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  1. Splash Screen

  2. Lesson 11-1Area of Parallelograms Lesson 11-2 Area of Triangles and Trapezoids Lesson 11-3 Circles and Circumference Lesson 11-4 Area of Circles Lesson 11-5 Problem-Solving Investigation: Solve a Simpler Problem Lesson 11-6 Area of Complex Figures Lesson 11-7 Three-Dimensional Figures Lesson 11-8 Drawing Three-Dimensional Figures Lesson 11-9 Volume of Prisms Lesson 11-10 Volume of Cylinders Chapter Menu

  3. Five-Minute Check (over Chapter 10) Main Idea and Vocabulary California Standards Key Concept: Area of a Parallelogram Example 1: Find the Area of a Parallelogram Example 2: Find the Area of a Parallelogram Example 3: Real-World Example Lesson 1 Menu

  4. Find the areas of parallelograms. • base • height Lesson 1 MI/Vocab

  5. Standard 6AF3.1 Use variables in expressions describing geometric quantities(e.g., P = 2w + 2, C = πd—the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Standard 6AF3.2 Express in symbolic form simple relationships arising from geometry. Lesson 1 CA

  6. Lesson 1 KC1

  7. Find the Area of a Parallelogram Find the area of the parallelogram. EstimateA = 8 ● 6 or 48 cm2 A = bh Area of a parallelogram A = 7.5 ● 6.4 Replace b with 7.5 and h with 6.4. A = 48 Multiply. Answer: The area of the parallelogram is 48 square centimeters. Lesson 1 Ex1

  8. Find the area of the parallelogram. • A • B • C • D A. 13 in2 B. 26 in2 C. 52 in2 D. 208 in2 Lesson 1 CYP1

  9. Find the Area of a Parallelogram Find the area of the parallelogram. The base is 8 centimeters, and the height is 4.5 centimeters. EstimateA = 8 ● 5 or 40 cm2 Lesson 1 Ex2

  10. Find the Area of a Parallelogram A = bh Area of a parallelogram A = 8 ● 4.5 Replace b with 8 and h with 4.5. A = 36 Multiply. Answer: The area of the parallelogram is 36 square centimeters. Lesson 1 Ex2

  11. Find the area of the parallelogram to the right. • A • B • C • D A. 5.4 m2 B. 10.8 m2 C. 10.92 m2 D. 13.81 m2 Lesson 1 CYP2

  12. FARMING A farmer planted the three fields shown with rice. What is the total area of the three fields? Find the area of one of the fields and then multiply that result by 3. A = bh Area of a parallelogram A = 56.7 ● 75 Replace b with 56.7 and h with 75. A = 4,252.5 Multiply. Lesson 1 Ex3

  13. Answer:The area of one of the fields is 4,252.5 m2. So, the area of the three fields together is 3 ● 4,252.5 or 12,757.5 m2. Lesson 1 Ex3

  14. LANDSCAPING Sue is designing a new walkway from her back patio to a garden. She is using stones that are shaped as parallelograms to create the walkway. Each of the stones has a base of 18 inches and a height of 24 inches. It takes 30 stones to complete the walkway. What is the total area of the walkway? • A • B • C • D A. 720 in2 B. 1,250 in2 C. 7,348 in2 D. 12,960 in2 Lesson 1 CYP3

  15. End of Lesson 1

  16. Five-Minute Check (over Lesson 11-1) Main Idea California Standards Key Concept: Area of a Triangle Example 1: Find the Area of a Triangle Key Concept: Area of a Trapezoid Example 2: Find the Area of a Trapezoid Example 3: Real-World Example Lesson 2 Menu

  17. Find the areas of triangles and trapezoids. Lesson 2 MI/Vocab

  18. Standard 6AF3.1 Use variables in expressions describing geometric quantities(e.g., P = 2w + 2, C = πd—the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Standard 6AF3.2 Express in symbolic form simple relationships arising from geometry. Lesson 2 CA

  19. Lesson 2 KC1

  20. Find the Area of a Triangle Find the area of the triangle below. Lesson 2 Ex1

  21. Find the Area of a Triangle A = 14.4 Multiply. Answer: The area of the triangle is 14.4 square centimeters. Lesson 2 Ex1

  22. Find the area of the triangle to the right. • A • B • C • D A. 10.5 ft2 B. 13.5 ft2 C. 21.75 ft2 D. 27 ft2 Lesson 2 CYP1

  23. Interactive Lab:Area of Trapezoids Lesson 2 KC2

  24. Find the Area of a Trapezoid Find the area of the trapezoid below. The bases are 4 meters and 7.6 meters. The height is 3 meters. Lesson 2 Ex2

  25. Find the Area of a Trapezoid Replace h with 3, b1 with 4, and b2 with 7.6. Answer: The area of the trapezoid is 17.4 square meters. Lesson 2 Ex2

  26. Find the area of the trapezoid to the right. • A • B • C • D A. 26.5 cm2 B. 60.5 cm2 C. 61.5 cm2 D. 73.5 cm2 Lesson 2 CYP2

  27. GEOGRAPHYThe shape of the state of Montana resembles a trapezoid. Find the approximate area of Montana. Lesson 2 Ex3

  28. Replace h with 285, b1 with 542, and b2 with 479. Answer: The area of Montana is about 145,493 square miles. Lesson 2 Ex3

