1. Five-Minute Check (over Lesson 1–5) Mathematical Practices 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: Largest Area
Example 4: Perimeter and Area on the Coordinate Plane
Lesson Menu

2. 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

3. 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

4. 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. 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

6. Refer to the figure. Name an angle supplementary to  BEC.
A.  AEB
B.  AED
C.  AEC
D.  CEB
5-Minute Check 3

7. Refer to the figure. Name an angle supplementary to  BEC.
A.  AEB
B.  AED
C.  AEC
D.  CEB
5-Minute Check 3

8.  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

9.  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

10. If RS is perpendicular to ST and SV is the angle bisector of  RST, what is m TSV?
5-Minute Check 5

11. If RS is perpendicular to ST and SV is the angle bisector of  RST, what is m TSV?
5-Minute Check 5

12. The supplement of  A measures 140 degrees
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

13. The supplement of  A measures 140 degrees
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

14. Mathematical Practices 2 Reason abstractly and quantitatively.
6 Attend to precision.
Content Standards
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. MP

15. You measured one-dimensional figures.
Identify and name polygons.
Find perimeter, circumference, and area of two-dimensional figures.
Then/Now

16. polygon equiangular polygon regular polygon perimeter
circumference
area
vertex of a polygon
concave
convex
n-gon
equilateral polygon
Vocabulary

17. Concept

20. Name and Classify Polygons
A. Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
Example 1

21. There are 4 sides, so this is a quadrilateral.
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

22. There are 9 sides, so this is a nonagon.
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.
Lines 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:
Example 1

23. There are 9 sides, so this is a nonagon.
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.
Lines 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

24. A. triangle, concave, regular B. triangle, convex, irregular
A. Name the 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

25. A. triangle, concave, regular B. triangle, convex, irregular
A. Name the 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

26. A. quadrilateral, convex, irregular B. pentagon, convex, irregular
B. Name the polygon by the number of sides. Then classify it as convex or concave and regular or irregular.
A. quadrilateral, convex, irregular
B. pentagon, convex, irregular
C. quadrilateral, convex, regular
D. quadrilateral, concave, irregular
Example 1b

27. A. quadrilateral, convex, irregular B. pentagon, convex, irregular
B. Name the polygon by the number of sides. Then classify it as convex or concave and regular or irregular.
A. quadrilateral, convex, irregular
B. pentagon, convex, irregular
C. quadrilateral, convex, regular
D. quadrilateral, concave, irregular
Example 1b

28. Concept

29. A. Find the perimeter and area of the figure.
Find Perimeter and Area
A. Find the perimeter and area of the figure.
P = 2ℓ + 2w Perimeter of a rectangle
= 2(4.6) + 2(2.3) ℓ = 4.6, w = 2.3
= 13.8 Simplify.
Answer:
Example 2

30. A. Find the perimeter and area of the figure.
Find Perimeter and Area
A. Find the perimeter and area of the figure.
P = 2ℓ + 2w Perimeter of a rectangle
= 2(4.6) + 2(2.3) ℓ = 4.6, w = 2.3
= 13.8 Simplify.
Answer: The perimeter of the rectangle is 13.8 cm.
Example 2

31. A. Find the perimeter and area of the figure.
Find Perimeter and Area
A. Find the perimeter and area of the figure.
A = ℓw Area of a rectangle
= (4.6)(2.3) ℓ = 4.6, w = 2.3
= Simplify.
Answer:
Example 2

32. A. Find the perimeter and area of the figure.
Find Perimeter and Area
A. Find the perimeter and area of the figure.
A = ℓw Area of a rectangle
= (4.6)(2.3) ℓ = 4.6, w = 2.3
= Simplify.
Answer: The area of the rectangle is about 10.6 cm2.
Example 2

33. B. Find the circumference and area of the figure.
Find Perimeter and Area
B. Find the circumference and area of the figure.
≈ 25.1 Use a calculator.
Answer:
Example 2

34. B. Find the circumference and area of the figure.
Find Perimeter and Area
B. Find the circumference and area of the figure.
≈ 25.1 Use a calculator.
Answer: The circumference of the circle is about 25.1 inches.
Example 2

35. B. Find the circumference and area of the figure.
Find Perimeter and Area
B. Find the circumference and area of the figure.
≈ 50.3 Use a calculator.
Answer:
Example 2

