Vocabulary. Term Page Definition Clarifying Example. apothem. center of a circle. center of a regular polygon. central angle of a regular polygon

Transcription

1 CHAPTER 9 Vocabulary The table contains important vocabulary terms from Chapter 9. As you work through the chapter, fill in the page number, definition, and a clarifying example. apothem Term Page Definition Clarifying Example center of a circle center of a regular polygon central angle of a regular polygon circle 190 Geometry

2 CHAPTER 9 Vocabulary The table contains important vocabulary terms from Chapter 9. As you work through the chapter, fill in the page number, definition, and a clarifying example. apothem Term Page Definition Clarifying Example center of a circle The perpendicular distance from the center of a regular polygon to a side of the polygon. The point inside a circle that is the same distance from every point on the circle. center center of a regular polygon 601 The point that is equidistant from all vertices of the regular polygon. center central angle of a regular polygon 601 An angle whose vertex is the center of the regular polygon and whose sides pass through consecutive vertices. central angle circle 600 The set of points in a plane that are a fixed distance from a given point called the center of the circle. P 190 Geometry

3 CHAPTER 9 VOCABULARY CONTINUED composite figure Term Page Definition Clarifying Example geometric probability Geometry

4 CHAPTER 9 VOCABULARY CONTINUED composite figure geometric probability Term Page Definition Clarifying Example A plane figure made up of triangles, rectangles, trapezoids, circles, and other simple shapes, or a three-dimensional figure made up of prisms, cones, pyramids, cylinders, and other simple threedimensional figures. A form of theoretical probability determined by a ratio of geometric measures such as lengths, areas, or volumes. red 3 ft ft ft yellow blue green The probability of the pointer landing on red is Geometry

5 CHAPTER 9 Chapter Review 9-1 Developing Formulas for Triangles and Quadrilaterals Find each measurement. 1. the area of the rectangle 2. the area of the parallelogram x in. 4.2 in. 2x in. 3. the value of x when A 240 ft 2 4. the height of the trapezoid with A m 2 14 m x 15 ft 20 m h 3. The geoboard shows a rectangle, a triangle and a trapezoid. Find the perimeter and area of each. 9-2 Developing Formulas for Circles and Regular Polygons Find each measurement. 6. the circumference of C in 7. the area of O in terms of terms of C 6 in. O 3x in. 201 Geometry

6 CHAPTER 9 Chapter Review 9-1 Developing Formulas for Triangles and Quadrilaterals Find each measurement. 1. the area of the rectangle 2. the area of the parallelogram x in. 4.2 in. 2x + 3 2x 2 7x in in the value of x when A 240 ft 2 4. the height of the trapezoid with A m 2 14 m x 15 ft 20 m h 8 ft 6.5 m 3. The geoboard shows a rectangle, a triangle and a trapezoid. Find the perimeter and area of each. rectangle: P 20; A 21 triangle: P 12; A 8 trapezoid: P ; A Developing Formulas for Circles and Regular Polygons Find each measurement. 6. the circumference of C in 7. the area of O in terms of terms of C 6 in. 12 O 3x in. 9 4 x Geometry

7 CHAPTER 9 REVIEW CONTINUED Find the area of each regular polygon. Round to the nearest tenth. 8. a regular pentagon with perimeter 9. a regular octagon with apothem 8 in. 75 m 9-3 Composite Figures Find the shaded area. Round to the nearest tenth, if necessary mm 8 mm 10 mm 18 cm 28 cm 10 mm 12. A map of an irregularly shaped pond is shown on the grid. The grid has squares with lengths of 1 yd. A clarifying chemical is added to the pond, based on the area of the pond. The chemical costs $13.88 per square yard. Find the total cost of applying the clarifying chemical to the pond. 202 Geometry

8 CHAPTER 9 REVIEW CONTINUED Find the area of each regular polygon. Round to the nearest tenth. 8. a regular pentagon with perimeter 9. a regular octagon with apothem 8 in. 75 m m in Composite Figures Find the shaded area. Round to the nearest tenth, if necessary mm 8 mm 10 mm 18 cm 28 cm 10 mm 120 mm 2 2 cm A map of an irregularly shaped pond is shown on the grid. The grid has squares with lengths of 1 yd. A clarifying chemical is added to the pond, based on the area of the pond. The chemical costs $13.88 per square yard. Find the total cost of applying the clarifying chemical to the pond. $ Geometry

9 15 cm CHAPTER 9 REVIEW CONTINUED 9-4 Perimeter and Area in the Coordinate Plane Draw and classify the polygon with the given vertices. Find the perimeter and area of the polygon. 13. A( 2, 1), B(5, 1), C( 2, 4) 14. D( 2, 3), E(6, 3), F(6, 3), G( 2, 3) y y x x 4 8 Find the area of each polygon with the given vertices. 15. H( 3, 3), I(3, 3), J(5, 2), 16. L( 3, 2), M(4, 2), N(7, 1), K( 4, 2) P(0, 1) 9-5 Effects of Changing Dimensions Proportionally Describe the effect of each change on the perimeter and area of the given figure. 17. The length of each diagonal of the rhombus is halved. 8 cm 203 Geometry

