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Splash Screen. Five-Minute Check (over Lesson 1–5) Then/Now New Vocabulary Key Concepts: Polygons Example 1:Name and Classify Polygons Key Concepts: Perimeter, Circumference, and Area Example 2:Find Perimeter and Area Example 3:Standardized Test Practice

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Splash screen

Splash Screen


Lesson menu

Five-Minute Check (over Lesson 1–5)

Then/Now

New Vocabulary

Key Concepts: Polygons

Example 1:Name and Classify Polygons

Key Concepts: Perimeter, Circumference, and Area

Example 2:Find Perimeter and Area

Example 3:Standardized Test Practice

Example 4:Perimeter and Area on the Coordinate Plane

Lesson Menu


5 minute check 1

A

B

C

D

Refer to the figure. Name two acute vertical angles.

A.AED and BEC

B.AEB and DEC

C.DEA and DEC

D.BEC and BEA

5-Minute Check 1


5 minute check 2

A

B

C

D

Refer to the figure. Name a linear pair whose vertex is E.

A.AED, BEC

B.AEB, BEA

C.CED,AEB

D.AEB, AED

5-Minute Check 2


5 minute check 3

A

B

C

D

Refer to the figure. Name an angle supplementary to BEC.

A.AEB

B.AED

C.AEC

D.CEB

5-Minute Check 3


5 minute check 4

A

B

C

D

1 and 2 are a pair of supplementary angles, and the measure of 1 is twice the measure of 2. Find the measures of both angles.

A.m1 = 60, m2 = 120

B.m1 = 100, m2 = 80

C.m1 = 100, m2 = 50

D.m1 = 120, m2 = 60

5-Minute Check 4


5 minute check 5

A

B

C

D

If RS is perpendicular to ST and SV is the angle bisector of RST, what is mTSV?

A.30

B.45

C.55

D.60

5-Minute Check 5


5 minute check 6

A

B

C

D

The supplement of A measures 140 degrees. What is the measure of the complement of A?

A.40

B.50

C.80

D.140

5-Minute Check 6


Then now

You measured one-dimensional figures. (Lesson 1–2)

  • Identify and name polygons.

  • Find perimeter, circumference, and area of two-dimensional figures.

Then/Now


Vocabulary

  • equiangular polygon

  • regular polygon

  • perimeter

  • circumference

  • area

  • polygon

  • vertex of a polygon

  • concave

  • convex

  • n-gon

  • equilateral polygon

Vocabulary


Concept

Concept


Example 1

Name and Classify Polygons

A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

There are 4 sides, so this is a quadrilateral.

No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex.

The sides are not congruent, so it is irregular.

Answer: quadrilateral, convex, irregular

Example 1


Example 11

Name and Classify Polygons

B. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

There are 9 sides, so this is a nonagon.

A line containing some of the sides will pass through the interior of the nonagon, so it is concave.

Since the polygon is concave, it must be irregular.

Answer: nonagon, concave, irregular

Example 1


Example 1a

A

B

C

D

A. Name each polygon by the number of sides. Then classify it as convex or concave and regular or irregular.

A.triangle, concave, regular

B.triangle, convex, irregular

C.quadrilateral, convex, regular

D.triangle, convex, regular

Example 1a


Example 1b

A

B

C

D

B. Name each polygon by the number of sides. Then classify it as convex or concave and regular or irregular.

A.quadrilateral, convex, regular

B.pentagon, convex, irregular

C.quadrilateral, convex, irregular

D.quadrilateral, concave, irregular

Example 1b


Concept1

Concept


Example 2

Find Perimeter and Area

A.Find the perimeter and area of the figure.

P= 2ℓ + 2wPerimeter of a rectangle

= 2(4.6) + 2(2.3)ℓ = 4.6, w = 2.3

= 13.8Simplify.

Answer: The perimeter of the rectangle is 13.8 cm.

Example 2


Example 21

Find Perimeter and Area

A.Find the perimeter and area of the figure.

A= ℓwArea of a rectangle

= (4.6)(2.3)ℓ = 4.6, w = 2.3

= 10.58Simplify.

