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**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**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**Find the areas of parallelograms.**• base • height Lesson 1 MI/Vocab**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**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**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**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**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**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**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**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**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**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**Find the areas of triangles and trapezoids.**Lesson 2 MI/Vocab**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**Find the Area of a Triangle**Find the area of the triangle below. Lesson 2 Ex1**Find the Area of a Triangle**A = 14.4 Multiply. Answer: The area of the triangle is 14.4 square centimeters. Lesson 2 Ex1**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**Interactive Lab:Area of Trapezoids**Lesson 2 KC2**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**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**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**GEOGRAPHYThe shape of the state of Montana resembles a**trapezoid. Find the approximate area of Montana. Lesson 2 Ex3**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**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**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**Find the circumference of circles.**• circle • center • diameter • circumference • radius • π(pi) Lesson 3 MI/Vocab**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**C = 2r**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**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**.** 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**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**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**Find the areas of circles.**Lesson 4 MI/Vocab**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**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**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**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**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**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**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