Lesson 13 - Room 12mrpack.weebly.com/uploads/8/5/0/5/8505687/math... · Lesson 13.3 Skills Practice...

Chapter 13 Skills Practice • 719

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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

720 • Chapter 13 Skills Practice

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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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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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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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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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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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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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Name ________________________________________________________ Date _________________________

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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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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Name ________________________________________________________ Date _________________________

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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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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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


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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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Name ________________________________________________________ Date _________________________

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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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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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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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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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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Name ________________________________________________________ Date _________________________

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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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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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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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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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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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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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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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.


Name ________________________________________________________ Date _________________________


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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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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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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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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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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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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?

3 in.

6 in.

4 in.

4 in.

9 in.


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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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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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5. The polygon is a kite. 6. The polygon is a kite.


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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.


8.5 m

7 m


12 yd

11 yd


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Name ________________________________________________________ Date _________________________

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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12. In the given kite, SZ 5 WZ 5 10 yards, TZ 5 12 yards, and RZ 5 32 yards.

ZTR

W

S


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


Name ________________________________________________________ Date _________________________


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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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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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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.


Name ________________________________________________________ Date _________________________


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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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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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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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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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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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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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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

Lesson 13 - Room 12mrpack.weebly.com/uploads/8/5/0/5/8505687/math... · Lesson 13.3 Skills Practice...

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