&&66 **Derive and )LQGWKHDUHDRIULJKWWULDQJOHVRWKHUWULDQJOHVVSHFLDO MG 1.1 use the formula for the area of a right triangle and of a TXDGULODWHUDOVDQGSRO\JRQVE\FRPSRVLQJLQWRUHFWDQJOHVRUGHFRPSRVLQJLQWRWULDQJOHV parallelogram by comparing it with the area of a rectangle (i.e., two of DQGRWKHUVKDSHVDSSO\WKHVHWHFKQLTXHVLQWKHFRQWH[WRIVROYLQJUHDOZRUOGDQG the same triangles make a parallelogram with twice the area; a PDWKHPDWLFDOSUREOHPV UNDERLYING SKILLS AND CONCEPTS: find area of rectangles; find area of right triangles parallelogram is compared with a rectangle of the same area found by cutting and pasting a right triangle on the parallelogram). Find the Area of Parallelograms You can use what you know about the area of rectangles to find the area of a parallelogram. Area of rectangles is very useful! 7 12 Cut the parallelogram. Move one piece to make a rectangle. h b Very Important: The height of a figure is always measured perpendicular to the base of the figure. 12 The length of the base is still 12 units. The height is still 7 units. Now you can find the area of the rectangle. A!b"h A ! 12 " 7 A ! 84 The area of the rectangle is 84 square units. You made the rectangle from the parallelogram. So, the area of the parallelogram is also 84 square units. The formula for the area of a parallelogram: A!b"h page 316 E x am p l E Find the area of the parallelogram. 5 in. b ! 6 in. The height is 5 inches. The base is 6 inches. A!b"h A!6"5 A ! 30 in.2 The area is 30 square inches. Chapter 27 – Lesson 2 E – © CSL Associates, Inc. All rights reserved. 7 Name P RAC T I C E Find the area of each parallelogram. 1. 2. 3. 2 cm 5.5 m b 7 cm 4 ft b6m b 3 ft 14 cm2 12 ft2 4. 5. 33 m2 6. 5 mm 9 in. 6 yd 3 mm 5 yd 6 in. 54 in.2 7. b 8 in. E – © CSL Associates, Inc. All rights reserved. h 6 in. 30 yd2 15 mm2 8. b 12 ft 9. b 15 mm 10. b 20 cm 108 ft2 150 mm2 320 cm2 h 9 ft 48 in.2 11. Which expression can you use to find the area of a parallelogram that has a base of 12.5 units and a height of 3.25 units? Math Reasoning h 10 mm A B C D h 16 cm 12.5 3.25 12.5 3.25 12.5 3.25 12.5 3.25 Area Algebra MR2.2 12. A parallelogram has a base of 10 cm and an area of 50 cm2. What is its height? Explain how you decided. 5 cm I know that base height area. I know that base is 10 cm and the area is 50 cm2. So, I can find 10 some number 50. I can use inverse operations or mental math. 50 10 5. So, the height is 5 centimeters. Chapter 27 – Lesson 2 page 317 MCX94.HW.CL.G5.FM&Lesson.v211 8/2/04 18:03 Page 212 Name …at home! P RAC T I C E Find the area of each parallelogram. 2. 1. 3. 2 cm 5.5 m b 8 cm 5 ft b7m b 3 ft 16 cm2 5. 38.5 m2 6. 6 mm 12 yd 8 in. 4 mm 10 yd 6 in. 48 in.2 120 yd2 24 mm2 7. b 16 in. 8. b 18 ft 9. b 30 mm 160 in.2 216 ft2 600 mm2 h 10 in. h 12 ft 11. Which expression can you use to find the area of a parallelogram that has a base of 14.5 units and a height of 6.25 units? Math Reasoning h 20 mm A B C D 10. b 40 cm h 32 cm 1,280 cm2 14.5 6.25 14.5 6.25 14.5 6.25 14.5 6.25 Area Algebra MR2.2 12. A parallelogram has a base of 25 cm and an area of 75 cm2. What is its height? Explain how you decided. I know that base height area. I know that base is 25 cm and the area is 75 cm2 So, I can find 25 some number 75. I can use inverse operations or mental math. 75 25 3. So, the height is 3 centimeters. page 212 Home Resource and Homework Chapter 27 Lesson 2 E – © CSL Associates, Inc. All rights reserved. 4. 15 ft2 MCX94TEG5CH01_32.v7.4.2 2/24/01 19:50 Page 583 Name P RAC T I C E Find the area of each parallelogram. 1. 2. 3. 2 cm 5.5 m b 7 cm 4 ft b6m b 3 ft 14 cm2 12 ft2 4. 5. 33 m2 6. 5 mm 9 in. 6 yd 3 mm 5 yd 6 in. 54 in.2 7. b 8 in. E – © CSL Associates, Inc. All rights reserved. h 6 in. 30 yd2 15 mm2 8. b 12 ft 9. b 15 mm 10. b 20 cm 108 ft2 150 mm2 320 cm2 h 9 ft 48 in.2 11. Which expression can you use to find the area of a parallelogram that has a base of 12.5 units and a height of 3.25 units? Math Reasoning h 10 mm A B C D h 16 cm 12.5 3.25 12.5 3.25 12.5 3.25 12.5 3.25 Area Algebra MR2.2 12. A parallelogram has a base of 10 cm and an area of 50 cm2. What is its height? Explain how you decided. 5 cm I know that base height area. I know that base is 10 cm and the area is 50 cm2. So, I can find 10 some number 50. I can use inverse operations or mental math. 50 10 5. So, the height is 5 centimeters. Chapter 27 – Lesson 2 Student Book Page page 317 Name …at home! P RAC T I C E Find the area of each parallelogram. 2. 1. 3. 2 cm 5.5 m b 8 cm 5 ft b7m b 3 ft 16 cm2 5. 38.5 m2 6. 6 mm 12 yd 8 in. 4 mm 10 yd 6 in. 48 in.2 120 yd2 24 mm2 7. b 16 in. 8. b 18 ft 9. b 30 mm 160 in.2 216 ft2 600 mm2 h 10 in. h 12 ft 11. Which expression can you use to find the area of a parallelogram that has a base of 14.5 units and a height of 6.25 units? Math Reasoning h 20 mm A B C D 10. b 40 cm h 32 cm 1,280 cm2 14.5 6.25 14.5 6.25 14.5 6.25 14.5 6.25 Area Algebra MR2.2 12. A parallelogram has a base of 25 cm and an area of 75 cm2. What is its height? Explain how you decided. I know that base height area. I know that base is 25 cm and the area is 75 cm2 So, I can find 25 some number 75. I can use inverse operations or mental math. 75 25 3. So, the height is 3 centimeters. page 212 Home Resource and Homework Chapter 27 Lesson 2 E – © CSL Associates, Inc. All rights reserved. 4. 15 ft2