Where do hexagonsWhere do hexagonsWhere do hexagons

appear in nature?appear in nature?appear in nature?

Basaltic columns are geologicalformations that result from rapidlycooling lava. Most basaltic columns arehexagonal (six-sided) shapes.

The Giant’s Causeway on the Irish coast features hexagonal columns that reach a height of 82 feet.

Learn More About ItLearn More About ItLearn More About ItYou will learn more about rockformations in Exercise 31 on p. 436.

ChapterChapter 88

408

7.8 in.

9 in.

Polygons andAreaPolygons andArea

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Who usesPolygons and Area?

How will you use these ideas?

• Measure the angles of home plate on a baseball field. (p. 422)• Find the area of a judo mat. (p. 428)• Estimate the cost of planting a cornfield maze. (p. 429)• See how cranberries are harvested. (p. 456)• Determine the area covered by a lawn sprinkler. (p. 457)

LANDSCAPE ARCHITECTLandscape architects useengineering knowledge andcreativity to design outdoorenvironments, such as parks, gardens, andrecreational areas. (p. 457)

FLOORING INSTALLERFlooring installers are hired by flooring contractorsto install, repair, or replacefloor coverings, such ascarpet and hardwood. (p. 414)

409

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410 Chapter 8 Polygons and Area

Chapter Study GuideStudy Guide88

What’s the chapter about?

• Finding measures of interior and exterior angles of polygons• Finding the area of squares, rectangles, triangles, parallelograms,

and trapezoids• Finding the circumference and area of circles

Key Words

Take this quick quiz. If you are unsure of an answer, look at the

reference pages for help.

Vocabulary Check (refer to p. 325)

1. Which term does not describe the polygon below?

�A rhombus �B quadrilateral

�C rectangle �D parallelogram

Skill Check (refer to p. 305)

2. What is the sum of the measures of the interior angles of aquadrilateral?

�F 90� �G 180� �H 360� �J 540�

PREVIEWPREVIEW

Chapter Readiness QuizPREPAREPREPARE

Breaking Polygons into PartsVISUAL STRATEGYVISUAL STRATEGY

Visualize It!

• convex, p. 411• concave, p. 411• equilateral, p. 412• equiangular, p. 412• regular, p. 412

• area, p. 424• radius, p. 452• diameter, p. 452• circumference, p. 452• sector, p. 454

You can break a complexpolygon into simpler partswhose areas you know.

Total = Area of + Area of Area rectangle triangle

= +

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8.1 Classifying Polygons 411

Goal

Describe polygons.

Key Words

• convex

• concave

• equilateral

• equiangular

• regular

The Iranian tile pattern at the right shows several polygons. These polygons can be classified as convexor concave.

A polygon is if no line that contains a side of the polygonpasses through the interior of the polygon. A polygon that is notconvex is called .

Convex polygon Concave polygon

None of the extended sides At least one extended side pass through the interior. passes through the interior.

concave

convex

8.18.1 Classifying Polygons

Decide whether the polygon is convex or concave.

a. b.

Solution

a. At least one extended side b. None of the extended sidespasses through the interior. pass through the interior.So, the polygon is concave. So, the polygon is convex.

EXAMPLE 111 Identify Convex and Concave Polygons

interiorinterior

Extended side

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A polygon is if all of its sides are congruent. A polygon is

if all of its interior angles are congruent. A polygon is

if it is both equilateral and equiangular.

Equilateral Equiangular

All sides are congruent. All angles are congruent.

Regular Polygons

All sides are congruent and all angles are congruent.

regularequiangular

equilateral

412 Chapter 8 Polygons and Area

Decide whether the polygon is regular. Explain your answer.

a. b. c.

Solution

a. Although the polygon is equiangular, it is not equilateral. So, thepolygon is not regular.

b. Because the polygon is both equilateral and equiangular, it is regular.

c. Although the polygon is equilateral, it is not equiangular. So, thepolygon is not regular.

EXAMPLE 222 Identify Regular Polygons

Decide whether the polygon is convex or concave. Then decide

whether the polygon is regular. Explain your answer.

1. 2. 3.

Describe Polygons

MORE EXAMPLES

More examples atclasszone.com

IStudent HelpI C L A S S Z O N E . C O M

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8.1 Classifying Polygons 413

1. Sketch a concave polygon.

2. Describe the difference between an equilateral polygon and anequiangular polygon.

3. What is a regular polygon?

Decide whether the polygon shown in black is convex or concave.

4. 5. 6.

Match the polygon with the description.

A. concave B. equilateral C. convex equiangular

7. 8. 9.

Convex and Concave Polygons Decide whether the polygon is

convex or concave.

10. 11. 12.

Equilateral and Equiangular Polygons Decide whether the polygon

is equilateral, equiangular, or neither.

13. 14. 15.

Practice and Applications

Skill Check

Vocabulary Check

Guided Practice

Exercises8.18.1

Example 1: Exs. 10–12Example 2: Exs. 13–21

Homework Help

Extra Practice

See p. 689.

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414 Chapter 8 Polygons and Area

LOOK BACK

To review the namesgiven to polygons, seep. 304. For example, a pentagon has fivesides.

Student Help

FLOORING INSTALLERS arehired by flooring contractorsto install, repair, or replacefloor coverings such ascarpet and hardwood.

Careers

Regular Polygons Decide whether the polygon is regular. Explain

your answer.

16. 17. 18.

19. 20. 21.

Flooring Decide whether the polygon outlined in red in the floor

pattern is convex or concave.

22. 23. 24.

Web site Icons Use the polygons outlined on the website icons

shown below.

25. Which polygons are convex? Which polygons are concave?

26. Do any of the polygons appear to be regular? Explain.

Logical Reasoning Answer the question about the polygon.

27. Is the triangle 28. Is the parallelogramequiangular? equilateral? Explain.Explain.

Decide whether it is possible to sketch a polygon that

fits the description. If so, sketch it.

29. A concave pentagon 30. A convex quadrilateral

31. A polygon that is equilateral 32. A polygon that is equiangularbut not equiangular but not equilateral

Visualize It!

60�

60�

A B C

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8.1 Classifying Polygons 415

Finding Perimeters In Exercises 33–35, the polygons are equilateral.

Find the perimeter of the polygon.

33. 34. 35.

Using Algebra In Exercises 36–38, the polygons are regular.

Find the value of x.

36. 37. 38.

Multiple Choice In Exercises 39 and 40, use the terms below.

I. Equilateral II. Equiangular III. Convex IV. Concave

39. Which of the terms best describe the polygon below?

�A I and III �B III only

�C I and IV �D I, II, and III

40. Which of the terms best describe the polygon below?

�F I and III �G I, II, and IV

�H I and IV �J IV only

Classifying Polygons Decide whether the figure is a polygon.

If so, tell what type. (Lesson 6.1)

41. 42. 43.

Evaluating Powers Evaluate the expression. (Skills Review, p. 668)

44. 52 45. (�4)2 46. 63 47. 25

Evaluating Radicals Evaluate. Give the exact value if possible.

If not, approximate to the nearest tenth. (Skills Review, p. 668)

48. �3�6� 49. �1� 50. �1�6�9� 51. �5�

Algebra Skills

Mixed Review

Standardized Test

Practice

(5x � 5)�

60�

15

x � 9120� 2x�

4 ft

7 cm3 in.

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