Name ________________________________________ Date __________________ Class__________________ LESSON 9-1 Reteach Developing Formulas for Triangles and Quadrilaterals Area of Triangles and Quadrilaterals Parallelogram Triangle A= A = bh Trapezoid 1 bh 2 A= 1 ( b1 + b2 ) h 2 Find the perimeter of the rectangle in which A = 27 mm2. Step 1 Find the height. A = bh Area of a rectangle 27 = 3h Substitute 27 for A and 3 for b. 9 mm = h Step 2 Divide both sides by 3. Use the base and the height to find the perimeter. P = 2b + 2h Perimeter of a rectangle P = 2(3) + 2(9) = 24 mm Substitute 3 for b and 9 for h. Find each measurement. 1. the area of the parallelogram 2. the base of the rectangle in which A = 136 mm2 _________________________________________ ________________________________________ 3. the area of the trapezoid 4. the height of the triangle in which A = 192 cm2 _________________________________________ ________________________________________ 6. b2 of a trapezoid in which A = 5 ft2, h = 2 ft, and b1 = 1 ft 5. the perimeter of a rectangle in which A = 154 in2 and h = 11 in. _________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 9-6 Holt Geometry Name ________________________________________ Date __________________ Class__________________ LESSON 9-1 Reteach Developing Formulas for Triangles and Quadrilaterals continued Area of Rhombuses and Kites Rhombus A= Kite 1 d1d 2 2 A= 1 d1d 2 2 Find d2 of the kite in which A = 156 in2. A= 156 = 1 d1d 2 2 Area of a kite 1 ( 26 ) d2 2 Substitute 156 in2 for A and 26 in. for d1. 156 = 13d2 12 in. = d2 Simplify. Divide both sides by 13. Find each measurement. 8. d1 of the kite in which A = 414 ft2 7. the area of the rhombus _________________________________________ ________________________________________ 9. d2 of the rhombus in which A = 90 m2 10. d1 of the kite in which A = 39 mm2 _________________________________________ ________________________________________ 11. d1 of a kite in which A = 16x m2 and d2 = 8 m 12. the area of a rhombus in which d1 = 4ab in. and d2 = 7a in. ____________________________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 9-7 Holt Geometry 7. 〈7, −3〉 8. 19 9. 5 10. 3. 58 , or 7.6 11. 5 58 , or 38.1 12. 0.5 13. 60° 14. 45° 12 cm x 4. b1 = x in. 5. A = 660 mm2 6. A = (45a + 18ac) km2 7. P = 30.4 yd 15. 143° 8. A = (xy − 2x + 4y − 8) m2 16. They are perpendicular. If the dot product is 0, then the numerator of the expression r is equals 0, and the value of the r s entire expression is 0. A calculator tells us that cos−10 = 90°. 9. d2 = 4a ft Practice C 1. Possible answer: Draw a segment showing the height from B to AD and label it h. The area of a parallelogram is bh. Since b is known and h = c sin A, a formula for the area of the parallelogram is A = bc sin A. Problem Solving 1. 23° 2. 13 units 3. 〈4.9, 0.5〉 4. 4.9 mi/h 5. 6° or N 84° E 6. C 7. F 8. C 2. Possible answer: A rectangle is a parallelogram in which the measure of each angle is 90°. sin 90° = 1. So A = bc sin A becomes A = bc, the product of the length and the width of the rectangle. 9. H 3. A ≈ 79.9 mm2 Reading Strategies 2 1. Equal 2. 〈3, 8〉 5. A ≈ 177.5 mi 3. 69° 4. 5 7. Possible answer: 5. 6.3 6. 5.1 4. b2 ≈ 6.4 in. 6. x ≈ 60.3 7. 〈−3, 1〉 LESSON 9-1 Practice A 1. triangle 2. 1 d1d 2 2 Reteach 1. A = 60 in2 3. areas 3. A = 91 m 4. parallelogram or rectangle 5. P = 50 in. 5. 2. b = 17 mm 2 1 (b1 + b2)h 2 8. A = 567 mm2 7. A = 70 cm 8. d1 = 36 ft 9. d2 = 12 m 10. d1 = 13 mm 11. d1 = 4x m 2 9. h = 30 ft 10. A = 30 km 12. A = 14a2b in2 Challenge 11. d2 = 9 yd 1. A = Practice B 1. P = (4x + 2y) mi 2 6. b2 = 4 ft 2 6. A = 48 m2 7. b = 3 in. 4. h = 16 cm 1 (PK)(MN) 2 2. midsegment; Midsegment 2 2 2 2. A = (a − b) = (a − 2ab + b ) ft 3. 21 + 15; 18 cm; Trapezoid Midsegment 4. PL TS; Proportionality Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A16 Holt Geometry

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