of Regular Polygons
VocabularyDraw an example of each given term.
1. congruent polygons
2. apothem
Problem SetDetermine whether each polygon is a regular polygon.
1. 2.
The polygon is not a regular polygon.
Lesson 13.6 Skills Practice
Name ________________________________________________________ Date _________________________
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Lesson 13.6 Skills Practice page 2
3.120° 120°
120°120°
120° 120°
5 cm
5 cm
5 cm
5 cm
5 cm
5 cm
4. 4 inches
4 inches4 inches
7 inches
70° 70°
110° 110°
5.
3 ft
3 ft 3 ft120°
100° 100°
110°110°
3 ft
3 ft
6.
135° 135°
135°
135° 135°
135° 135°
135°
Draw an apothem of each given figure.
7. 8.
9. 10.
11. 12.
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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
A 5 ( 1 __ 2
ha ) 8 5 4 ha
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. 8 cm
6.3 cm
20.
12 ft
8.3 ft
A 5 1 __ 2
(8)(6.3)(6)
A 5 151.2
The area is 151.2 square centimeters.
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Lesson 13.6 Skills Practice page 4
21.
20 km
24.1 km
22. 10 yd
10.4 yd
23.
15 in.
4.3 in.
24. 4 in.
7.5 in.
25.
2 m
1 m
26. 12 m
6 m
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?
A 5 1 __ 2 (26)(40)(10)
5 5200
The area of the regular decagon is 5200 square yards.
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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?
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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.
9 in.
20 in.
13 in.
The area of the square is: The area of the pentagon is:
A 5 s2 A 5 ( 1 __ 2
la ) n5 (20)2 5 1 __
2 (13)(9)(5)
5 400 square inches 5 292.50 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.
8.7 ft
11 ft
10 ft
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Lesson 13.6 Skills Practice page 7
Name ________________________________________________________ Date _________________________
35. The figure is composed of a regular pentagon and 2 congruent trapezoids.
19 cm
10 cm
13.3 cm 9.7 cm
14 cm
36. The figure is half of a regular octagon.
14.5 in.
12 in.
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Lesson 13.6 Skills Practice page 8
37. The figure is composed of 2 regular pentagons.
10.3 m
10 m
15 m
6.9 m
38. The figure is composed of 4 congruent regular hexagons.
22 ft
19 ft