Answer: The area of the rectangle is about 10.6 cm2.

Example 2


Example 22

Find Perimeter and Area

B.Find the circumference and area of the figure.

≈25.1Use a calculator.

Answer: The circumference of the circle is about 25.1 inches.

Example 2


Example 23

Find Perimeter and Area

B.Find the circumference and area of the figure.

≈50.3Use a calculator.

Answer: The area of the circle is about 50.3 square inches.

Example 2


Example 2a

A

B

C

D

A. Find the perimeter and area of the figure.

A.P = 12.4 cm, A = 24.8 cm2

B.P = 24.8 cm, A = 34.83 cm2

C.P = 34.83 cm, A = 69.66 cm2

D.P = 24.4 cm, A = 32.3 cm2

Example 2a


Example 2b

A

B

C

D

B. Find the circumference and area of the figure.

A.C ≈ 25.1 m, A ≈ 50.3 m2

B.C ≈ 25.1 m, A ≈ 201.1 m2

C.C ≈ 50.3 m, A ≈ 201.1 m2

D.C ≈ 201.1 m, A ≈ 402.1 m2

Example 2b


Example 3

Terri has 19 feet of tape to mark an area in the classroom where the students may read. Which of these shapes has a perimeter or circumference that would use most or all of the tape?

A square with side length of 5 feet

B circle with the radius of 3 feet

C right triangle with each leg length of 6 feet

D rectangle with a length of 8 feet and a width of 3 feet

Read the Test Item

You are asked to compare the perimeters orcircumference of four different shapes.

Example 3


Example 31

Solve the Test Item

Find each perimeter or circumference.

Square

P= 4sPerimeter of a square

= 4(5)s = 5

= 20 feetSimplify.

Circle

C= 2rCircumference

= 2(3)r = 3

= 6Simplify.

≈ 18.85 feetUse a calculator.

Example 3


Example 32

.

Right Triangle

Use the Pythagorean Theorem to find the length of the hypotenuse.

c2= a2+b2Pythagorean Theorem

= 62+62a = 6, b = 6

= 72Simplify.

≈ 8.49Use a calculator.

P= a + b + cPerimeter of a triangle

= 6 + 6 + 8.49Substitution

= 20.49 feetSimplify.

Example 3


Example 33

Rectangle

P= 2ℓ+2wPerimeter of a rectangle

= 2(8)+2(3)ℓ = 8, w = 3

= 22 feetSimplify.

The only shape for which Terri has enough tape is the circle.

Answer: The correct answer is B.

Example 3


Example 34

A

B

C

D

Each of the following shapes has a perimeter of about 88 inches. Which one has the greatest area?

A.a rectangle with a length of 26 inches and a width of 18 inches

B.a square with side length of 22 inches

C.a right triangle with each leg length of 26 inches

D.a circle with radius of 14 inches

Example 3


Example 4

Perimeter and Area on the Coordinate Plane

Find the perimeter and area of a pentagon ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3, 1).

Example 4


Example 41

Perimeter and Area on the Coordinate Plane

Step 1

Example 4


Example 42

Perimeter and Area on the Coordinate Plane

The perimeter of pentagon ABCDE is 5.7 + 4.1 + 6 + 5 + 4.2 or about 25 units.

Example 4


Example 43

Perimeter and Area on the Coordinate Plane

Step 2

Divide the pentagon into two triangles and a rectangle.

Find the area of the triangles.

Area of Triangle1

Area of a triangle

Substitute.

Simplify.

Example 4


Example 44

Perimeter and Area on the Coordinate Plane

Area of Triangle 2

Substitute.

Simplify.

Example 4


Example 45

Perimeter and Area on the Coordinate Plane

Find the area of the rectangle.

Area of a rectangle

Substitute.

Simplify.

The area of pentagon ABCDE is 9 + 2.5 + 30 or 41.5 square units.

Answer:The perimeter is about 25 units and the area is 41.5 square units.

Example 4


Example 46

A

B

C

D

Find the perimeter of quadrilateral WXYZ with W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1).

A.17.9

B.22

C.13.3

D.9.1

Example 4


End of the lesson

End of the Lesson


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