10 15 cm CHAPTER 9 REVIEW CONTINUED 9-4 Perimeter and Area in the Coordinate Plane Draw and classify the polygon with the given vertices. Find the perimeter and area of the polygon. 13. A( 2, 1), B(5, 1), C( 2, 4) 14. D( 2, 3), E(6, 3), F(6, 3), G( 2, 3) y y C A B x 8 D 4 4 G 4 8 E 4 8 F x right triangle; P ; A 17.5 rectangle; P 28; A 48 Find the area of each polygon with the given vertices. 15. H( 3, 3), I(3, 3), J(5, 2), 16. L( 3, 2), M(4, 2), N(7, 1), K( 4, 2) P(0, 1) A 37.5 A Effects of Changing Dimensions Proportionally Describe the effect of each change on the perimeter and area of the given figure. 17. The length of each diagonal of the rhombus is halved. The perimeter is halved. The area is quartered. 8 cm 203 Geometry

11 CHAPTER 9 REVIEW CONTINUED 18. The base and height of the parallelogram are both tripled. 20 in. 8 in. 10 in. 19. The base and height of a right triangle with base 7 mm and height 24 mm are doubled. 20. The radius of a circle with radius 5 cm is doubled. 21. A square has vertices (0, 1), (0, 3), (4, 3) and (4, 1). If the area of the square is doubled, what happens to the side length? 22. A pizza shop specializes in two sizes of pizza, the regular and the extra large. The regular has a 16-in diameter and requires 4 cups of dough. The diameter of the extra large pizza is 20 inches. About how much dough is needed to make an extra large pizza? 204 Geometry

12 CHAPTER 9 REVIEW CONTINUED 18. The base and height of the parallelogram are both tripled. The perimeter is tripled. The area is increased by a factor of The base and height of a right triangle with base 7 mm and height 24 mm are doubled. 20 in. 8 in. 10 in. The perimeter is doubled. The area is increased by a factor of The radius of a circle with radius 5 cm is doubled. The circumference is doubled. The area is increased by a factor of A square has vertices (0, 1), (0, 3), (4, 3) and (4, 1). If the area of the square is doubled, what happens to the side length? The side length is increased by a factor of A pizza shop specializes in two sizes of pizza, the regular and the extra large. The regular has a 16-in diameter and requires 4 cups of dough. The diameter of the extra large pizza is 20 inches. About how much dough is needed to make an extra large pizza? cups of dough 204 Geometry

13 CHAPTER 9 REVIEW CONTINUED 9-6 Geometric Probability Use the spinner to find the probability of each event. 23. the pointer landing on red green 30 red 24. the pointer landing on blue or green blue yellow 25. the pointer not landing on yellow 26. the pointer on yellow, red, or blue 27. A bus makes a stop at an intersection five times each hour. The stops last three minutes each, find the probability that a bus will be waiting if you randomly walk up to the bus stop. 205 Geometry

14 CHAPTER 9 REVIEW CONTINUED 9-6 Geometric Probability Use the spinner to find the probability of each event. 23. the pointer landing on red green red 24. the pointer landing on blue or green blue yellow 25. the pointer not landing on yellow the pointer on yellow, red, or blue A bus makes a stop at an intersection five times each hour. The stops last three minutes each, find the probability that a bus will be waiting if you randomly walk up to the bus stop % Geometry

15 CHAPTER 9 Postulates and Theorems Postulate (Area Addition Postulate) The area of a region is equal to the sum of the areas of its nonoverlapping parts. 206 Geometry

16 CHAPTER 9 Postulates and Theorems Postulate (Area Addition Postulate) The area of a region is equal to the sum of the areas of its nonoverlapping parts. 206 Geometry

17 CHAPTER 9 Big Ideas Answer these questions to summarize the important concepts from Chapter 9 in your own words. 1. Explain the difference between area and perimeter. 2. Explain what is wrong with the following: To find the area of a parallelogram with sides 8 and 5, multiply 8 by 5 and get a product of Explain the process for finding the area of a composite figure. 4. What are the effects on the area and perimeter of a figure if the dimensions of the figure are multiplied by n? For more review of Chapter 9: Complete the Chapter 9 Study Guide and Review on pages of your textbook. Complete the Ready to Go On quizzes on pages 615 and 639 of your textbook. 207 Geometry

18 CHAPTER 9 Big Ideas Answer these questions to summarize the important concepts from Chapter 9 in your own words. 1. Explain the difference between area and perimeter. Answers will vary. Possible answer: Area is the amount of surface that a figure covers. Perimeter is the distance found by adding the length of the sides of a figure. 2. Explain what is wrong with the following: To find the area of a parallelogram with sides 8 and 5, multiply 8 by 5 and get a product of 40. Answers will vary. Possible answer: The area of a parallelogram is found by multiplying the base and height, not the lengths of the sides. The given description only works if the parallelogram is a rectangle. 3. Explain the process for finding the area of a composite figure. Answers will vary. Possible answer: Divide the composite figure into figures such as rectangle, triangles, etc. that have area formulas. Find the area of these figures and them together for the area of the composite figure. 4. What are the effects on the area and perimeter of a figure if the dimensions of the figure are multiplied by n? Answers will vary. Possible answer: The perimeter is multiplied by n and the area is multiplied by a factor of n 2. For more review of Chapter 9: Complete the Chapter 9 Study Guide and Review on pages of your textbook. Complete the Ready to Go On quizzes on pages 615 and 639 of your textbook. 207 Geometry