36. B. Find the circumference and area of the figure.
Find Perimeter and Area
B. Find the circumference and area of the figure.
≈ 50.3 Use a calculator.
Answer: The area of the circle is about 50.3 square inches.
Example 2

37. A. Find the perimeter and area of the figure.
A. P = 12.4 cm, A = 24.8 cm2
B. P = 24.8 cm, A = cm2
C. P = cm, A = cm2
D. P = 24.4 cm, A = 32.3 cm2
Example 2a

38. A. Find the perimeter and area of the figure.
A. P = 12.4 cm, A = 24.8 cm2
B. P = 24.8 cm, A = cm2
C. P = cm, A = cm2
D. P = 24.4 cm, A = 32.3 cm2
Example 2a

39. B. Find the circumference and area of the figure.
A. C ≈ 25.1 m, A ≈ 50.3 m2
B. C ≈ 25.1 m, A ≈ m2
C. C ≈ 50.3 m, A ≈ m2
D. C ≈ m, A ≈ m2
Example 2b

40. B. Find the circumference and area of the figure.
A. C ≈ 25.1 m, A ≈ 50.3 m2
B. C ≈ 25.1 m, A ≈ m2
C. C ≈ 50.3 m, A ≈ m2
D. C ≈ m, A ≈ m2
Example 2b

41. A square with side length of 5 feet B circle with the radius of 3 feet
Largest Area
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 or circumference of four different shapes.
Example 3

42. Find each perimeter or circumference.
Largest Area
Solve the Test Item
Find each perimeter or circumference.
Square
P = 4s Perimeter of a square
= 4(5) s = 5
= 20 feet Simplify.
Circle
C = 2r Circumference
= 2(3) r = 3
= 6 Simplify.
≈ feet Use a calculator.
Example 3

43. Use the Pythagorean Theorem to find the length of the hypotenuse.
Largest Area
Right Triangle
Use the Pythagorean Theorem to find the length of the hypotenuse.
c2 = a2 + b2 Pythagorean Theorem
= a = 6, b = 6
= 72 Simplify. .
≈ 8.49 Use a calculator.
P = a + b + c Perimeter of a triangle
 Substitution
 feet Simplify.
Example 3

44. P = 2ℓ + 2w Perimeter of a rectangle = 2(8) + 2(3) ℓ = 8, w = 3
Largest Area
Rectangle
P = 2ℓ + 2w Perimeter of a rectangle
= 2(8) + 2(3) ℓ = 8, w = 3
= 22 feet Simplify.
The only shape for which Terri has enough tape is the circle.
Answer:
Example 3

45. P = 2ℓ + 2w Perimeter of a rectangle = 2(8) + 2(3) ℓ = 8, w = 3
Largest Area
Rectangle
P = 2ℓ + 2w Perimeter of a rectangle
= 2(8) + 2(3) ℓ = 8, w = 3
= 22 feet Simplify.
The only shape for which Terri has enough tape is the circle.
Answer: The correct answer is B.
Example 3

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

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

48. 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

49. Perimeter and Area on the Coordinate Plane
Step 1
By counting squares on the grid, we find that CD = 6 units and DE = 5 units. Use the Distance Formula,
to find AB, BC, and EA.
Example 4

50. Perimeter and Area on the Coordinate Plane
The perimeter of pentagon ABCDE is or about 25 units.
Example 4

51. Divide the pentagon into two triangles and a rectangle.
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 Triangle 1
Area of a triangle
Substitute.
Simplify.
Example 4

52. Area of Triangle 2 Substitute. Simplify.
Perimeter and Area on the Coordinate Plane
Area of Triangle 2
Substitute.
Simplify.
Example 4

53. Find the area of the rectangle.
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 or 41.5 square units.
Answer:
Example 4

54. Find the area of the rectangle.
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 or 41.5 square units.
Answer: The perimeter is about 25 units and the area is 41.5 square units.
Example 4

55. Find the perimeter of quadrilateral WXYZ with W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1).
B. 22
C. 13.3
D. 9.1
Example 4

56. Find the perimeter of quadrilateral WXYZ with W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1).
B. 22
C. 13.3
D. 9.1
Example 4