  29. PAINTING The diagram below is of a canvas resembling a trapezoid that will be painted. In order to determine how much paint will be needed, estimate the area of the canvas in square feet. • A • B • C • D A. 75 ft2 B. 150 ft2 C. 300 ft2 D. 450 ft2 Lesson 2 CYP3

  30. End of Lesson 2

  31. Five-Minute Check (over Lesson 11-2) Main Idea and Vocabulary California Standards Key Concept: Circumference of a Circle Example 1: Real-World Example:Find Circumference Example 2: Find Circumference Lesson 3 Menu

  32. Find the circumference of circles. • circle • center • diameter • circumference • radius • π(pi) Lesson 3 MI/Vocab

  33. Standard 6MG1.1 Understand the concept of a constant such as π; know the formulas for the circumference and areaof a circle. Standard MG1.2Know common estimates of π and use these values to estimate and calculate the circumference and area of circles; compare with actual measurements. Lesson 3 CA

  34. Lesson 3 KC1

  35. C = 2r Replace  with 3.14 and r with 3. C = 2r𝝅 OR C = 2𝝅r OR C = 𝝅d PETS Find the circumference around the hamster’s running wheel. Round to the nearest tenth. Answer: The distance around the hamster’s running wheel is about 18.8 inches. Lesson 3 Ex1

  36. C = 2r𝝅 OR C = 2𝝅r OR C = 𝝅d SWIMMING POOL A new children’s swimming pool is being built at the local recreation center. The pool is circular in shape with a diameter of 18 feet. Find the circumference of the pool. Round to the nearest tenth. • A • B • C • D A. 28.6 ft B. 32.9 ft C. 56.5 ft D. 254.3 ft Lesson 3 CYP1

  37. .   Find Circumference Find the circumference of a circle with a diameter of 49 centimeters. Answer: The circumference of the circle is about 154 centimeters. Lesson 3 Ex2

  38. Find the circumference of a circle with a radius of 35 feet. • A • B • C • D A. 54 ft B. 123 ft C. 178 ft D. 220 ft Lesson 3 CYP2

  39. End of Lesson 3

  40. Five-Minute Check (over Lesson 11-3) Main Idea California Standards Key Concept: Area of a Circle Example 1: Find the Area of a Circle Example 2: Real-World Example Example 3: Standards Example Lesson 4 Menu

  41. Find the areas of circles. Lesson 4 MI/Vocab

  42. Standard 6MG1.1 Understand the concept of a constant such as π; know the formulas for the circumference and areaof a circle. Standard MG1.2Know common estimates of π and use these values to estimate and calculate the circumferenceand areaof circles; compare with actual measurements. Lesson 4 CA

  43. Lesson 4 KC1

  44. A = 𝝅r2 Find the Area of a Circle Find the area of the circle shown here. Round to the nearest hundreth. A = πr2 Area of a circle A = π●42 Replace r with 4. A = 3.14 ● 4 ● 4 = 50.24 Lesson 4 Ex1

  45. A = 𝝅r2 Find the area of the circle shown here. • A • B • C • D A. approximately 32.97 ft2 B. approximately 65.9 ft2 C. approximately 121.3 ft2 D. approximately 346.2 ft2 A = πr2 Area of a circle A = π●10.5 2 Replace r with 10.5. A = 3.14 ● 10.5 ● 10.5 = 346.185 Lesson 4 CYP1

  46. A = 𝝅r2 KOIFind the area of the koi pond shown. Round to the nearest tenth. The diameter of the koi pond is 3.6 m. Therefore, the radius is 1.8 m. A = πr2 Area of a circle A = π(1.8)2 Replace r with 1.8. A. ≈ (3.14) (1.8) (1.8) A≈(3.14) 10.2 Multiply. A ≈ 32.028 ≈ 32.0 Lesson 4 Ex2

  47. A = 𝝅r2 PARACHUTEBluehills Elementary School has a parachute that is used for an activity in physical education class. The diameter of the parachute is 15 feet. Find the area of the parachute. • A • B • C • D A. 54.5 ft2 B. 121.5 ft2 C.176.6 ft2 D. 214.4 ft2 15 ÷ 2 = 7.5 A = πr2 A = π(7.5)2 A. ≈ (3.14) (7.5) (7.5) A≈(3.14) (56.25) A ≈ 176.625 ≈ 176.6

  48. A = 𝝅r2 Mr. McGowan made an apple pie with a diameter of 10 inches. He cut the pie into 6 equal slices. Find the approximate area of each slice. A 3 in2 B 13 in2 C 16 in2 D 52 in2 A = πr2 Area of a circle A = π(5)2 Replace r with 5. A≈3.14 ● 5 ● 5 ≈ 78.5 ≈ 78 Find the area of one slice: 78 ÷ 6 = 13 Answer: B Lesson 4 Ex3

  49. A = 𝝅r2 MERRY-GO-ROUND The floor of a merry-go-round at the amusement park has a diameter of 40 feet. The floor is divided evenly into eight sections, each having a different color. Find the area of each section of the floor. • A • B • C • D 40 ÷ 2 = 20 A = πr2 A = π(20)2 A. ≈ (3.14) (20) (20) A≈(3.14) (400) A ≈ 1256 1256 ÷ 8 = 157 A. 157 ft2 B. 225 ft2 C. 264 ft2 D. 312 ft2 Lesson 4 CYP3

  50. End of Lesson 4